kinematic modeling and calibration of a human body

8/10/2019 Kinematic Modeling and Calibration of a Human Body

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Kinematic Modeling and Calibration of a Human Body


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KINEMATIC MODELING AND

CALIBRATION OF A HUMAN BODY

Author

Quoc-Khanh Huynh

Thesis Submitted to the Chung Yuan Christian University

In partial fulfillment of the requirements for the degree of

Master of Science in Mechanical Engineering

Supervisor: Dr. Ting Yung, Chair

Dr. Yuan Kang

May 2011

Chung Li, Taiwan, R.O.C.


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5 12

99mm 19mm

1950.9mm 365mm


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ABSTRACT

Golf swing is one of the most sophisticated motions because of the complex human

muscular skeleton structure. A comprehensive model including 12 DOF provided by 5 joints

significantly influential to the swing motion is considered in this study. With known kinematics

parameters and assigned end-effector position and orientation, significant parameters are

determined using forward kinematics so that a reduced-order model of 6DOF and 11DOF

respectively is found. On the basis of derived human-body model, several unknown dominant

kinematic parameters, the link length in this study, of any arbitrary player are identified by using

forward and inverse kinematics.

The identification process is divided into the course step and the fine-tune step. The

purpose of the course step is to overcome unpredictable errors and approximate the actual values

of body dimensions so that providing suitable initial values for the later fine-tune step. In this

step, players are asked to touch two defined points. In the fine-tune step, precise calibration

process is carried out step by touching minimum four pre-defined points in order to improve the

identification accuracy. A number of gyros are employed to the appropriate location of the

human body respectively to measure the joint motion. Base on measured, an algorithm together

with a set of cost functions to minimize the errors of the end-effector is developed. Finally, target

of the golf ball is assigned for the player to swing and touch. The end-effector is calculated by

the measured joint motion as well as the forward kinematics, which indicates the error. Via

experiment, average error of the identified link lengths is about 99 mm and 19 mm for 11DOF and

6DOF model respectively; and the resultant error in the target point is about 1950.9 mm and

365 mm for the 11DOF and 6DOF model respectively.

Keywords: Golf swing model, Calibration, Body segment dimensions


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ACKNOWLEDGEMENT

Thanks for my parents, Mr. Phuoc-Minh Huynh and Mrs. Thi-Huy Huynh who always

encourage me to overcome the difficulties. They are also my best supports, both emotional and

financial, throughout my work.

I would like to thank my supervisor, Professor Ting Yung, for his invaluable advice,

support and guidance throughout the running of this thesis. Without him this thesis would not

have been possible. I honestly appreciate his smart ideas which lead me up in a right direction to

finish this thesis on time.

I would also like to thank Miss Hong-Phuc Vo-Nguyen and my older brother, Mr. Quoc-

Khai Huynh whose wise words, humour and enduring support have spurred me on through

frustration.

Finally, I would like to thank my friends and lab-mates who devote their time, energies and

knowledge to discuss and share idea with me.

Quoc-Khanh Huynh

[email protected]


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CONTENTS

.................................................................................................................... I

ABSTRACT ............................................................................................................ II

ACKNOWLEDGEMENT ................................................................................... III

CONTENTS ........................................................................................................... IV

LIST OF TABLES ............................................................................................... VII

LIST OF FIGURES ............................................................................................ VIII

CHAPTER 1 INTRODUCTION ....................................................................... 1 1.1 Research objectives ......................................................................................................... 1

1.2 Thesis Outline ................................................................................................................. 2

1.3 Golf Swing Model and Golf Swing Robot ...................................................................... 3

1.3.1 Modeling the Golf Swing ........................................................................................ 31.3.1.1 The Double Pendulum Model ............................................................................. 31.3.1.2 Complex Swing Models ...................................................................................... 4

1.3.2 The Golf Robot ........................................................................................................ 6

1.3.2.1 True Temper Sports ............................................................................................. 81.3.2.2 Golf Laboratories ................................................................................................ 91.3.2.3 Miyamae Shot Robo III ....................................................................................... 91.3.2.4 Miyamae Shot Robo V ...................................................................................... 10

1.4 Generator of Body Data (GEBOD) ............................................................................... 12

1.5 Gyro Motion Sensors .................................................................................................... 15

1.5.1 Physical Effects in Gyroscopes ............................................................................. 161.5.1.1 Sagnac Effect ..................................................................................................... 161.5.1.2 Coriolis Force Effect ......................................................................................... 17

1.5.2 Typical Types of Gyros ......................................................................................... 191.5.2.1 He-Ne and Solid-State Ring Laser Gyroscopes ................................................ 191.5.2.2 Fiber Optic Gyroscopes ..................................................................................... 191.5.2.3 Integrated Optical Gyroscopes .......................................................................... 201.5.2.4 MEMS Gyroscopes ........................................................................................... 21

CHAPTER 2 GOLF SWING MODELING AND ITS KINEMATICS ....... 23 2.1 Twelve-DOF Human Body Model ................................................................................ 23

2.2 Reduction from Twelve-DOF Model to Eleven-DOF Model ....................................... 24

2.3 Reduction from Twelve-DOF Model to Six-DOF Model ............................................. 27

2.3.1 Six-DOF Golf Swing Model ................................................................................. 272.3.2 Forward Kinematic ................................................................................................ 282.3.3 Verify Forward Kinematic ..................................................................................... 29


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2.4 Denavit-Hatenberg Representation Method .................................................................. 30

CHAPTER 3 PARAMETER IDENTIFICATION ......................................... 32 3.1 Gyro Sensors Attachment .............................................................................................. 32

3.2 First Identification Method ............................................................................................ 33

3.2.1 Simulation Real Body ........................................................................................... 343.2.2 Cost Function and Solving .................................................................................... 353.2.3 Results of First Identification Method .................................................................. 36

3.3 Second method .............................................................................................................. 36

3.3.1 Identify Procedures ............................................................................................... 363.3.2 Four-DOF Model ................................................................................................... 37

3.3.2.1 Forward Kinematics of Four-DOF Model ......................................................... 383.3.2.2 Inverse Kinematics of Four-DOF Model .......................................................... 38

3.3.3 Sub-step One, Identify First Two Parameters a 1 and d 1 ........................................ 39

3.3.4 Sub-step Two, Identify Last Three Parameters a 3, a4 and d 6 ................................. 393.3.5 Comparison between two methods ....................................................................... 413.4 Optimization Algorithm Used to Solve the Set of Cost Functions ............................... 41

CHAPTER 4 MODEL CALIBRATION ......................................................... 46 4.1 Touched Point Assignment ........................................................................................... 46

4.2 Compensation Algorithm .............................................................................................. 48

4.3 Simulation and Results .................................................................................................. 50

4.3.1 Simulation inputs and outputs ............................................................................... 504.3.2 Simulation for Actual Body ................................................................................... 504.3.3 Compensation ........................................................................................................ 514.3.4 Calibration results ................................................................................................. 51

4.4 The Effect of Number of Calibration Points ................................................................. 52

CHAPTER 5 EXPERIMENTS AND RESULTS ............................................ 55 5.1 Gyros Reading ............................................................................................................. 55

5.1.1 Introduction to our gyros ....................................................................................... 555.1.2 Wire Connection for Six Gyros ............................................................................. 56

5.1.3 Labview Program .................................................................................................. 575.1.4 Gyro Test ............................................................................................................... 59

5.2 Experiment Process ....................................................................................................... 59

5.2.1 Base and Touched Points Preparation ................................................................... 595.2.2 Gyro Attachment and Golf Club ........................................................................... 605.2.3 Experiment Process ............................................................................................... 61

5.3 Transformation from Absolute Orientation to Relative Orientation ............................. 62

5.4 Experiments Results ...................................................................................................... 63

5.4.1 Identify Results ..................................................................................................... 63

5.4.1.1 First Identify Method Results ............................................................................ 635.4.1.2 Second Identify Method Results ....................................................................... 645.4.2 Calibration Results ................................................................................................ 65


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5.5 Implementation into Model to Draw Out Trajectory .................................................... 66

CHAPTER 6 CONCLUSION AND FUTURE WORK ................................. 68

REFERENCES ...................................................................................................... 70

APPENDIX A CODE OF 1 ST IDENTIFICATION METHOD ......................... 73

APPENDIX B CODE OF 2 ND IDENTIFICATION METHOD SUB-STEP-1 . 74

APPENDIX C CODE OF 2 ND IDENTIFICATION METHOD SUB-STEP-2 . 75

APPENDIX D CODE OF CALIBRATION STEP ............................................. 76

APPENDIX E FORWARD KINEMATICS OF TWELVE-DOF MODEL ..... 80

APPENDIX F SET OF COST FUNCTIONS OF TWELVE-DOF MODEL ... 82


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LIST OF TABLES

Table 1: List of 32 body dimensions ............................................................................................. 12Table 2: Kinematic Parameters of Twelve-DOF model ................................................................ 23Table 3: Error Comparison ............................................................................................................ 25Table 4: Link Length Values ......................................................................................................... 25Table 5: Link Length Errors .......................................................................................................... 25Table 6: Kinematics Parameters of Six-DOF Model ..................................................................... 28Table 7: Assumed Exact Link Lengths .......................................................................................... 35Table 8: Actual Joint Movement Results ....................................................................................... 35Table 9: First Identify Method's Results ....................................................................................... 36Table 10: Kinematics Parameter of Four-DOF Model .................................................................. 38Table 11: Identify first two parameters ......................................................................................... 39Table 12: Identify last three parameters ........................................................................................ 40Table 13: Five parameters Identification ....................................................................................... 40Table 14: Parameter identification for shorter link lengths ........................................................... 41Table 15: Parameter identification for longer link lengths ............................................................ 41

Table 16: Comparison of two identification method ..................................................................... 41Table 17: Identified Link Lengths ................................................................................................. 46Table 18: Identified Link Lengths and Induced Errors ................................................................. 48Table 19: Compensate Values for Link Lengths ........................................................................... 51Table 20: Simulation Results of Calibration Step ......................................................................... 52Table 21: Calibration Touch Point Positions ................................................................................. 52Table 22: Link Lengths after Compensation vs. Number of Calibration Point ............................. 53Table 23: List of Touched Points ................................................................................................... 59Table 24: Experiment Process ....................................................................................................... 62Table 25: Angle Transformation of First Identification Method ................................................... 64Table 26: Link Length Results of First Identify Method .............................................................. 64

Table 27: Simulation vs. Experiment Errors of First Identify Method ......................................... 64Table 28: Angle Transformation of Identify Method2/Sub-Step1 ................................................. 64Table 29: Link Length Results of Second Identify Method .......................................................... 65Table 30: Simulation vs. Experiment Errors of Second Identify Method ..................................... 65Table 31: Angle Transformation of Calibration Process ............................................................... 66Table 32: Link Length Results of Calibration Step ....................................................................... 66Table 33: Simulation vs. Experiment Errors of Calibration Step .................................................. 66


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LIST OF FIGURES Figure 1: Double Pendulum Arrangement, Cochran and Stobbs (1968) ......................................... 3Figure 2: Wrist Axis Centre of Rotation - a) TOBS b) Impact, Milburn (1982) ........................... 4Figure 3: Shifting Pivot Double Pendulum Model, Jorgensen (1999) ............................................ 4Figure 4: Constant Torque Triple Pendulum Swing Simulation, Turner and Hills (1999) ............... 5

Figure 5: Swing Models - a) Four Link b) Double Pendulum, Iwatsubo et al (2002) .................... 6Figure 6: Prototype Golf Robots a) Ming (2006) b) Hoshino (2005) ............................................. 7Figure 7: Iron Byron - a) Wilson (2002), b) USGA Test Centre, Thomas (1978) ............................ 8Figure 8: Golf Labs Robot, Golf Laboratories (2005) ...................................................................... 9Figure 9: Miyamae Shot RoboIII design schematic, Miyamae (2000) ......................................... 10Figure 10: Miyamae Shot Robo V, Miyamae (2004) .................................................................... 11Figure 11: Robo5 Motion Axes Schematic ................................................................................... 11Figure 12: Procedures used in generating adult male and female subjects ................................... 13Figure 13: Procedures used in generating child subjects .............................................................. 14Figure 14: Procedures used in generating with user supplied dimensions .................................... 15Figure 15: Sagnac ring interferometer ......................................................................................... 17Figure 16: Two-DOF spring-mass-damper system in a rotating reference frame ......................... 18Figure 17: Link Coordinate of Twelve-DOF Model ..................................................................... 24Figure 18: Angles vs. Time for Eleven-DOF Model ..................................................................... 26Figure 19: Ending Positions of 11DOF Model ............................................................................. 26Figure 20: Link Coordinates of Six-DOF Model .......................................................................... 27Figure 21: Gyro 1 And 4 Attachment Positions ............................................................................ 32Figure 22: Gyro 2 And 3 Attachment Positions ............................................................................ 33Figure 23: Procedure of First Method ........................................................................................... 33Figure 24: Simulation Flow Chart ................................................................................................. 34Figure 25: Procedure for Second Method ..................................................................................... 37Figure 26: Four-DOF Model ......................................................................................................... 37Figure 27: Contact Point Definition on Golf Club Head .............................................................. 47Figure 28: Assignment of Calibration Point .................................................................................. 47Figure 29: Definition of Calibration Points ................................................................................... 48Figure 30: Actual Body Simulation Flow Chart ............................................................................ 50Figure 31: Simulation Flow Chart ................................................................................................. 51Figure 32: Calibration Error vs. Number of Calibration Points .................................................... 53Figure 33: Norm of Ending Error vs. No. of Calibration Points .................................................. 54Figure 34: Gyro Sensors ................................................................................................................ 55Figure 35: Gyro Connection Diagram ........................................................................................... 56Figure 36: On-Site Wire Connection without Players ................................................................... 56

Figure 37: ADC circuit board and bag .......................................................................................... 56Figure 38: Labview Program Flow Chart ..................................................................................... 57Figure 39: Labview Program ......................................................................................................... 58Figure 40: Gyro Reading Program Interface ................................................................................. 58Figure 41: Gyro Calibration Equipments ...................................................................................... 59Figure 42: Base Model in A0-Size Paper ...................................................................................... 60Figure 43: Gyro Attachment .......................................................................................................... 61Figure 44: Zero Posture ................................................................................................................. 62Figure 45: Absolute Angles Extracted From Gyros ...................................................................... 67Figure 46: Ending Positions .......................................................................................................... 67


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Chapter 1

INTRODUCTION

Since the golf shot is one of the most difficult biomechanical motions in sport to execute, a

detailed understanding of the mechanics of the swing would be beneficial to the golfer and

teacher. It would also provide equipment manufacturers with useful data for club analysis and

design.

The golf swing is a high-speed, complex sequence of three-dimensional (3D) motions; and

large variability between individual players has supported the common belief that individual

golfers perform unique swing motions. However, golfers are inconsistent in performance

and they tire. One method of overcoming these shortcomings lies in the development of

golf swing simulation devices. Simple mechanical examples of these devices date back to

the 1920's, but, the first 'advanced' robot was developed by True Temper Sports (TTS) in

1966. The swing motions were based upon cinematic footage of top professional golfer Byron

Nelson and the machine became known as the "Iron Byron".

Other golf robots perform simplified swing motions, based upon a double pendulum

arrangement, with the upper lever representing the golfers' arms and the lower lever

representing the club. They also generate additional perceived technological advancement

amongst consumers, thus it is easy to see why mechanical swing devices have become favored

amongst many of the leading golf equipment manufacturers worldwide.

New technologies allow increasingly complex models and simulations of human motion,

e.g. by applying methods of inverse dynamic modeling and forward dynamic simulation. These

modeling endeavors have yielded important information on various mechanical quantities of the

golf swing. Usually, the input data of these models includes the 3D kinematics of the movement.Therefore, it has to be assured that the input parameter data is accurate before 3D models of the

golf swing can be constructed and used for further studies.

To satisfy this requirement, the authors recognized the need to develop an effective method

allowing us to obtain critical body segment dimensions. In this method, gyro sensors will be

attached at some essential landmarks. Then, players are asked to touch points in order to get their

posture and parameter information.

1.1 Research objectives

The objectives of this thesis are to:


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Propose a kinematic model of golf player

Develop a method which allow us to recognize body segments dimensions

Improve the accuracy of this method by calibrating the system

1.2 Thesis Outline

This thesis presents the research conducted in the improvements of a method which can

recognize actual body segments dimensions. This is the first basic work in order to perform

individual golfer swings and other activities related to bodys dimensions. Computer programs

are written in Matlab to validate this technique. The outline of this thesis is as follow:

Chapter one introduces reasons and the necessaries to propose new method in order to

identify body segment dimensions. Typical scientific works associated with golf playing models

and golf swings are also investigated in literature review to give readers a general view in thisfield. The previous popular identify method, GEBOD, is also briefly presented in this chapter. In

addition, a brief introduction of gyro sensors is also reported.

Chapter two describes human body model. It consists of 6-DOFs including one-two-one-

two DOFs representing hip, shoulder, elbow and wrist respectively. Denavit-Hatenberg (D-H)

representation method is used to find out ending vector with respect to base coordinate.

Chapter three is identification step. This chapter depicts an identifying method which

allows us to find out initial body segment dimensions (also called identified dimensions). In this

method, gyro sensors are attached at body landmarks. Then, players are asked to touch two

points I1 and I2. These two points I1 and I2 are called identified touch points. Outputs from

gyros are inputted into identifying algorithm to calculate identified dimensions. The rules for

choosing touch points are also discussed in this chapter.

Chapter four is calibration step. The purpose of this chapter is to improve the accuracy of

the process by touching another set of touch points. This set of touch points is call calibration

touch point and must be difference from previous identified touch points. The effects of number

of calibration touch point are analyzed in order to obtain appropriate number of calibration point.

Chapter five reports experiment works. The results presented include read-out technique to

deal with data from gyro sensors and experiment set up. The final target, body segment

dimensions, is also shown through both two identification and calibration steps.

Chapter six discusses the advantages and disadvantages of this identify method during the

undertaking of this thesis. The author assumes future works in order to improve the accuracy andconvenient of processes. Ending of this chapter presents the conclusions approached from

completion of this research study.


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1.3 Golf Swing Model and Golf Swing Robot

This literature survey presents an overview of the published literature on the modeling of

golf swing, robotic devices that simulate golf swing motions. The surveyed literature has primarily

comprised journal articles, theses, books and other sources.

1.3.1 Modeling the Golf Swing

1.3.1.1 The Double Pendulum Model

Cochran and Stobbs [1] defined a 'model' as a representation of something complicated

or ill-understood by something simple or familiar. They presented the first model of the golf swing as

a simple two lever system in a double pendulum arrangement, as illustrated in Fig. 1. Their double

pendulum model has been used extensively by subsequent researchers to analyze the swings of

skilled and unskilled golfers, including research articles published by [2], [3] and [4]. The double

pendulum model has also been used to investigate optimization of golfer performance, including

research articles published by [5], [6], and [7].

The upper link represents the golfer's shoulders and arms which rotate about a fixed pivot or

'hub' located at the golfer's upper torso, approximately between the shoulders. The lower link

represents the golf club, which is rotated about a hinge point located at the golfer's hands/wrists.

The angular position of the upper link is measured against the vertical axis from the fixed pivot,

and the angle created between the upper link and the lower link, wrist , is referred to as the 'wrist-

cock' angle.

Figure 1: Double Pendulum Arrangement, Cochran and Stobbs (1968)

Four assumptions exist within the basic double pendulum model of the golf swing. Firstly

the model assumes that the golfer's arms remain at a constant length throughout the performance of

their swing; this assumption stems largely from modern practice of keeping the left arm straight

during the downswing. Secondly the model assumes a fixed hinge position joining the upper and

lower levers, located between the golfer's hands/wrists. Thirdly the model assumes a fixed

centre of rotation for the two-lever system and that the rotational efforts of the golfer are equated to a


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single torque applied about this central pivot. Lastly, the model assumes that the two-lever system

will rotate in a single plane, inclined to the vertical, called the swing plane ( swing ).

Figure 2: Wrist Axis Centre of Rotation - a) TOBS b) Impact, Milburn (1982)

Milburn [8], however, found the anatomical location of golf club centre of rotations to

change during the golf swing. At the TOBS the centre of rotation was located at the middle of the left

hand close to the knuckles of the 2 nd and 3 rd fingers, as shown in Fig. 2a. Whilst at impact, the centre

of rotation was located towards the centre of the golfer's left wrist, as illustrated in Fig. 2b.

Figure 3: Shifting Pivot Double Pendulum Model, Jorgensen (1999)

Hendry [9] identified the neck as the closest approximation of a fixed pivot (hub) location

during golfer swings, whilst, Wiren [10] believed that the golfer's left armpit provided the best

approximation of the hub location at impact. However, [6] found that a better agreement

between modelled positions and observed golfer positions could be achieved if the fixed centre ofrotation constraint was replaced by a laterally shifting pivot location; a diagrammatical

representation of the shifting pivot double pendulum model is shown in Fig. 3.

1.3.1.2 Complex Swing Models

The golf swing has also been modeled as a three link system by a number of researchers,

including [11-13]. Betzler [14] has also Similar to the double pendulum model, all levers in the triple

pendulum model rotate about a fixed pivot in a single inclined plane ( swing ). Typically the two

levers that comprise the double pendulum model form the second and third levers in the triple

pendulum swing model, and the first lever from the swing hub represents the rotation of the golfers'


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shoulders.

Turner and Hills (1999) performed a number of player tests to determine the torques exerted

by golfers when performing a swing. Separate couples were applied to all three levers in the

backswing and downswing enabling swing simulations to be conducted. A diagrammatical

representation of the swing simulations performed is shown in Fig. 4. The simulation of realistic

swings was found to be most sensitive to changes in the shoulder torque, as this was found to

have the biggest effect on club position. The authors commented that "if the shoulder motion is

incorrect it is almost impossible to simulate a 'good' golf swing" Turner and Hills (1999).

Iwatsubo [15] compared the conventional double pendulum model with a four lever swing

model, where all axes rotated about a fixed pivot in a single inclined plane ( swing ). An illustration of

the four lever swing model is shown next to a conventional double pendulum model in Fig. 5. The

four levers represent the upper part of the torso, the left upper arm, the left forearm and the club,

jointed at the neck, left shoulder, left elbow and left wrist. The angular velocities and accelerations

of the wrist joint compared consistently between the two models for four different golf swings.

Small differences in the joint torques applied at the neck and wrist were observed between

simulations for two of the four players' swings, which also brought about differences in downswing

timings for these two swings.

Figure 4: Constant Torque Triple Pendulum Swing Simulation, Turner and Hills (1999)

The peak joint torques of the neck, shoulder and elbow were found to occur during the

second half of the downswing in the quadruple-link model, and the peak neck torque of the double-

link model was found to occur at the midpoint of the downswing. The authors concluded that the

four lever swing model was more suitable for analyzing golf swings because the double pendulum

model lacks consideration of the golfers shoulder and elbow motions. The four link model which

takes motion of the shoulder and elbow joint into consideration simulates swing motion better


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than the two link model in order to evaluate player's skill level and the instruments for a player

[15].

Figure 5: Swing Models - a) Four Link b) Double Pendulum, Iwatsubo et al (2002)

1.3.2 The Golf Robot

The primary reasons for the development of robotic devices to perform golf swing motions are

the repeatability of movements and the elimination of human factors from test methodologies.

The removal of human subjects from testing procedures will often provide many of the following benefits: no fatigue, no preconceptions, no loss of concentration, increased testing accuracy,

increased data sampling, reduced test durations, direct comparison of results, reduced subject

recruitment problems and increased testing availability.

Suzuki [16] identified that many of these benefits will become available as mechanical golf

swing devices are developed, the authors stated that "for these reasons, it is hoped that golf-

swing robots can be used instead of professional golfers for the evaluation of golf club

performance".

Simple mechanical devices were developed in the 1920's by equipment manufacturers to strike

balls with a rotating end effecter, driven by drop weight and spring mechanisms to represent club/ball

impacts. In 1966, the first advanced swing machine was introduced by TTS which was designed to

perform golf swings representative of top professional golfer Byron Nelson. The mechanical swing

device was pneumatically driven and used a double pendulum arrangement with fixed gearing to

deliver the club head to the ball at impact with speeds up to 60 m/s.

Suzuki [16, 17] identified many of the primary limitations associated with advanced golf

swing robots "The performance of golf clubs and balls is generally evaluated by using golf-swing


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robots that conventionally have two or three joints with completely interrelated motion. This

interrelation allows the user of this robot to specify only the initial posture and swing velocity of the

robot and therefore the swing motion of this type of robot cannot be subtly adjusted to the specific

characteristics of individual golf clubs. Consequently, golf swing robots cannot accurately emulate

advanced golfers and this causes serious problems for the evaluation of golf club performance"

Ming [18] reported the development of motion control circuitry to perform a learning

control from the motion output of a golf robot using an integrated feedback system. Initial testing

supported the use of feed-forward control to improve the accuracy of swing simulations to observed

golfer motions. A prototype golf swing robot was developed using feed-forward control based

upon IDM with angular feedback control over the double pendulum joint arrangement, as shown

by Fig. 6a.

Feedback control is a robust and proven robot control system that has been successfully

implemented to manage many automated devices. However, feedback control is limited by the

problem of 'time-lag' where the control system is unable to process and react quickly enough to

residual feedback data. Time-lag errors are most commonly suffered during control of high-speed

motions, such as a golf swing replication [19].

Figure 6: Prototype Golf Robots a) Ming (2006) b) Hoshino (2005)

Ming [19] reported the use of artificial neural networks (ANN) to achieve learning control

based upon direct joint angle feedback enabling accurate joint control of robotic golf swing

simulations. Joint angle data recorded directly from a resolver mounted on the robot indicated that

more accurate swing simulations were performed with learning control using recurrent ANN than

by using previous control methods based upon motion equations.

Hoshino [20] presented a prototype golf robot with variable wrist release control, thus the robot


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was capable of performing swings with either a 'natural release' or a 'delayed wrist release' to emulate

'late hitting'. The robot comprised two levers in a double pendulum arrangement, as shown in Fig.

6b.

Hoshino [21] investigated wrist release timings to achieve optimal club head velocity at impact,

using simulations performed under variable torque profiles. The author reported that optimal club

head speeds at impact could be achieved when the wrist axis was released at the zero-crossing point of

the lead/lag shaft deflection, and that increased club head velocities could be achieved if the shaft

deflection zero-crossing point was delayed.

A number of swing machines are commercially available from specialized retailers such as

TTS [22], Golf Laboratories Inc. [23] and Miyamae Corporation Ltd [24-26] which offer

varying levels of programmability and performance. The majority of the swing devices developed

perform swing motions based upon a planar double pendulum arrangement which is inclined to

represent golfers' swing plane angles.

1.3.2.1 True Temper Sports

In 1964, the first advanced swing machine was developed by TTS in conjunction with Battelle

Memorial Institute to provide a controlled test methodology for comparative shaft analyses. After

several months of analyses swing motions of numerous professional and skilled amateur golfers', TTS

chose Byron Nelson's swing because it was smooth and proved to be the most efficient in terms ofenergy transfer during the downswing.

Figure 7: Iron Byron - a) Wilson (2002), b) USGA Test Centre, Thomas (1978)

The TTS swing machine was the first device to replicate a golfers' swing and the first golf

hitting machine to use an actual club, comprising a single robotic arm which was driven by a series of pneumatic valves. The club was rigidly clamped at the distal end of the arm and fixed gearing ensured a


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consistent swing motion in a double pendulum arrangement. The robotic golfer was introduced in 1966

simply as the "Golf Club Testing Device", as illustrated in Fig. 7. Several years later the device took

on the lasting moniker 'Iron Byron'.

For the last four decades, Iron Byron has provided critical feedback for every major equipment

manufacturer and also by the United States Golf Association (the governing body of the game of golf in

America) to determine equipment standards. One of the key features of the robot was its ability to mimic

the energy transfer present in the golf swing.

1.3.2.2 Golf Laboratories

In 1989 Golf Laboratories presented a golf swing robot that used a single servomotor to

control the rotation of the main arm (upper lever) based upon an operator-specified torque

curve. The club gripping mechanism rotated about two geared axes which simulated the

cocking of the wrist and the longitudinal rotation of the club. The wrist mechanism was not

powered by an individual motor or geared to the arm axis motion, and thus, was considered

'free' as illustrated in Fig. 8.

Figure 8: Golf Labs Robot, Golf Laboratories (2005)

The Golf Laboratories robot has a strong and reliable structure which enables basic club and ball comparison tests to be completed effectively and quickly. However, the free geared wrist

arrangement limits the functionality of the robot because the device is only capable of providing

proportional wrist and club rotations during the downswing, through a maximum peak range of

motion of 90; which may not be representative of golfers' swings. In addition, no feedback

information is provided by the robot, so it is impossible to determine what motions the robot

has actually performed.

1.3.2.3 Miyamae Shot Robo III

The Miyamae Shot Robo III golf robot (Robo3) is typical of many current golf swing


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machines. The device uses a single electric motor to power a geared double pendulum

mechanism to provide swing motions representative of golfers' swings. The RoboIII comprises

three main sections; a lower body, an upper body and an arm mechanism, as illustrated in Fig. 9.

Figure 9: Miyamae Shot RoboIII design schematic, Miyamae (2000)

The lower body comprises a base of four heavy feet and a rigid housing that holds the upper

robot section secure. The upper body is hinged enabling the swing plane to be adjusted for different clubs;

golfers typically swing longer clubs on a flatter plane than shorter clubs. The robot arm mechanism

comprises two rigid sections which are joined together using fixed gearing. The robot's gripping

mechanism is attached to the lower arm section. Thus, the motions of all three swing axes are

dependent upon the motion of the arm axis, which makes the RoboIII capable of performing only

one swing profile. The swing speed of the Robo3 may be varied to enable driver club head

velocities at impact up to 130 mph.

1.3.2.4 Miyamae Shot Robo V

The Miyamae Shot RoboV golf robot (Robo5) is an advanced golf robot that supersedes the

RoboIII. The RoboV was marketed as 'the world's first controllable swing robot', and each swing

performed by the machine is controlled via a computer interface. The Robo5 was designed to

enable multiple swing profiles to be performed, thus providing representation of different

golfers' swings. A lower body stabilizes the robot, an upper body houses motors and provides

set-up variability and an arm with club gripping mechanism secures the club and provides the

swinging motion.

As illustrated in Fig. 10. The arm and wrist axes of the Robo5 provide the primary shape and

power of the swing simulations, whilst the grip axis controls the longitudinal orientation of theclub.


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Arm axis - the arm axis is driven by the largest servomotor, 5kW AC.

Wrist axis - the wrist axis is driven by a smaller servomotor, 1.5kW AC.

Grip axis - the grip axis is powered by the smallest servomotor, 30W AC, which provides

rotation about the longitudinal axis of the club. Unlike the arm and wrist servomotors the

grip motor is located on the robot arm, adjacent to the gripping mechanism.

Figure 10: Miyamae Shot Robo V, Miyamae (2004)

Unlike the Robo3, the Robo5's motion axes are independently controlled which enables

variable swing profiles to be performed. This is a major advantage over the Robo3 because

different swing profiles representative of individual golfers may be performed, rather than justreplicating the club head speeds achieved by golfers' using a generic swing motion. Independent

control of the motion axis also enables the Robo5 to perform swing profiles representative of

different shot types, e.g. full swing, punch shot, pitch, chip and putt.

Figure 11: Robo5 Motion Axes Schematic


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1.4 Generator of Body Data (GEBOD)

GEBOD (Generator of Body Manual) [27, 28] is a computer program which was developed to

generate human and dummy data sets. The data sets include the body segments' geometric and

mass properties, and the joints' locations and mechanical properties. Regression equations from

anthropometric surveys and stereo photometric data [29-33] are used in computing these data sets.

The program is written in FORTRAN and has a simple user interface. It creates an occupant

description data file formatted to be directly inserted into an ATB occupant simulation input file.

GEBOD used a set of 32 body dimensions to compute the joint center locations and the

segment sizes, masses and principal moments of inertia. They are shown in following table 1.

No. Body Dimension No Body Dimension

0 Weight 16 Hip Breadth, Standing

1 Standing Height 17 Shoulder to Elbow Length

2 Shoulder Height 18 Forearm-Hand Length

3 Armpit Height 19 Biceps Circumference

4 Waist Height 20 Elbow Circumference

5 Seated Height 21 Forearm Circumference

6 Head Length 22 Waist Circumference

7 Head Breadth 23 Knee Height, Seated

8 Head to Chin Height 24 Thigh Circumference

9 Neck Circumference 25 Upper Leg Circumference

10 Shoulder Breadth 26 Knee Circumference

11 Chest Depth 27 Calf Circumference

12 Chest Breadth 28 Ankle Circumference

13 Waist Depth 29 Ankle Height, Outside

14 Waist Breadth 30 Foot Breadth

15 Buttock Depth 31 Foot Length

Table 1: List of 32 body dimensions


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Version III of GEBOD has additional options for 17 segments (separate lower arm and

hand segments) and dummy data sets. GEBODIII also uses the stereo photometric survey data in

the calculation of the joint center locations, and segment masses and inertial properties, improving

the accuracy of these data. The joint and ellipsoid location calculations are corrected to

provide accurate sitting and standing heights in version IV.

GEBOD is an interactive, menu-driven program. Upon starting, the user is asked for a

subject description and an output filename. Next the user is asked to select one of the subject

types: child (2-19 years), adult human female, adult human male, user-supplied body

dimensions, seated hybrid III dummy (50th %tile), standing hybrid III dummy (50th

%tile), hybrid ii dummy (50th %tile).

Figure 12: Procedures used in generating adult male and female subjects

Depending on the chosen subject type, one of four methods is used to generate the required body data. The data for the Hybrid II and III dummies are contained in the GEBOD.DAT file

and GEBOD simply reads these data and transforms them into the appropriate units. The

procedures used in generating the adult male and female, child, and user-supplied dimensions

option data sets are illustrated in Fig. 12, 13, and 14 respectively. The rectangular boxes

symbolize sets of data, and the ovals symbolize processes or equations that operate on the data.

These data and processes are described in the following sections.

Regression Equations

Regression equations are used in the child, and adult human male and female options. It is


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a method widely used in anthropometry for predicting unknown body dimensions from

known body dimensions, using a database of measurements taken from several human subjects.

In GEBOD, there are four groups of regression equations which are used to determine the

body dimension set, joint location coordinates, segment volumes, and principal moments of

inertia. Each group has two sets of equations for female and male subjects respectively,except for the body dimension set which has a third set for children. Each regression

equation is a first order linear equation with either standing height or body weight, or both of

them as the independent variables.

Figure 13: Procedures used in generating child subjects

For the child regression equations, an additional independent variable of age is used. For

example, the regression equation to predict adult female shoulder height can be found as

follows:

Shoulder Height = 0.07182(Body Weight) + 42.77Shoulder Height = 0.8751(Standing Height) - 3.936

Shoulder Height = 0.00755(Body Weight) + 0.8469(Standing Height) - 3.096

Where: the body weight and standing height are the input variables which the user supplied.

Depending on the user input, one of the above three equations is used to obtain the shoulder

height.

The average values for the above three equations are 0.3094, 0.9194 and 0.9218,

respectively. As expected, the equation using both weight and height has the best predictive

ability.


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Figure 14: Procedures used in generating with user supplied dimensions

Body Dimensions

For the child and adult human options, the body dimensions in Table 1 are generated from

regression equations based on input height, weight, and/or age. These regression equations are

stored in GEBOD and were computed from data given by [29, 30, 32]. As the name implies, theuser supplied body dimensions option obtains the body dimensions from an input file supplied by

the user.

Body Geometry

The structure and appearance of the human model as depicted by the ATB model is

determined from contact ellipsoid semi axes and joint locations. A contact ellipsoid is associated

with each body segment, giving the segment shape and providing an interaction surface

between the segment and its environment. The joints connect segments and serve as pivot points

about which rotational motion is allowed. A joint is located relative to the two segments it

connects. For example, the elbow joint is located by two sets of three-dimensional coordinates:

one set relative to the local reference system of the upper arm; the other relative to the local

reference system of the forearm.

1.5 Gyro Motion Sensors

Inertial Measurement Units (IMUs) which can measure the acceleration along three axes

and angular velocity around the same three axes are very complex systems. The

improvements of IMUs have decreased weight, power consumption and increased sensitivity,

reliability which is needed for new missions.

Gyroscope (also named gyro) can detect the angular rate around a fixed axis with respect to

their inertial space. In the last decades, intense research fund and effort have been devoted to

design, improve, optimize and fabricate different kinds of gyros essentially based on angular

momentum conservation, Sagnac and Coriolis effects.

It is easy to identify three different kinds of gyro: spinning mass gyros, optical gyros and


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vibrating gyros. In the first spinning mass gyros, all of them have a mass which spin steadily

with respect to a free movable axis. The second categories, optical gyros, are based on Sagnac

effect which states that phase shift between two waves counter-propagating in a rotating ring

interferometer is proportional to the loop angular velocity. The last kind, vibrating gyros, are

based on Coriolis effect that induces a coupling between two resonant modes of a mechanicalresonator.

The basic working methodology of gyroscope use the special properties of a wheel when

it spins at high speed, which tends to keep the direction of its spin axis by virtue of the tendency

of a body to resist to any change in the direction of its moment. A typical gyro which has been

developed based on this physical principle is Dynamically Tuned Gyroscope (DTG) [34].

Control Moment Gyroscope (CMG) [35] is one of the most successful spinning mass

gyros. It consists of a spinning rotor and one or more motorized gimbals that tilt the rotor

angular moment. As the rotor tilts, the changing angular moment causes a gyroscopic torque that

rotates the spacecraft. CMGs were used for decades in spaceship and space industries.

The Hemispherical Resonator Gyro (HRG) is a highly performing vibrating gyro which was

created in 1980s. The sensing part of HRG is a fused silica hemispherical shell covered by a thin

metal film [36]. This device is a very sensitive and expansive gyro and it was used in some

space missions.

Two other types of gyros are silicon and quartz MEMS gyros which are innovative

miniaturized vibrating angular rate sensors. They can be produced at low cost, while its

performance is constantly improved. MEMS gyros global market is significantly growing up.

When the first Ring Laser Gyroscope (RLG) was invented in 1963 [37], it opened a new

era of photonic gyroscopes. Many types have been proposed and demonstrated, including fiber

optic gyroscopes (FOGs) and integrated-optics gyroscopes [38-40].

Recently, some sophisticated technologies for future gyros have been demonstrated suchas the nuclear magnetic resonance gyro [41, 42] and the super fluid gyro [43].

1.5.1 Physical Effects in Gyroscopes

1.5.1.1 Sagnac Effect

Sagnac effect is the main operating principle of all optical gyros. It induces either a phase

shift between two optical signals propagating in opposite directions within a ring

interferometer rotating around an axis perpendicular to the ring, or a frequency shift between tworesonant modes propagating in clockwise (CW) and counter-clockwise (CCW) directions within


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an optical cavity rotating around an axis perpendicular to it.

We first take a view of a circular ring interferometer in which two waves counter-

propagate in the vacuum (see Fig. 15).

Figure 15: Sagnac ring interferometer

Light is generated and lead to enter the interferometer at point P. It is split into CW and

CCW propagating signals by a beam splitter. When the interferometer is at rest with respect to

a motionless inertial frame of reference, optical path lengths of the two optical signals

propagating in opposite directions (CW and CCW signals) are equal. Also the speeds of the two

signals are equal to light speed in the free space c. After propagating in the loop, both waves

come back into the beam splitter after a time interval r . When the ring interferometer is

rotating at a rate , the beam splitter located in P moves during the time interval r by a length

l .

CW (co-directional with ) beam experiences a path length slightly greater than 2 R in

order to complete one round trip, since the ring interferometer rotates through a small angle during

the round-trip transit time. CCW beam experiences a path length slightly less than 2 R during

one round trip. The phase shift between CW and CCW optical signals due to the

interferometer rotation can be described as:

==

c

Rct

2282

Where: is the optical signal wavelength.

1.5.1.2 Coriolis Force Effect

All vibrating gyros are based on the effect of Coriolis force on a vibrating mass. A vibrating

angular rate sensor can be represented by a two degree-of-freedom spring-mass-damper system

shown in following Fig. 16.


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Figure 16: Two-DOF spring-mass-damper system in a rotating reference frame

Coriolis force is a force experienced by a mass m moving in a rotating reference frame. It is

equal to:

( )= m F C 2

where is the mass velocity in the rotating reference frame and is the angular velocity of the

reference frame.

The effect of Coriolis force on the two degree-of-freedom spring-mass-damper system can

be derived from dynamic equations describing the motion in a rotating reference frame. The

mass m can move along x and y axes and is directed along z . The oscillation along x, namelydrive or primary oscillating mode, is excited by the force F x directed along x whereas the

oscillation along y, sense or secondary oscillating mode, is due to system rotation around z axis.

Motion equations of the two degree-of-freedom system can be written in the form:

=+++

=++

02

2

2

2

2

2

dt dx

m yk dt dy

Ddt

yd m

F dt dy

m xk dt dx

Ddt

xd m

y y

x x x

where is the module of reference system angular rate, D x and D y are the damping coefficient

along x and y axes, and k x and k y are the spring constants along x and y axes.

The primary oscillating mode is excited by a sinusoidal force F x and its amplitude is kept

constant at a x. To maximize a x, the angular frequency of the exciting force d is typically very

close to the resonance frequency mk x x = of the primary resonator. So x (t) can be written as:

( ) ( ) ( )t at at x x xd x sinsin =

a y and y(t) are derived as follows:


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( ) 2222222

y y x y x

x x y

Q

aa

+

=

( )( )

( ) y x y y x y x

x x t Q

at y

+

+

= cos2222222

These equations show that the amplitude of sense mode is directly proportional to the

angular rate . Then the angular rate of the two degree-of-freedom spring-mass-damper system

can be easily estimated by measuring the amplitude of the oscillation along y.

1.5.2 Typical Types of Gyros

There are four typical types of gyroscope. They are HeNe and solid-state ring laser

gyroscopes, fiber optic gyroscopes, integrated optical gyroscopes, MEMS gyroscopes. In the

following sections, author will present brief introduction of every type of gyroscope.

1.5.2.1 He-Ne and Solid-State Ring Laser Gyroscopes

He-Ne Ring Laser Gyroscopes

Two main architectures for its realization have been proposed. The fundamental difference

between them is the shape of the optical cavity in which the counter-propagating laser beams are

excited. In the first architecture, two corner mirrors and a spherical mirror have been used to

realize an equilateral triangular optical cavity. In the second architecture, exploited in the first

proposed HeNe RLG and in some commercially available RLGs, a square optical cavity

realized by four corner mirrors has been used.

Solid-State RLGs

The gaseous gain medium exploited in the HeNe RLG limits its reliability and lifetime. In

solid-state RLGs, the HeNe gain medium is replaced with a solid-state one consisting of a

Nd:YAG optical amplifier.

1.5.2.2 Fiber Optic Gyroscopes

FOG performance can be very high, but also medium and low, depending on the used ber

and on the accuracy of the read-out optoelectronic system. In this part, operation principles of

interferometric fiber optic gyros (IFOGs), resonant fiber optic gyros (RFOGs) and fiber optical

gyros based on a fiber ring laser are described. Then main characteristics, advantages and

drawbacks of these devices are summarized.

Interferometric Fiber Optic Gyros (IFOGs)


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A light source generates an optical signal, which is divided in two different beams by a

beam splitter. The beams are coupled into the two ends of a multi-turn fiber coil by two lenses.

The counter-propagating signals at the output of the two fiber ends are recombined by the beam

splitter and the optical signal resulting from the interference is sent to the photodetector.

Resonant Fiber Optic Gyros (RFOGs)

The ber ring resonator, which is the RFOG basic building block, includes a circular

resonator formed by a single-mode ber and one or two bers to excite the resonator and to

observe its spectral response. The resonator and bers are connected by ber couplers. The

configuration including only one ber coupler has one input port and one output port. Spectral

response at this port exhibits several minima corresponding to resonance frequencies. The

configuration including two ber couplers has two output ports. Spectral response at drop port

exhibits several maxima corresponding to resonance frequencies.

In a ring resonator, resonance condition is given by: qd 2=

Where: q is an integer number usually called resonance order, is the propagation constant

within the ring and d is the ring diameter.

Optical Gyros Based on a Fiber Ring Laser

The laser beam generated by the pump laser is split in two beams which have the same

frequency. As the pump signals propagate in the ber ring, the two Stokes signals are excited. A

portion of these two signals is extracted from the ring and the resulting signals interfere in the

directional coupler. The beat signal is sent to a photodetector (PD) and electric signal coming out

from it has a frequency which is proportional to the angular rate.

1.5.2.3 Integrated Optical Gyroscopes

By integrated optics technology, fabrication of optical gyros allows us to reduce weight and

dimension, lower cost, decrease power consumption and increase reliability. It becomes a veryattractive research target and held a lot of research fund.

In active optical gyros, two resonant modes are excited within a ring laser and they

experience a rotation-induced frequency shift that can be measured by an interferometric

technique.

Passive optical angular rate sensors can be phase sensitive or frequency sensitive. In

frequency sensitive gyros two resonance frequencies of an optical cavity relevant to clockwise

and counter-clockwise propagation directions are measured. In phase sensitive gyros the

rotation-induced phase shift between two beams counter-propagating in a ring interferometer is


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measured.

Both active and passive integrated optical gyros have been proposed and fabricated. Most

of passive integrated optical gyros are frequency sensitive, but slow-light phase sensitive

integrated optical gyros have been recently proposed.

1.5.2.4 MEMS Gyroscopes

MEMS are vibratory gyros because they use vibrating mechanical elements to sense

rotation. MEMS gyros consist of some typical types: z-axis, lateral-axis and dual-axis MEMS

gyros.

Z-Axis MEMS Gyros

First MEMS gyroscope fabricated by bulk silicon micromachining has two-gimbal

supported by torsional exures. The outer gimbal is a rectangular frame connected to the

supporting substrate by thin beams allowing its rotation around x-axis. The inner gimbal

represents a platform that can rotate around the y-axis. The outer gimbal is electrostatically

driven into oscillatory motion out of the wafer plane at constant amplitude by using the driving

electrodes. The oscillation amplitude is kept constant by automatic gain control. When subjected

to a rotation around the axis perpendicular to the wafer plane (z-axis), Coriolis force induces the

oscillation of the inner gimbal around y-axis. Electrodes over the inner gimbal detect the

amplitude of secondary resonating mode.

Lateral-Axis MEMS Gyros

The first tuning-fork lateral-axis MEMS gyroscope has been fabricated on silicon-on-glass

substrate [44], and includes two proof masses coupled to each other by a mechanical suspension.

The primary motion is the anti-phase vibration of proof masses long x-axis. When the sensor

rotates around y-axis, Coriolis force will force masses vibrate in the direction perpendicular to

the substrate (z-axis). This is the secondary motion that allows angular rate estimation. The

actuation is electrostatic and detection is capacitive. Both actuation and detection are provided

by interdigitated comb electrodes.

Dual-Axis MEMS Gyros

These kinds of MEMS gyros are capable of sensing angular motion about two axes

simultaneously. The sensor is based on angular resonance of a rigid polysilicon rotor suspended

by four torsional springs anchored to the substrate.

The inertial rotor is induced to rotate about the z-axis perpendicular to the substrate by

comb electrodes. A rotation rate around the x-axis induces a Coriolis angular oscillation around


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the y-axis and likewise a rotation rate around the y-axis induces a Coriolis angular oscillation

around the x-axis. This Coriolis oscillation is measured using the change in capacitance between

the rotor and four quarter circle electrodes beneath the inertial rotor. Dual axes operation can

be achieved by using a different modulation frequency for each couple of electrodes.


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Chapter 2

GOLF SWING MODELING

AND ITS KINEMATICS

This chapter will present proposed golf player model and its kinematic. Also presented

here is a brief description of Denavit-Hatenberg representation method which is used to represent

model kinematic.

2.1 Twelve-DOF Human Body Model

As we have known, human body is a very complicated system which includes a lot of

degree of freedoms (DOF). A comprehensive model including almost all joints and linksinfluential to the swing motion is considered. Starting with twelve-DOF model, it is represented

by Denavit-Hatenberg representation method which is introduced detail in section 2.3. Link

coordinate and kinematic parameters are respectively shown in Table 2 and Fig. 17.

Axis d a Home

1 1 0 0 pi/2 pi/2

2 2 0 a 2 pi/2 pi/2

3 3 0 a 3 0 pi/2

4 4 0 0 pi/2 0

5 5 0 0 pi/2 pi/2

6 6 0 a 6 0 0

7 7 0 0 pi/2 pi/2

8 8 0 0 pi/2 pi/2

9 9 0 a 9 0 pi/2

10 10 0 0 pi/2 0

11 11 0 0 pi/2 pi/2

12 12 d12 0 0 0

Table 2: Kinematic Parameters of Twelve-DOF model


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Figure 17: Link Coordinate of Twelve-DOF Model

The forward kinematic of this twelve-DOF model is shown in App. E.

2.2 Reduction from Twelve-DOF Model to Eleven-DOF ModelThe increase of DOFs will increase the complex both in terms of mathematical modeling

and experiment. Thus some DOFs are considered to be neglected in order to reduce the model

within solving possibility. This section will describe a simple analysis which is used to recognize

what DOFs are the most important and neglect other unimportant ones.

At first, twelve-DOF human model is defined and shown in Fig. 17. In that model, wrist,

elbow and shoulder joints contain three DOFs, whilst waist movement and the dip of the

shoulder are presented by two and one DOFs respectively. It is assumed that we have known all

link lengths, and then every DOF is considered to be rotated a certain angle. The errors of ending

vector are compared to realize which one has the most influence on ending vector.

Table 3 shows the comparison of errors when we neglect one of twelve DOFs with respectto full twelve-DOF model. In Table 3, wrist, elbow and shoulder are represented by DOFs 10~12,


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7~9 and 4~6 respectively. Similarly, the movement of waist and the dip of shoulder are

represented by first, second and third DOF. In order to simplify the model, DOFs which have

less influence on ending vector are neglected. That is DOF 12.

Neglect DOF 1 2 3 4 5 6

Ending error (mm) 278.976 184.026 182.737 305.399 182.231 341.450

Neglect DOF 7 8 9 10 11 12

Ending error (mm) 270.498 126.760 251.848 181.882 214.063 .743e-11

Table 3: Error Comparison

The identification method presented in Chap. 3&4 is applied. A set of cost functions is built

based on ending vector. This set of cost functions is presented in Appendix F. The method which

is used to solve it is described in section 3.4. Whenever the set of cost functions is defined, an

experiment is run to get input data which is used to calculate coefficients of the set of cost

functions. This experiment is done in the same way as the one described in Chap. 5.

In this experiment, six gyros are attached in order to measure angular movement of six

DOF: 1~6. Then, touching procedure is done and data is extracted. After measuring first six

DOFs, gyros are removed and reattached at DOF: 7~9. Touching procedure is repeated again to

obtain their rotary motions. Finally, these data are analyzed and implemented into algorithm to

estimate link lengths.

Table 4 shows link length results of twelve-DOF model.

Link a 2 (mm) a3 (mm) a6 (mm) a9 (mm) d12 (mm)

Identification 1289.263 214.371 463.046 158.717 816.337

Calibration 1213.518 274.323 619.170 -15.534 789.368

Table 4: Link Length Values

Table 5 shows link length results of calibration step of twelve-DOF model.

ModelErrors of Links

a2 (mm) a3 (mm) a6 (mm) a9 (mm) d12 (mm)

Identification 160.737 15.629 -133.046 181.283 3.663

Calibration 236.483 -44.323 -289.17 355.534 30.632

Table 5: Link Length Errors


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With link lengths shown in Table 4, a slow swing was done twice. Then, angular

movements of twelve DOFs are compared to make them compatible at the hitting moment.

Result angles are shown in Fig. 18.

Figure 18: Angles vs. Time for Eleven-DOF Model

Rotary values are implemented into forward kinematics together with identified linklengths in Table 4 to estimate ending positions. This result is shown in Fig. 19.

Figure 19: Ending Positions of 11DOF Model


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At the hitting point, the estimated position is (14.4, 2188.45, -1261.05), whilst the exact

hitting point is (0, 700, 0). Thus the norm of error of this experiment at the hitting point is about

1950.9 mm. At first sight, this error is strange. It makes us confuse about its sources. They may

come from many factors because of such a complex model. In order to recognize the source of

errors easily, the author proposed another reduced-model with six-DOF. This is a simple onewhich is hypothesized to be useful in start both in terms of building algorithm and doing

experiment. More detail of this simple model is presented in further sections.

2.3 Reduction from Twelve-DOF Model to Six-DOF Model

2.3.1 Six-DOF Golf Swing Model

In this section, a reduction from twelve to six DOFs is presented. Base on the analysis in

Table 3, DOFs which have less influence on ending vector are 2, 3, 5, 8, 9 and 12. They areneglected in order to form a new model contains six DOFs: 1, 4, 6, 7, 10 and 11. This model

represents four joints: waist, shoulder, elbow and wrist respectively by DOF 1, 4&6, 7, and

10&11.

Figure 20: Link Coordinates of Six-DOF Model


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Applying step 1 to step 8 of the D-H algorithm to this model, we get the diagram of link

coordinates in Fig. 20.

Axis d a Home

1 1

d1

a1

pi/2 0

2 2 0 0 pi/2 pi/2

3 3 0 a 3 0 pi

4 4 0 a 4 0 0

5 5 0 0 pi/2 pi/2

6 6 d6 0 0 0

Table 6: Kinematics Parameters of Six-DOF Model

Next, we apply steps 9 to 14 of the D-H algorithm starting with k = 1 . Using Fig. 20, this

yields the set of kinematic parameters shown in Table 6. Since this is articulated-coordinate robot,

the vector of joint variables is q = . The values of q listed in the last column of Table 6

correspond to the home position pictured in the link-coordinate diagram of Fig. 20.

2.3.2 Forward Kinematic

Transformation matrix from foot to shoulder is:

==

1000

010

0

0

1

1111

1111

10 d

S aC S

C aS C

T T shoulder foot

Transformation matrix from shoulder to elbow is:

32

21

31 T T T T

elbow shoulder

==

=

1000

01000

0

1000

001000

00

3333

3333

22

22

S aC S

C aS C

C S

S C

=

1000

0 3333

32323232

3232322

S aC S C S aC S S C S

C C aS S C C C

Transformation matrix from elbow to wrist:

==

1000

0100

0

0

4344

4444

43

S aC S

C aS C

T T wrist elbow

Transformation matrix from wrist to club head:


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65

54

64

lub T T T T head cwrist ==

=

1000

100

00

00

1000

0010

00

00

6

66

66

55

55

d

C S

S C

C S

S C

=

1000

0066

5656565

5656565

C S

C d C S S C S

S d S S C C C

Transformation matrix from foot to club head:

64

43

31

10

60

lub T T T T T T head c foot == ( ) ( )

=

10001333 x x P R

With

( )( ) ( )( ) ( )

+++

++++

=

345262634526263452

34513452162163451345216216345134521

34513452162163451345216216345134521

S S C C S C S S C C C S

C C S C S C S S S S C S C S S S C C S C S C S

C S S C C C S C S S S C C C S S C C S S C C C

R

is called rotation matrix.

( )( ) ( ) ( )( ) ( ) ( )

++++++++++++

=

1323342434526

11313213341342143451345216

11313213341342143451345216

d C S aC S aS S d

S aS C C C S aS C C C S aC C S C S d

C aS S C C C aS S C C C aC S S C C d

P

is called translation matrix.

In here, to simplify the notation, we have used notations:

jk kjC += cos and jk kjS += sin

jk iikjC ++= cos and jk iikjS ++= sin

2.3.3 Verify Forward Kinematic

This part will check the compatible of home position by comparing home position in Fig.20 and homes joint values shown in the last column in Table 6. From Table 6, home joint values

are

= 0,2

,0,,2

,0

q , which yields the transformation matrix from base (foot) to tool (club

head) at home position is:

( )

=

1000100

0001

010

home6431

1

lub

d aad

a

T head c foot


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Checking the orientation Fig. 20 reveals that this is consistent with the link-coordinate

diagram. The first column of matrix indicates that, in home position, x-axis of club head has

coordinate (0, 1, 0) with respect to base coordinate (foot). This mean that x-axis of club head has

same orientation with y-axis of the base. We can clearly check it in Fig. 20. Same explanation is

applied for y-axis of club head. The last column which represents z-axis of club head hascoordinate (0, 0, -1) in the base frame. Thus z-axis of club head points in the opposite direction

of z-axis of the base frame.

Finally, the position vector P indicates that the coordinates of the origin of the club head

relative to the base frame are (a 1, 0, d 1-a3-a4-d6). Thus the position of club head is located a

distance a 1 in front of base and (d 1-a3-a4-d6) above the base. This is also consistent with Fig. 20.

2.4 Denavit-Hatenberg Representation Method

This section will briefly describe Denavit-Hatenberg representation method which is used

in my work. Denavit-Hatenberg is a systematic notation for assigning right-handed orthogonal

coordinate frames, one to each link in an open kinematic chain of links. Once these link-attached

coordinate frames are assigned, transformations between adjacent coordinate frames can then be

represented by a single standard 44 homogeneous coordinate transformation matrix.

Let Lk be the frame associated with link k , that is:

k k k k z y x L ,,= 0 k n

Coordinate frame Lk will be attached to the distal end of link k for 0 k n. This puts the

last coordinate frame, Ln, at the tool tip. The coordinate frames to the links using the following

procedure:

1. Number the joints from 1 to n starting with the base and ending with the tool yaw, pitch,

and roll, in that order

2. Assign a right-handed orthonormal coordinate frame L0 to the robot base, making surethat z 0 aligns with the axis of joint 1. Set k = 1 .

3. Align z k with the axis of joint k+1

4. Locate the origin of Lk at the intersection of the z k and z k-1 axes. If they do not intersect,

use the intersection of z k with a common normal between z k and z k-1.

5. Select xk to be orthogonal to both z k and z k-1. If z k and z k-1 are parallel, point xk away from

z k-1

.6. Select yk to form a right-handed orthogonal coordinate frame Lk .


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7. Set k = k + 1 . If k < n , go to step II; else, continue.

8. Set the origin of Ln at the tool tip. Align z n with the approach vector, yn with the sliding

vector, and xn with the normal vector of the tool. Set k = 1 .

9. Locate point bk at the intersection of the xk and z k-1 axes. If they do not intersect, use the

intersection of xk with a common normal between xk and z k-1.

10. Compute k as the angle of rotation from xk-1 to xk measured about z k-1.

11. Compute d k as the distance from the origin of the frame Lk-1 to point bk measured along

z k-1.

12. Compute ak as the distance from point bk to the origin of frame Lk measured along xk .

13. Compute k as the angle of rotation from z k-1 to z k measured about xk .

14. Set k = k + 1 . If k n, go to step VIII; else, stop.

By following above procedure, the values for kinematic parameters are determined. The

link-coordinate transformation from frame Lk-1 to Lk is:

[ ] [ ]k k k k qT q 11 =

Where: [ ] 1k q and [ ]k q are the homogeneous coordinates of point q with respect to frame

Lk-1 and Lk

k k T 1 is the transformation matrix. It is defined as:

=

1000

01 k k k

k k k k k k k

k k k k k k k

k k d C S

S aC S C C S

C aS S S C C

T

With shorthand notation ( ) xSx sin= and ( ) xCx cos= D-H representation method was used widely and proved to be effective in many serial

robot models. It is also the simplest method to find out ending-vector of a robot. Thus I use D-H

method to represent my model.

For more detail information about D-H representation method, see Ref. [45, 46].


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Chapter 3

PARAMETER IDENTIFICATION

In order to recognize body segment dimensions, the author proposes a method which

includes two steps. The first step is called identification step. This will help us to identify coarse

values or initial values link lengths. Whilst the second step, calibration step, tries to improve the

accuracy and gives us more exact results.

This chapter will describe identification step. There were two methods which have been

proposed and simulated. Every method has its advantages and disadvantages. A comparison will

be done to give a general view which helps us to choose suitable method.

Golfer body is represented by a 6-DOF robot model. Link length is considered as the

unknown segment dimension needs to be identified. In this study, a method is proposed using

only two touch points that is enough to identify the unknown link dimensions.

3.1 Gyro Sensors Attachment

Gyro sensors are attached to human body in order to obtain joint movements. Locations of

gyros are evaluated base on the motion of players while they swing or hit the ball. They are

chosen at some remarkable body landmarks. In this work, every gyro sensor can detect rotarymotion around one axis. Thus for six-DOF model, six gyros are employed.

Figure 21: Gyro 1 And 4 Attachment Positions

Gyros number one and four locations are shown in Fig. 21. Gyro ones axis is adjusted to

be vertical orientation in order to measure waist motion, whilst gyro fours axis measure elbow

rotary motion and is set parallel to Z 3 axis (see Fig. 20).


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Gyros number two and three are set up at left elbow for right-handed people and vise versa

in order to recognize two DOFs of shoulder movements. Axis of gyro two and three are

respectively X 1 and Z 1 axis (see Fig. 20). Their graphical descriptions are drawn out in Fig. 22.

Figure 22: Gyro 2 And 3 Attachment Positions

Gyros number five and six are used to identify two DOFs of writs movement and attached

at the golf club, near to the club head. Gyro fives axis is set parallel to club and gyro sixs axis is

parallel to Z 4 axis of six-DOFs model (see Fig. 20).

3.2 First Identification Method

Figure 23: Procedure of First Method

In this first method, players are asked to touch 2 points I1 and I2 freely. It means that they

can touch those points at free movements of body. This is convenient for them. Although we can

ask the player to touch more than two points, this is only the first step which allows us to get


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coarse values of link lengths. Thus I choose only two touched points.

Fig. 23 shows the procedure of this first method. When the players touch two points I1 and

I2, data are extracted from gyro sensors. Forward kinematic from six-DOF model and initial

guest link lengths are combined with joint angle movement to generate set of cost functions.

Solving these functions will give us results which are coarse values of link lengths.

The simulation of this method includes two steps:

First, simulate the real body

Second, follow procedure in Fig. 23 and solve the set of cost functions to identify

coarse body parameters

3.2.1 Simulation Real BodyThe purpose of this section is to find out joint movements with respect to every touched

point. This is a kind of numerical inverse kinematic. Inputs are the touched point positions,

starting positions, assumed exact link lengths.

In this simulation, it is clear that only first five DOFs influence ending position. While the

sixth DOF only generates the ending orientations, thus it is not included and is set to zero.

Outputs are first five joint movements 1 , 2 , 3 , 4 , 5.

Figure

kinematic modeling and calibration of a human body

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