a novel design of variable stiffness linkage with distributed leaf springs for robots

ICIEA 2013June 19-21, 2013

Xingming Wu, Zijian Zhao, Jianhua Wang*, Dong Xu, Weihai Chen

School of Automation Science and Electrical Engineering

Beihang University, Beijing, China

[email protected]

A Novel Design of Variable Stiffness Linkage with

Distributed Leaf Springs

ICIEA 2016June.5. 2016

A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs

2 Contents

Introduction1

Design of VSL 2

Stiffness Model of VSL3

Conclusions and Future Work4


3 Contents

IntroductionIntroduction1

Design of VSL 2




4 Introduction - Significance - Safety Assurance

Physical human-robot interaction inevitably occurs in applications such as service robots, wearable robots and rehabilitation robots


5 Introduction - Significance - Stability Improvement

Rigid joint can only transmit constant stiffness and may results in system vibration;While variable stiffness device have relatively flexible terminals that have adjustable stiffness. Variable stiffness device is often applied to damp out the undesirable vibration and ensure the dynamic stability.


6 Introduction - Significance - Energy Conservation

In addition, variable stiffness devices similar to muscles, are also beneficial to system energy efficiency. During the execution of the periodic motions, part of kinetic energy will be temporarily transformed and reserved as elastic potential one. Later, the energy will be turned back in the next cycle. As a consequence, in the long run, the whole system will reduce the energy consumption and improve the propulsive efficiency by a considerable amount.

Furthermore, it has been proved by many researchers that energy would be effectively saved by adjusting the nature frequency of the link to match the actual one during the specific motion, while the nature frequency is determined by the link’s inertia and stiffness

Nature Frequency

Motion Frequency


7 Introduction - Significance

Conclude the Significance

Safety Assurance Stability Improvement Energy Conservation


8 Introduction – Related Works Equilibrium-Controlled Stiffness

G. A. Pratt and M. M. Williamson, ‘‘Series elastic actuators,’’ in Proc. IEEE Int. Workshop on Intelligent Robots and Systems (IROS’95), Pittsburg, USA, 1995, pp. 399–406.


9 Introduction – Related Works Antagonistic-Controlled Stiffness


10

Introduction – Related Works Antagonistic-Controlled Stiffness

Migliore S, Brown E, DeWeerth S P. Biologically inspired joint stiffness control[C]// Robotics and Automation, 2005. ICRA 2005. Proceedings of the 2005 IEEE International Conference on. IEEE, 2005: 4508-4513.


11


Tonietti G, Schiavi R, Bicchi A. Design and control of a variable stiffness actuator for safe and fast physical human/robot interaction[C]//Robotics and Automation, 2005. ICRA 2005. Proceedings of the 2005 IEEE International Conference on. IEEE, 2005: 526-531.


12


(b)

(a) J. W. Hurst, J. Chestnutt, and A. Rizzi, ‘‘An actuator with mechanically adjustable series compliance,’’ Carnegie Mellon Univ., USA,CMU-RI-TR-04-24, Apr. 2004.

(b) Thorson I et al. Design considerations for a variable stiffness actuator in a robot that walks and runs[C]//Proceedings of the Robotics and Mechatronics Conference (RoboMec). 2007: 1-4.


13

Introduction – Related WorksStructure-Controlled Stiffness

Jafari A, et al. A novel actuator with adjustable stiffness (AwAS)[C]//(IROS 2010)

AwAS-II: A New Actuator with Adjustable Stiffness based on the Novel Principle of Adaptable Pivot point and Variable Lever ratio[C]// (ICRA 2011)


14

Introduction – Related Works


15 Introduction

Special Points in My Work However, products mentioned above are almost can only be used in actuated

joints but can hardly act as a middle link to make the stiffness of original segment adjustable.

In this paper, we introduce a novel variable stiffness linkage (VSL) with distributed leaf springs, which is designed in the conception of structure controlled stiffness to save the energy from holding the stiffness. In addition, as the position control part and the stiffness control part are designed separately, the position control part is optional according to the specific application occasions.


16 Contents

Introduction1

Design of VSL Design of VSL 2




17Design of VSL - Concept of VSL

Vertical Principle

The source power to adjust the stiffness should be vertical to the force generated by the elastic element.

Only then the extra energy to counteract the force from the elastic deformation could be saved.

Direction of the force from elastic deformation

Direction of the force to adjust the stiffness

(1)

(2)

(3)

(4)


18Design of VSL - Concept of VSL

Vertical Principle Structure Control Stiffness

The vertical principle is realized by applying screw-slider-linkage-slider mechanism


19

Design of VSL - Two Scheme for Selection

(a) Case of the spring set at the rim

(b) Case of the spring set at the middle of the joint

(c) Force distribution of the two cases


20

Design of VSL - Two Scheme for Selection

(a) Design of VSL (b) Mechanical realization of VSL


21Design of VSL


22Design of VSL


23 Contents

Introduction1

Design of VSL 2

Stiffness Model of VSLStiffness Model of VSL3



24Stiffness Model of VSL

The deflection of each leaf spring is given as :3

3FlwEI

3

12abI

0

sin wR l

03

3 ( )sin

EI R lF

l

Where E is the Young’s modulus of the leaf spring and I is the inertia moment of cross section relative to the neutral axis. If the leaf spring’s width is a and the thickness is b, I can be described as :

The relation between the bending leaf spring and the torsional joint is : Then the force applied to the leaf spring could be de-scribed by the effective length of the leaf spring (l) and the torsional angle (θ):

(3)

(2)

(1)

(a) Schematic of slider and leaf springs (b) measurement of slider and leaf spring model



Considering the little change of the direction of F and distributed three leaf springs in parallel, moment equation is approximated as:

Substitute formula (3) into formula (4), we can get the torque as the function of l and θ:

Torsional stiffness can be calculated by the formula so the torsional stiffness k is also the function of l and θ:

In practical application, the torsional angle θ would less than 10°, so considering approximation , torsional stiffness k could be formulated as:

03 ( )F R l

3 20

3

3 ( ) sin4

Eab R ll

K

3 20

3

3 ( ) sin4

Eab R lKl

3 20

3

3 ( )4

Eab R lK

l

3

3FlwEI

0

sin wR l

03

3 ( )sin

EI R lF

l

(1) (2) (3)

(4)

(5)

(6)

(7)



Table.1 Model parameters for the VSL Parameter unit value

E GPa 206 a mm 6 b mm 0.5 R0 mm 23 lmin mm 2.5 lmax mm 24.5 θmin ° 0 θmax ° 10

For the prototype of VSL, parameters of each components is measured as follows:



3 20

3

3 ( ) sin4

Eab R ll

(a) Torque for different effective length of the leaf spring (l) and the torsional angle (θ)

(b) Effect of effective length (l) on the torque for discrete values of the torsional angle (θ)

(c) Effect of torsional angle (θ) on the torque for discrete values of the effective length (l)

(a)

(b) (c)

(5) τ = f (θ , l)



Torsional stiffness (K) for different effective length (l).

3 20

3

3 ( )4

Eab R lKl

(7) τ = f (θ , l)


29 Contents

Introduction1

Design of VSL 2


ConclusionsConclusions4


30Conclusion

In this paper, a novel variable stiffness linkage (VSL) with distributed leaf springs is designed to help achieving safety assurance, stability improvement and energy conservation in robots and mechanical applications.

By using a screw-slider-linkage-slider mechanism and applying the symmetry conception, VSL could work stably and effectively. By building an effective stiffness model, VSL could be widely used in applications where stiffness is expected to be controlled.

From the simulation result, it verifies the effectiveness of the VSL that the stiffness could be effectively controlled with in the expected range from 18 N/m to more than 1000 N/m.

Conclusion


31 Contents

Introduction1

Design of VSL 2


Conclusions and Future WorkConclusions and Future Work4


32Conclusion and Future Work

In this paper, a novel variable stiffness linkage (VSL) with distributed leaf springs is designed to help achieving safety assurance, stability improvement and energy conservation in robots and mechanical applications.

By using a screw-slider-linkage-slider mechanism and applying the symmetry conception, VSL could work stably and effectively. By building an effective stiffness model, VSL could be widely used in applications where stiffness is expected to be controlled.

From the simulation result, it verifies the effectiveness of the VSL that the stiffness could be effectively controlled with in the expected range from 18 N/m to more than 1000 N/m.

Conclusion



Provide the variable stiffness joint to some specific.

Future Work

ICIEA 2013June 19-21, 2013

ICIEA 2016June.5. 2016

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