design and control system of parallel kinematic manipulator
TRANSCRIPT
Design and Control System of Parallel Kinematic Manipulator
Tadeusz Mikolajczyk1,a, Dariusz Dorsz1,b, Lukasz Romanowski1,c University of Technology and Life Sciences, Bydgoszcz, Poland
[email protected], [email protected], [email protected]
Keywords: parallel kinematics, manipulator, step motor, control system
Abstract. This paper presents parallel kinematic manipulator design. A manipulator with three axis and parallelogram mechanism was made using aluminium profile rods. This mechanism was controlled by PC with the use of stepper motors. Kinematics analysis was conducted and its findings were used to make a special software to generate G-code control file. X and y mouse cursor indications with given z value were used as data showing the position of the effector to establish the movement of the arms of the presented manipulator. Step2CNC software was used to control the manipulator. Tests have confirmed the correctness of the study.
Introduction A parallel manipulator is a closed-loop mechanism in which a mobile platform is connected to a
base by many parallel serial kinematics chains [1-6]. It has high structural rigidity, high positioning capability, high accuracy and high strength-to-weight ratio. However, the design of the planned trajectory and the development of the usage of parallel robots are challenging due to the closed-loop nature of the mechanism. This mechanism is in many cases more accurate than a serial manipulator with the same number of degrees of freedom (DOF)[1].
The kinematics manipulator structure is described by the kinematics token entry [5]: P - prismatic joint, Pa – parallelogram, R - revolute joint, S - ball-and-socket joint.
The modular concept is emerging to address such issues [2,3]. A reconfigurable parallel robot consists of a set of independently designed modules, such as actuators, passive joints, rigid links (connectors), mobile platforms and end-effectors that can be rapidly assembled into various configurations with different kinematics characteristics and dynamic behaviors.
There are planar and spatial robotics manipulators in use [4,5]. A characteristic feature of the flat parallel manipulators is the mobility of the effector in only one
plane. The spatial parallel manipulators have three rotational degrees of freedom from a work platform. They include three kinematics chains the connection of the output with the base, wherein each of these chains has got one swivel or sliding joint [4,5]. Depending on the structure and the number of DOF there are two groups of manipulators: based on the platform and having usually six DOF using the properties of parallelograms, and with a reduced number of DOF. There are also manipulators who use both features and are difficult to qualify for any of the groups. They contain additional kinematics elements on the working platform. They are called hybrid manipulators [4]. Often compared to parallel manipulators uses terminology associated with the number of DOF such as: Tripod (3 DOF) (Fig. 1) and Hexapod (6 DOF) [4,5]. The control is done by changing the location of the ends of the arms or by changing their length.
Parallel manipulators are used as: Parallel-type multi-axis machining tools, Platform for pilot training simulators, Sanding, the precise machining of materials,
Precise assembly tools, Water, laser, plasma cutting, Large size machine tools for the production of moulds and dies, Manipulating very small objects, Positioning devices for high precision surgical tools.
Fig. 1. The main concepts of structure manipulator tripod type: a) vertical moved base, b) horizontal moved base, c) variable length of arms,
d) rotary base (delta type manipulator) The paper presents a design the manipulator of parallel kinematics, a tripod type, implemented in
the Department of Production Engineering of the University of Technology and Life Sciences from Bydgoszcz (Poland).
Theoretical analysis of tripod The chosen concept (Fig. 1 b) was analysed theoretically. In order to formulate mathematical relationships necessary to develop machine control algorithm
it is required to solve the problem of inverse kinematics. Built device consists of three identical pairs of arms I, II and III. Each of these forms a
kinematics chain, where one end is linked to the spindle platform and the other end with the moving trolley placed on the body. Changing the position of one of the three trolleys has a direct impact on the position of the effector of the spindle.
The formulation of the geometrical relationships resulting from the mechanical structure will serve an explanatory drawing of one of the arms of the marked characteristic dimensions. An explanatory drawing of one of the arms with marked characteristic dimensions will be used to formulate the geometrical relationships resulting from the mechanical structure. Figure 2 shows a coordinate system of the axes linear motors. Points P1, P2 and P3 are the places where the arms are attached to the trolleys. The location of these points is closely dependent on the eject R. Diagram of one of the arms of the device is shown in Figure 3. Letter L is the length of the tendon. Point P is the location of the effector in the xyz coordinate system and is highly dependent on P1. Line K is the projection of the arm length L on the plane. In order to control the machine tool, it is required to determine the value of R, which is the length of the linear drives ejected depending on the position of point P in the xyz space.
Fig. 2. Top view of Tripod workspace Fig. 3. Side view of Tripod arm The general equation determining the position of a point P in the equation is:
222 Kzl (1) Section K is the distance between point P1 and P. The equation for the length of the section K is described by the formula:
22 )()( pp yyxxK (2)
After substituting equations 1 and 2 the below was obtained for I arm: 2
122 )( Ryxzl
(3) Equation 3 describes the length of the arm depending on the position of the effector in the xyz space. In order to control the manipulator, R value must be known, therefore the equation 3 is converted to the form below:
yzxlR 2221 (4)
The resulting equation (4) describes the distance of hanging carriage which is attached to the frame number 1. The amount of travel/distance depends heavily on the global coordinates xyz.
Based on the mathematical formula, for the II arm the below was received:
22
22
2 )21()
23( RyRxzl
(5)
233
21
41
43 2222
2xyxyxyzlR
(6)
Based on the mathematical derivation for the III arm:
23
23
2 )21()
23( RyRxzl
(7)
233
21
41
43 2222
3xyxyxyzlR
(8)
The above equations are used to calculate the value of R1, R2 and R3. They allow planning of the parallel manipulator’s platform’s trajectory. The picture is simplified, since it does not take into account the lack of the central point of the effector’s connection arms. This is not required for the purposes of this study. Graphs were created for the sample of the effector movements based on the developed relationships ((4), (6), (8)). Examples of graphs are shown in Figures 4-5.
Fig. 4. Characteristics of linear carriage movement for effector displacement along the x axis for
z=350 mm, L=400
Fig. 5. Characteristics of linear carriage movement for effector displacement along a line inclined
by 45o to the x, y and z axis, L=400 The observed phenomenon of non-linearity (Fig. 4-5) is very unfavourable, since the effect on
spindle positioning accuracy in Cartesian coordinates. The presented results is irregular and depends on the position of the effector in the space (Fig. 4-5). All this makes it difficult to create software generating G-code capable to compensate the nonlinear effect occurring during machine operation without a thorough analysis. The kinematics of the developed solution provides a workspace as shown in Figure 6.
Fig. 6. Effector workspace: b) spatial visualization, a,c) flat sections selected levels of workspace
Design of parallel manipulator The construction of a parallel kinematics manipulator decided to implement using commercially
available components of the drive control and the possibility of building the mechanical parts of the structure. It was decided to use commercially available components for building mechanical parts of the structure and the drive control. The construction of the prototype also includes implementing the options available.
The developed concept was implemented using 50x50 structural aluminum elements as the legs of the manipulator. The horizontal arms are made of structure 100x50 mm connected together in a
b) a) c)
central point using a special made element. Prototype was built using a ball-bearing linear guides (Fig. 7) attached to the arms. Guides combined with linear carriage cooperate with TR10 screws supported by two bearings (Fig. 8). Stepper motor controlling the manipulator was attached to the end of the rails. Their axes were connected with the screws using flexible coupling. The structure of parallel mechanism was made using 6 aluminum links connected with ball couplings. Linkages were coupled, the upper ends were attached to carriages, lower to moveable platform in which mini grinder was installed (Fig. 9). Aluminum links are connected in pairs with the sliders on one side and on the other side with the mobile platform. The entire parallel mechanism is shown on the figure 10.
Fig. 7. Ball-bearing guides
Fig. 8. View of one tripods axis Fig. 9. View of effector with minigridder
Fig. 10. View of Tripod
Control system of manipulator The manipulator is equipped with a motor control circuit consisting of a motherboard drivers
(Fig. 11) combined with stepper motors interfaces (Fig. 12). Posted unipolar motors 23HP-K245-P1V (torque - 0.5 Nm, supply voltage - 2.5 V, current - 1.9 A, step - by 1.8o, the number of pin-6.
Fig. 11. Main board of controller Fig. 12. Stepper motor interface
Presented interface was connected to the Dell GX620 computer (3.2 GHz, 512MB RAM, 40GB HDD, integrated grafics card, 8 USB port, COM port). The advantage of this system is to provide a convenient parallel port to control the stepper motors. This computer is equipped with a 15” touch screen with a resolution of 1064x768 pixels. This provided good control of presented manipulator by computer with control system without using a keyboard and mouse.
The control system is based on the use of G-code. In order to generate a control code in the VB6 environment special CAM software was developed. VB6 is a good environment for developing a special software for CAM systems and machine control [7-9]. Main panel made software TripodG is presented in Figure 13. In order to administer the parameters of the effector motions reading of the mouse pointer in the xy plane is used, the value of z parameter is established by using a special slider located on the screen. Read coordinates of the effector in space were converted using special procedures developed with dependencies (4), (6), (8) with algorithm presented in figure 14. This values was used to made G code commands for control control the manipulator arm (Fig. 14). The division of the labor movement into smaller sections was used in order to ensure the accuracy of the traffic conditions. The resulting control programs are saved in a cnc file.
Fig. 13. View of main panel of TripodG software
monitor of mouse cursor
x, y trajectory R1, R2, R3 code
view of parameters
Fig. 14. Algorithm of procedure for generate of G-code parameter for moving of arm
To control the manipulator and its stepper motors using G-code was used Step2CNC software [10] (Fig. 15). This is equivalent to more known programs Mach 3 or EMC2 [11,12].
The program code developed takes into account developed relations (4), (6), (8) an example shown on graph, figures 4 and 5. Satisfactory precision in the effector movements was achieved by dividing the movements into smaller sections and the development of sub-G codes for carriage movements. With using touch screen was possible too manual control of Tripod but only directly by control I, II, III arms.
-
Fig. 15. View of main panel of Step2CNC control software
Tripod Data K,L
Optional parameter
Choose z value
Indicate x,y values
Calcultion of R1, R2, R3 values
Make G-code Add G-code line to list
End No
Save G-code Yes
Stop
Start
Manual control of I, II, III arms
G-Code panel
Conclusions Parallel kinematics manipulators are rapidly growing group of machines with versatile use. The
concept of parallel drive makes it possible to build such manipulators with various structures and multiple DOF.
This paper presents the design of manipulator, with parallel kinematics, of type of tripod. It was presented that it is possible to create a good design of manipulator with three axis and parallelogram mechanism using aluminum profile and other cheap components. The ability to control this mechanism using step motors and PC has also been proven. The results of conducted kinematic analysis were used to build special type CAM software generating G-code control file. The concept of using the software using indication by mouse x,y cursor position with given z value was a good idea for data acquisition.
Optimization of step G-code file is required in the future next studies. The use of Step2CNC software to control the manipulator arm efficiently and it also confirmed the correctness of the study. The aim would be to create a special control software for that type of a mechatronics tool [13] with control of step motors rotation.
References
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[11] http://www.machsupport.com/
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