Application Value of Slider-Crank Mechanism in Pick-and-Place Operation of Delta Robot

By absorbing the advantages of the rotary-driven Delta robot and linear-driven Delta robot, a Delta robot for pick-and-place operation that forms a crank-slider at the drive joint is designed.To take the most common gate shaped curve in Cartesian space as the motion trail of robotic pick-and-place operation, according to the kinematics inverse solution theory of Delta robot, this thesis mainly solves the output angular velocity of robot-driven joint. Establishing the static transfer mathematical model and solving the forced condition of driving joint. The simulation analysis show that after the upper slider-crank mechanism is connected to the driving joint, the angular velocity of the driving joint changes suddenly, which caused a rigid impact on the robot in the picking and releasing operation, though the force of the driving joint can be made smaller.


Introduction
Delta robots have been proposed by Dr. CLAVEL since 1985 [1] and many prototypes for different purposes have been made. Most of these robot widely apply used in electronics, food, medicine and other fields with the advantages of high bearing capacity, high positioning accuracy, simple structure, easy to achieve high-speed movement, etc [2][3][4][5][6]. Many research works have been developed the Delta series of robots include: Pierrot team delvelop H4 I4, Heli4 and Par4 and so on [7][8][9] in which industrial acceleration reaches 12g and experimental acceleration reaches 20g of Par4. Adept company developed a four degree of freedom high-speed SCARA parallel robot based on the prototype [10] of Par4 robot. And the robot claims to be the fastest in the world. Huang Tian [11] simplified Delta mechanism as Planar mechanism Diamond and invented TJU-Delta manipulator.
At present, to further improve the accuracy, stability and stiffness of the high-speed, high-frequency and pick-and-place operation, the present ways cover two aspects [12][13]: reducing the inertia of moving parts by lightweight design, improving the dynamic performance index by scale integrated; reducing the deviation between the actual pose and the pose of the command using high speed and high precision control system. Improve the precision, stability and rigidity of Delta robot's high-speed, high-frequency and pick-and-place operation play an important role in the design stage and running process.
This article by absorbing the advantages of the rotary-driven Delta robot and linear-driven Delta robot [14][15], a Delta robot for pick-and-place operation that forms a crank-slider at the drive joint is designed.To take the most common gate shaped curve in Cartesian space as the motion trail of robotic pick-and-place operation, according to the kinematics inverse solution theory of Delta robot, this thesis mainly solves the output angular velocity of robot-driven joint, the output force and torque of robot-driven joint, the output linear displacement of the slider that linked at the drive joints. Finally, analyze the value of the Slider-Crank Mechanism used for Pick-and-Place Operation of Delta Robot.

Trajectory planning for pick-and-place
The pick-and-place operation consists of three parts, including vertical, horizontal and vertical, as shown in Fig.1. The robot's ending part moves from point A at the time of t = 0, completes the entire pick-and-place operation at point D, and divides the whole motion process from A to D into N parts according to time shown in equation (1) Sequence, which is analyzing the position coordinates, velocity and acceleration about the robot's ending part relative to the time variable t [16].  (2) ② When , the robot's ending part moves from point B to point C in the horizontal direction. At this time, the motion path height z remains unchanged, the position coordinates, velocity and acceleration about are as follows (3) ③ Finally, the robot's ending part moves from point C down to point D along the vertical axis to complete the entire pick-up process when . At this time, the position coordinates, velocity and acceleraion about are as follows (4) Through the above equations (2) ~ (4), you can ensure the position coordinates , speed , acceleration that are relative to the changing of t about the robot's ending part movement in the entire pick-up cycle.
The sketch diagram of Delta mechanism, as shown in Fig.2.

Figure 2. Sketch diagram of Delta mechanism
After solving the motion position of coordinate about the robot's ending part in the base, the angular velocity of the drive joint can be solved by using the Delta parallel mechanism inverse theory, as the following equation (5) ~ (8)
The angular displacement-time curves of Fig.3 to Fig.5 as the control are added to the robot drive joint. The angular velocity of the robot-driven joint can be solved as follows Fig.6 to Fig.8    The door-shaped curve as the trajectory of the Delta robot pick-and -place operation will give the drive joints to bring the rigid impact.
From Fig. 6 to Fig. 8, it can be seen that when the crank-slider mechanism is applied to the Delta robot pick-and-place operation, the angular velocities of the three driving joints suddenly change at 3.55s and 19.05s. Although the rigid impact under this working condition of the pick-and-place curve of the door-shaped has not been eliminated yet.

Forms a crank-slider at the drive joint
Assuming that the load of the moving platform in the Delta parallel robot pick-up operation is G, the force of the three branches on the moving platform is shown in Fig.9, the force of the fixed platform is shown in Fig.10. The force and the torque of the drive joints can be solved by using the Fig. 9 and Fig. 10, as the following equation (9) ~ (11). The force and the torque of the drive joints can be solved by using the Fig. 9 and Fig. 11, as the following equation (12) ~ (13).

The effect of crank-slider on the driving
① On the impact of the force on the drive joints ， ， . If is less than zero, the Delta robot that drive joints forms a crank-slider mechanism will have less force on the drive joint during the pick-and-place operation. ② On the impact of the output coupling torque of the joint Through the formulas (11) and (13) we can draw the conclusion: the Delta robot that drive joints forms a crank-slider mechanism will have smaller output torqut on the drive joint during the pick-and-place operation.
Coefficients Solving the linear displacement of the slider that linked at the drive joints, it facilitates use to linear robot and rotary motor to coordinated control the Delta robot that performs the pick-and-place operations.

Conclusion
By absorbing the advantages of the rotary-driven Delta robot and linear-driven Delta robot, a Delta robot for pick-and-place operation that forms a crank-slider at the drive joint is designed. To take the most common gate