Joint clearance error analysis and simulation of a six-degree-of-freedom robot

Abstract: By analyzing the trajectory offset of a 6R robot, modeling and simulating the joint clearances, the actual trajectory offset was reproduced. The causes of the trajectory offset were identified, guiding improvements in the robot's structural design and enhancing its accuracy.

Keywords: robot; joint clearance; modeling; simulation

Abstract： Analsys the trace offset of the 6R robot,build the model of joint clearance,according to the simulation reappear the trace offset, get the result and then guide the structure reform, so get better performance.

Key words： Robot; joint clearance; model; simulation

1 System Introduction

The MR601 robot, independently developed and designed by Shenzhen Zhongweixing CNC Technology Co., Ltd., is a MINI type 6-DOF robot that integrates industrial and educational applications, as shown in Figure 1. The corresponding link coordinate system is shown in Figure 2.

The robot adopts an open control system based on a PC, as shown in Figure 3 below.

The control system software is developed using VC6.0 and has functions for point, spatial linear, and spatial curved motion. It can realize joint coordinate programming and spatial rectangular coordinate programming, and convert between spatial rectangular coordinates and joint coordinates.

2. Trajectory Experiment

Now, let the robot draw a square to verify its overall performance.

A black oil-based pen is fixed to the end of the robot, and a white tile with gray stripes is placed on the work platform, as shown in Figure 4 below, so that the robot can draw on it.

The robot's end effector posture is represented using ZYZ Euler angles, with the unit being degrees; the coordinate unit is millimeters. The coordinates of the robot's end effector in Cartesian coordinate space are set as follows:

First point: coordinates (350, 0, 5), attitude (0, 180, 0);

Second point: coordinates (450, 0, 5), attitude (0, 180, 0);

Third point: Coordinates (450, 100, 5), attitude (0, 180, 0);

Fourth point: Coordinates (350, 100, 5), attitude (0, 180, 0);

Fifth point: Coordinates (350, 0, 5), orientation (0, 180, 0);

The first point coincides with the fifth point to ensure that a closed square is drawn.

The Cartesian coordinates are converted to joint space coordinates. The robot then draws a square based on the generated joint coordinates. The positions of each point and the drawing result are shown in Figure 5 below.

The results show that the trajectory drawn by the robot is a parallelogram, which has the following problems:

(1) Point 1 is offset from the actual point by 2mm;

(2) The angle between sides 12 and 34 and the desired trajectory is 2 degrees;

(3) Edges 23 and 41 are approximately 1 degree off from the desired trajectory;

(4) The trajectory lines are uneven.

3. Error Analysis

The structural design and assembly of a robot have a significant impact on its overall performance. After checking the program and electrical components, the cause of the error was identified in the structural components.

The robot's first joint motor is mounted on the base, and the remaining five joint motors are mounted in the same direction, as shown in the negative X0 direction of the coordinate system X0Y0Z0 in Figure 2, where the weight is concentrated.

By manually shaking each joint, a joint gap was found in the second joint (see Figure 2, coordinate system X2Y2Z2). This gap was mainly caused by the axial clearance of the bearing. It was initially determined that the robot's trajectory deviation was likely due to the gap in the second joint. The weight of the robot arm caused the arm to roll at a certain angle in the direction of the gap, that is, to rotate counterclockwise around the X0 axis by a small angle.

4. Modeling and Simulation

Now, a virtual joint is added, equivalent to the rolling motion of the robotic arm. The axis of the virtual joint is perpendicular to the axis of the second joint, and the relevant robot coordinate system shown in Figure 6 is established.

Where: Z0 is the origin of the base, coordinate system X2Y2Z2 is the coordinate system of the second joint of the robot, coordinate system XmYmZm is the added virtual joint coordinate system of the robot, and axis Zm is perpendicular to axis Z2 of joint 2.

The robot's spatial motion equations are established based on the coordinate system shown in Figure 6. Based on the offset angles of edges 12 and 34, it is assumed that the virtual joints rotate by 2 degrees and their state remains unchanged during motion. A MATLAB dynamic simulation is performed, and the simulation results are shown in the figure below.

A comparison of the simulation diagram in Figure 7 and the actual trajectory diagram in Figure 5 shows that their trajectories are basically consistent. From the Z-axis error diagram in Figure 8, it can be seen that the mechanical clearance causes a change of nearly 0.1 mm in the Z-axis.

The simulation analysis results indicate that the trajectory deviation is mainly caused by the bearing clearance of the second joint.

From an intuitive perspective: (1) The joint gap causes the robot arm to roll within a certain range. The rolling angle remains unchanged. As the arm unfolds, the offset error increases continuously, resulting in the tilting of the edge line. (2) The Z-axis error causes the pen tip to move up and down, resulting in uneven line trajectories.

5. Postscript

This method treats the joint gap as an equivalent virtual joint that rotates by a certain angle, and obtains the quantitative error of the joint gap on the robot's accuracy while performing qualitative analysis.

The inverse kinematics of the robot is solved based on the established error equation, and some joint trajectories have complex solutions. This indicates that the algorithm's compensation for this error is very limited, and the overall mechanical structure of the robot is the key factor determining its accuracy.

Adjusting the bearing of the second joint resolved the trajectory offset problem, allowing for the creation of regular graphics.