Error Modeling and Accuracy of TAU Robot

Abstract

The TAU parallel configuration is rooted in a series of inventions and was masterminded by Torgny Brogardh [1][2][3][4]. The configuration of the robot simulates the shape of “τ ” like the name of the Delta after the “∇ ” shape configuration of another parallel robot. As shown in Fig. 1, the basic TAU configuration consists of 3 driving axes, 3 arms, 6 linkages, 12 joints and a moving (tool) plate. There are 6 chains connecting the main column to the end-effector in TAU configuration. The TAU robot is a typical 3/2/1 configuration. There are 3 parallel and identical links and another 2 parallel and identical links. Six chains will be used to derive all kinematic equations. Table 1 highlights the features of the TAU configuration. On the subject of D-H modeling, Tasi [5], Raghavan [6], Abderrahim and Whittaker[12] have applied the method and studied the limitations of various modeling methods. On the subject of forward kinematics, focus has been on finding closed form solutions based on various robotic configurations, and numerical solutions for difficult configurations of robots. It can be found in the work done by Dhingra [8], Shi [14], Didrit [16], Zhang [17], Nanua [18], Sreenivasan [19], Griffis and Duffy [20], Lin [21]. On the subject of error analysis, Wang and Masory [7], Gong [11], Patel and Ehmann [13] used forward solutions to obtain errors. Jacobian matrix was also used in obtaining errors. On the subject of the variation of parallel configurations, from the work done by Dhingra [9][ 10], Geng and Haynes [15], the influence of the configurations on the methods of finding closed form solutions can be found. In this paper, the D-H model is used to define the TAU robot, a complete set of parameters is included in the modeling process. Kinematic modeling and error modeling are established with all errors using Jacobian matrix method for the TAU robot. Meanwhile, a very effective Jacobian Approximation Method is introduced to calculate the forward kinematic problem instead of Newton-Raphson method. It denotes that a closed form solution can be obtained instead of a numerical solution. A full size Jacobian matrix is used in carrying out error analysis, error budget, and model parameter estimation and identification. Simulation results indicate that both Jacobian matrix and Jacobian Approximation Method are correct and have an accuracy of micron meters. ADAMS simulation results are used in verifying the established models.