A Numerical Approach for 3 PRS Parallel Manipulator

Arockia Selvakumar A

doi:10.14419/ijet.v7i4.10.20712

Abstract

This paper presents a numerical approach on kinematic analysis of 3-DOF parallel manipulator (PM). The proposed mechanisms constitute of PRS (Prismatic-Revolute-Spherical) parallel mechanism with two rotations and one translation. The forward and inverse kinematic equations of the PM are derived by position vector method. A total of 48 solutions are obtained for the forward kinematic equations using MATLAB.

Highlights

Based on the previous research, most of the parallel manipulators forward and inverse kinematics solutions are solved in closed form [1][2] and its solutions are compared by simulation results [3][4][5][6]
The kinematic design, architecture optimization and actuator layout angles of 3-PRS parallel manipulator are investigated based on the performance index and various simulation software packages are used to verify the results obtained [7][14][15]
Ghasem Abbasnejad et al explained the merits and demerits of the traditional numerical techniques to solve the kinematic equations and the results proved that that the homotopy continuation method performed better convergence to the forward kinematic problem with bad initial guesses compared to the Newton-Raphson method [8]

Summary

Introduction

Based on the previous research, most of the parallel manipulators forward and inverse kinematics solutions are solved in closed form [1][2] and its solutions are compared by simulation results [3][4][5][6]. A simulation and numerical analysis based on the kinematics of the PRS XY serial parallel manipulator is solved by using the steepest descent method and the motion trail of the tool tip based on the mobile platform kinematic solution is validated [9]. The kinematic analysis of 3-UPU I and 3-UPU II parallel kinematic machines with two rotations and one translation with the geometric constraints are solved by various analytic formulae and a simulation tool is used to verify the kinematic solutions [12]. Based on the position analysis of 5-DOF PM for various geometric topologies the output motion patterns are obtained and the translational and rotational tool motions relative to the system are defined by the Newton Raphson method [13]. First inverse and forward kinematics of the proposed PM are derived; second the various numerical results of the 3-PRS PMs are discussed in detail; concluding remarks are given

Inverse Kinematics

Results and Discussion

Conclusion