A new polynomial solution to the geometric design problem of spatial R-R robot manipulators using the Denavit and Hartenberg parameters

This paper presents a new method to solve the geometric design problem of s patial two degrees of freedom, open loop robot manipulators with revolute j oints that perform tasks, which require the positioning of the end-effector in three spatial locations. Tsai and Roth [3] solved this problem first us ing screw parameters to describe the kinematic topology of the R-R manipula tor and screw displacements to obtain the design equations. The new method which is developed in this paper; uses Denavit and Hartenberg parameters an d 4 x 4 homogeneous matrices to formulate and obtain the kinematic equation s. The loop-closure geometric equations provide eighteen design equations i n eighteen unknowns. Polynomial Elimination techniques are used to solve th ese equations and obtain the manipulator Denavit and Hartenberg parameters and the manipulator base and end-effec tor geometric parameters. A sixth or der polynomial is obtained in one of the design parameters. Only two of the six roots of the polynomial are real and they correspond to two different robot manipulators that can reach the desired end-effector, poses.