Kinematics of an n-Degree- of-Freedom Multi-Link Robotic System

Abstract

A kinematic model is developed for n-degree-of-freedom multi-link manipulator systems. An essential step in the de velopment is the formulation of modified Eulerian angles, to allow maximum flexibility in positioning each link. Using the modified Eulerian angle method the kinematics of a system can be solved by multiplying fewer transformation matrices than is required by existing methods, thus reducing the complexity of computation. By allowing for a maximum number of kinematic variables (three for position and three for orientation) for each link, the analysis can be pursued in a general form without preimposed constraints on the system. The resulting formulation can be used as a basis for off-line analysis and design of a multi-link system. The inverse kine matics problem is solved by minimizing an objectivefunction that quantifies the joint displacements. A 16-degree-of- freedom redundant system is presented as an illustrative problem. Our algorithm provides highly accurate numerical solutions. Also, using our method a PUMA 560 robot arm is analyzed, and theformulation is compared with that ob tained by the Denavit-Hartenberg method.