On certain aspects of the zero reference position method and its applications to an industrial manipulator

Abstract

The zero reference position method, proposed by Gupta in 1981, is based upon an arbitrary choice of the zero reference position, the principle of displacement similarity, and the hand-tothe-base sequence of changing the joint variables in a serial manipulator. Its applications in performing recursive computations, formulating explicit governing equations, and obtaining closed form solutions for serial manipulators are presented in this paper. A Bendix-type of industrial robot is used for illustrating the closed form solution procedure.

A numerical algorithm for solving robot inverse kinematics

“…The basis of the Zero Reference Position Method is the principle of the displacement similarity. 3 "" 6 According to this principle, when a joint axis 'a' is displaced to 'b', the displacements with identical parameters (6, s) with respect to these axes are related by the formula…”

“…In equation (6), the /th column represents a typical column when the /th joint is a revolute joint; g,P is a vector from point Q, on the /th joint (on the link i + 1) to point P on the end-effector. The /th column represents a typical column when the /th joint is a prismatic joint.…”

“…CPU time for e = 10~7 increased suddenly. A probable reason for this sudden increase is that a step cutting at an earlier point of the trajectory could not be doubled up later; on the other hand, a higher step size level was reached for e = 10- 6 or e = 10~8.…”