A Tabular Format for Computing Inverse Kinematic Equations for a 3DOF Robot Leg

Abstract

A method is presented for accurately computing the three servomechanism angles that place the leg tip of a 3DOF robot leg in cylindrical coordinate space, R, θ, Z. The method is characterized by (i) a multivariable integer power series for each degree of freedom that can be used to replace traditional trigonometrical functions, and, (ii) only integer numbers are used. A technique is shown that derives the coefficients, Ci j k, of each of the terms in the series that represents a servomechanism angle, S. This power series method has the advantage of; (i) satisfying accuracy requirements, (ii) producing a unique solution, (iii) high speed realtime computation, (iv) low memory requirement and (v) implementation into a generic algorithm or hardware such as a field programmable gate array. The series can represent many continuous kinematic systems just by changing the values of the coefficients. The coefficients are rapidly computed via a spreadsheet. The method can be extended to more than three degrees of freedom and also mapped into other coordinate frames such as a Cartesian or spherical.