Algebraic models based on trigonometric and Cramer's rules for computing inverse kinematics of robotic arm

Abstract

This study postulates applicable and high-performing solutions for the inverse kinematic (IK) problem of two-segmented robotic arm using algebraic models. The former section of models is acquired from the manipulation of trigonometric rules, specifically the sum and Pythagorean identities to solve the second joint angles. The latter part of models is drawn by exploiting a matrix mechanics called Cramer's rule for the results of first joint angle. For verification, the precision of solutions yielded are cross-checked with the manipulator's direct kinematics and tested with the statistical measure of minimum square error while tracking cubic Hermite spline, cubic Bezier, cubic B-spline, ellipse and circle curves. For validation, a spreadsheet-based IK application utilising built-in front-end capabilities including Visual Basic for applications, Math and Trig function library, name manager, data validation, ActiveX controls, and charts is developed to accommodate these models and simulate the feasible joint angles and orientations of robotic arm.