Inverse Kinematics of General 4R2P, 3R3P, 4R1C, 2R2C, and 3C Serial Manipulators

Abstract This paper presents a solution to the inverse kinematics problem for 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators of general geometry. The method used to solve these is based on a technique recently presented by the authors for solving the inverse kinematics of general 6R and 5R1P manipulators. In the 6R and 5R1P cases, the method initially starts using 14 linearly independent equations where as for the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulator only 3, 6, 7 or 10 linearly independent equations are required, depending on the case. Through the use of a linearization and dialytic elimination method all 4R2P, 3R3P, 4R1C, 2R2C and 3C cases are reduced to equating to zero the determinant of a matrix whose elements are linear in the tangent of a half angle of a joint variable. The size of this matrix is (8 × 8) for all 4R2P manipulators, (2 × 2) for all 3R3P and 3C manipulators, (16 × 16) for 4R1C manipulators, (4 × 4) for RCRC and CRCR manipulators and (8 × 8) for the remaining 2R2C manipulators providing 8th, 2nd, 16th, 4th and 8th degree inverse kinematic polynomial respectively. Thus, the determinant equated to zero gives us the characteristic equation of the degree expected. The unique form of the matrix allows us to obtain the solution by solving an eigenvalue problem. Many variations of the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators are presented and the solution methodology is illustrated by several numerical examples.