Three-dimensional flexural-joint stiffness analysis of flexible manipulator arms

Abstract

SUMMARY This paper presents a complete derivation of the combined flexural-joint stiffness matrix and the elastic deformation field of flexible manipulator arms treated in a three-dimensional fashion. The stiffness properties are derived directly from the differential equations used in the engineering beam theory. The expressions developed here can readily be used in the modeling, control and design of light weight flexible robot manipulators. A two-link arm is used to formulate these expressions and the results can be generalized to n –link manipulators. The stiffness matrix for a robotic link element in 3-D is of the order of 12 X 12, and for an n –link robotic arm the total elemental and system stiffness matrices will be of the order of the (12 n X 12 n ) and 6( n + 1) X 6( n + 1), respectively.