Geometric and kinematic analysis of a seven-bar three-fixed-pivoted compound-joint mechanism

This paper investigates a seven-bar three-fixed-pivoted compound-joint mechanism and presents a systematic classification based on the rotatability criterion of its various types evolved from the change of link parameters. By decomposing the mechanism into two closed loops that provide respectively position and orientation of the end-effector link, closed form kinematic equations are developed using two four-bar analytical equations in sequence for geometric analysis of the mechanism. The paper further derives the Jacobian matrices of the mechanism and presents its kinematic analysis. In the extended group of this mechanism, the paper investigates four typical mechanisms, examines their workspaces and singularity based on the Jacobian matrices and implements the condition number analysis to identify the isotropy distribution.