Mobility Analysis and Type Synthesis with Screw Theory: From Rigid Body Linkages to Compliant Mechanisms

Mobility analysis is one of fundamental problems in kinematics and an important tool in type synthesis of linkages. In this paper, we will review screw theory as a mathematical tool for mobility analysis of overconstrained linkages and compliant mechanisms. Established by Ball in late 1800, screw theory has become one of the fundamental theories for characterizing instantaneous kinematics of spatial movements. In mid to late 1960, Waldron was one of the first modern kinematicians who systematically developed screw theory and its applications to the constraint analysis and synthesis of overconstrained linkages. Due to the screw theory, several overconstrained spatial linkages have been invented and designed, including the well known Waldron six-bar loop overconstrained linkage. In recent years, mobility analysis has been extended to compliant mechanisms which achieve motion through deflection of flexure joints. By the concept of relative compliance/ stiffness, we can also define mobility of compliant mechanisms similar to their rigid body counterparts. This paper will summarize some recent work on applying screw theory to mobility analysis and synthesis of compliant mechanisms.