Mobility criteria of compliant mechanisms based on decomposition of compliance matrices

• A general procedure for determining the mobility for any compliant mechanisms.
• Using the eigentwist and eigenwrench decomposition of compliance matrix.
• Introducing the characteristic length and two properties of six eigencompliances.
• Two guidelines for choosing the characteristic length.
• Two mobility criteria for any spatial compliant mechanisms.

Mobility analysis is an important task in the conceptual design stage of kinematic mechanisms. Not like in rigid body mechanisms, identifying the mobility of compliant mechanisms is particularly challenging as their motion is determined by both kinematic pairs and deformable compliant joints. In this paper, we investigate the use of the eigentwist and eigenwrench decomposition of compliance matrices to identify the mobility of spatial compliant mechanisms. We first prove that the eigencompliances are invariant to the coordinate transformation. We then introduce the characteristic length to scale the eigencompliances and compliance matrices to compare translational compliances with rotational ones. We propose two mobility criteria for the compliance matrix of any given compliant mechanism. We have also proposed two guidelines for choosing the characteristic length for serial open chains and closed loop mechanisms respectively. The robustness of the chosen characteristic length is discussed. A general procedure for determining the mobility for any compliant mechanism is presented. Finally, one case study is provided to verify our method.