Chained Beam-Constraint-Model for Contact Modeling (CBCM-CT): Using Contact-Position as Undetermined Coefficient

Compliant mechanisms have attracted increasing attention due to their inherent advantages over rigid mechanisms, including high repeatability, and reduced wear and backlash. They often undergo large and nonlinear deflections, which makes modeling their kinetostatic performances very challenging, especially when there is contact with the object they interact with. In this work, a general method for modeling compliant mechanisms involving contact based on the chained beam-constraint-model (CBCM-CT) is proposed. CBCM-CT treats the position of the contact point on a flexible beam as an undetermined coefficient, from which the beam is divided into two segments, each of which is formulated by an independent CBCM. By applying appropriate geometric constraints at the contact point on the CBCM equations, a well-posed system of equations of CBCM-CT is established. The feasibility and robustness of CBCM-CT are demonstrated through comprehensive comparisons with finite element simulations and experimental measurements across several contact scenarios, including a general large-deflection flexible beam in contact with a rigid object, with or without a limit block, as well as its application to an adaptive fin-ray-inspired robotic finger.