Discrete Deformation Models for Real-Time Computation of Compliant Mechanisms

This paper presents the formulation of a reduced-order linear discrete–path approximation in state space and its solution as a function of path lengths for a 3D curvature-based beam model (CBM). Solutions to both forward and inverse problems are discussed; the former is essential for real-time deformed shape visualization whereas the latter is much needed for haptic force feedback. The method is illustrated with an application example where a 2D beam is characterized by a 6^th order CBM. Practical implementation shows that when external forces as system input are expressed in global coordinates, the CBM can be decoupled into two 2^nd order systems enabling parallel computing of the deformed shape and the orientation and moment, and effectively reducing the table size for storing the operating conditions. The proposed real-time computation method has been validated by verifying results against published experimental and MSM simulated data.