The numerical Reuleaux method (NRM) is a geometrical-computational algorithm to determine the instantaneous rotation center (IRC) for a deformable or pseudo-rigid body (PRB) in arbitrary movement. In recent International Scientific Contributions/ Publications, the forward mathematical IRC problem (FP) was presented/determined for deformable solids, that is, given a defined arbitrary movement and random deformation, find the approximated IRC. We develop complementary simulations for this FP to corroborate its theoretical validation, and subsequently inverse methods are carried out. In other words, given an arbitrary rotation angle and a fixed IRC, find the optimal PRB deformation. Furthermore, given a desired IRC, determine both the optimal rotation angle and deformation parameters for a movement. Analytic and numerical methods are carried out for these objectives with appropriate nonlinear optimization software. Results are presented and compared to theoretical calculations with error data. Finally, some practical/simple realistic applications in dynamics/kinematics for deformable-structures in bioengineering and dynamics, in general, are explained for better understanding.

IRC, objective function (OF), nonlinear optimization, rigid body (RB), pseudo-rigid body (PRB), deformable solid (DS), Reuleaux segments (RS).