Singular configurations analyses of the modifiable Theo Jansen-like mechanism by focusing on the Jacobian determinant — A finding limitations to exceed normal joint range of motion

Adaptive locomotion is an important topic for the design of mobile robots, and smooth leg movement is of interest for investigating an indicator of how much bio-inspired robot represents the essential mechanism in animal walking. Using the multibody dynamics approach, we have investigated a potential extension of the Theo Jansen mechanism, an eleven-bar linkage that generates the locomotion pattern of multi-legged animals. Our extension highlighted a flexibility of the mechanism's trajectory, but an unclear limitation beyond normal joint range of motion was found. In this study, we examined the theoretical limitation of joint range of motion by singular configuration analysis. Multibody dynamics provide the Jacobian matrix to represent whole kinetics with constraints from close linkages and enables a singularity from the Jacobian determinant to be found. The method of finding a singularity in the mechanism may help to understand spatio-temporal properties of the control parameter, thus generating various stable motions toward mobility in an uneven ground.