Computational Kinematic Analysis of Higher Pairs with Multiple Contacts

We present a computational kinematic theory of higher pairs with multiple contacts, including simultaneous contacts, intermittent contacts, and changing contacts. The theory systematizes single- and multiple-contact kinematic analysis by mapping it into geometric computation in configuration space. It derives the contact conditions, contact functions, and relations between contacts from the shapes and degrees of freedom of the parts. It helps identify common design flaws, such as undercutting, interference, and jamming, that cannot be systematically identified with current methods. We describe a program for the most common pairs: planar higher pairs with two degrees of freedom.