User manipulation of assembly models can provide insight during the early, formulative design stages into kinematic and dynamic characteristics of a mechanism. We present the advantages of kinematic representation of constraint equations in fully Cartesian coordinates, a departure from standard practice for interactive mechanical assembly at interactive rates.

Formulations of a surface rolling contact constraint equation and its Jacobian, defined as a joint between two NURBS surfaces via position, tangency and velocity constraint relations, are derived for use in dynamic simulation and assembly optimization. The constraint equation formulations use quaternions to represent orientation. An appendix develops appropriate differential algebra.

In this work we develop the use of constraints in global frame Cartesian coordinates for describing operator-in-the-loop interactions with mechanical assemblies under a unified framework combining lower-pair joints and more general surface contact interactions.

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