| Abstract | Degrees of freedom in an assembly are realized by creating mating features that permit relativemotion between parts. In complex assemblies, interactions between individual degrees of freedom
may result in a behavior different from the intended behavior. In addition, current methods perform
assembly reasoning by approximating curved surfaces as piecewise linear surfaces. Therefore, it is
important to be able to: reason about assemblies using exact representations of curved surfaces;
verify global motion behavior of parts in the assembly; and create motion simulations of the
assembly by examination of the geometry. In this paper, we present a linear algebraic constraint
method to automatically construct the space of allowed instantaneous motions of an assembly from
the geometry of its constituent parts. Our work builds on previous work on linear contact
mechanics and on our previous work on curved surface contact mechanics. We enumerate the
conditions under which general curved surfaces can be represented using a finite number of
constraints linear in the instantaneous velocities. We compose such constraints to build a space of
allowed instantaneous velocities for the assembly. The space is then described as a set-theoretic
sum of contact-preserving and contact-breaking motion sub-spaces. Analysis of each subspace
provides feedback to the designer, which we demonstrate through the use of an example assembly –
a 4-part arm. Finally, the results of the analysis of a 4-bar linkage are compared to those from
mechanism theory.
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