CAD systems offer a variety of techniques for designing and rendering models of static 3D objects and even of mechanisms, but relatively few tools exist for interactively specifying arbitrary movements of rigid bodies through space. Such tools are essential, not only for artistic animation, but also, for planning and demonstrating assembly and disassembly procedure of manufactured products. A rigid body motion is a continuous mapping from the time domain to a set of positions. To relieve the designers from the burden of specifying this mapping in abstract mathematical terms, combinations of simple rigid motion primitives, such as linear translations or constant axis rotations, are often used. These simple motions are planar and thus ill-suited for approximating arbitrary motions in 3D-space. Instead, we propose the screw motion primitive, a special combination of linear translations and constant axis rotations, which has a simple geometric representation that can be automatically and unambiguously computed from the starting and ending positions of the moving body. Although, any two positions may be interpolated by an infinity of motions, we chose the screw motion for its relative generality and its computational advantages. The paper covers original algorithms for computing the screw motions from interpolated positions and envelopes of swept regions to predict collisions.