In vertebrates, articulation is achieved at joints where a pair of smooth surfaces are in gliding contact within a synovial capsule. The paired surfaces comprise a system whose geometry constrains delimit the joint's range of movements. The biomechanical design of a given joint can be explored by creating a 3D model of the component surfaces and visualizing their relative movements from differing perspectives. Greater understanding comes from systematically varying the geometry of articular surfaces. To explore the space of geometrical designs, software for parameterically representing surfaces has been developed and integrated within a larger software framework for articulating skeletal systems.