Combining C-space maps and Constraints

The figure below shows a three-dimensional four-bar linkage; the two pink triangular prisms are free to rotate about the axes of their bases, and their apexes are joined by the long green rectangular link.  The grey cube is an obstacle to movement.  The green cube and red tetrahedron are not part of the problem, but flag (red) when the point in the system's configuration space enters the prohibited region.

                       
 
 
 

                       

The constraints system represented by the linkage and the configuration-space map of the linkage and the grey cube were computed. The constraints system was then used to animate the linkage, following its path in configuration space.  This path ended when the right-hand pink triangle struck the grey cube, as at that point the configuration-space map turned from a safe region to a prohibited region. The system was programmed to bounce---reversing its direction of motion whenever an obstruction was found---and so the four-bar linkage then moved in the opposite direction.

Click here for an animation of this from svLis-m (the file is 1.2MB, so don't click there if you're on a slow-speed line...).