Self-motions of Stewart–Gough platforms

We describe a large class of self-motions of Stewart–Gough type parallel manipulators. The spherical image of those motions is a planar curve of degree six in Euler parameters. All points of a cubic in the plane of the platform have spherical trajectories. As the equation of the motion is rather general and complex, it is in general not possible to parametrize it. To visualize trajectories of a space motion, we need parametric expressions of all trajectories. As this is not possible, it would be natural to use approximate parametrization and other methods of computer geometry.