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The class of linear pentapods with a simple singularity variety is obtainedby imposing architectural restrictions on the design in such a way that themanipulators singularity variety is linear in orientation position variables.It turns out that such simplification leads to crucial computational advantageswhile maintaining the machines applications in some fundamental industrialtasks such as five axis milling and laser cutting. We assume that a pathbetween a given start and end pose of the end effector is known which issingularity free and within the manipulators workspace. An optimization processof the initial path is proposed in such a way that the parallel robot increasesits distance to the singularity loci while the motion is being smoothed. In ourcase the computation time of the optimization is improved as we are dealingwith pentapods having simple singularity varieties allowing a closed formsolution for the local exterma of the singularity distance function. Formallythis process is called variational path optimization which is the systematicoptimization of a path by manipulating its variations of energy and distance tothe obstacle which in this case is the singularity variety. In this processsome physical limits of the mechanical joints are also taken into account.

Variational Path Optimization of Linear Pentapods with a Simple Singularity Variety