Bond theory for pentapods and hexapods
This provides theoretical insights for mechanical engineers working on parallel manipulators, but it appears incremental as it builds on existing mobility analysis.
The paper tackles the classical problem of determining necessary conditions for overconstrained mobility in pentapods and hexapods, showing that mobility implies either collinearity of anchor points or a geometric condition on normal projections.
This paper deals with the old and classical problem of determining necessary conditions for the overconstrained mobility of some mechanical device. In particular, we show that the mobility of pentapods/hexapods implies either a collinearity condition on the anchor points, or a geometric condition on the normal projections of base and platform points. The method is based on a specific compactification of the group of direct isometries of $\mathbb{R}^3$.