Self-motions of pentapods with linear platform
This work addresses a specific problem in kinematics and robotics, providing incremental advancements by re-examining and updating old results from historical figures like Darboux and Bricard.
The paper tackles the classification of pentapods with linear platforms that have self-motions beyond trivial rotations, resulting in a full classification and the design of such pentapods with simplified direct kinematics in terms of the number of real solutions.
We give a full classification of all pentapods with linear platform possessing a self-motion beside the trivial rotation about the platform. Recent research necessitates a contemporary and accurate re-examination of old results on this topic given by Darboux, Mannheim, Duporcq and Bricard, which also takes the coincidence of platform anchor points into account. For our study we use bond theory with respect to a novel kinematic mapping for pentapods with linear platform, beside the method of singular-invariant leg-rearrangements. Based on our results we design pentapods with linear platform, which have a simplified direct kinematics concerning their number of (real) solutions.