  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.
