Second order mobility analysis of mechanisms using closure equations

An overview of formulae for the higher-order kinematics of lower-pair chains with applications in robotics and mechanism theory

“…The equation (14) for the acceleration was presented in [98]. A version of the relation (15) for the jerk was reported in [99,39,40].…”

“…of the twist V i . The advantage of this recursive form is that it is easy to implement and accounts for arbitrary derivatives, in contrast to explicit relations, such as (14) and (15). The complexity indeed remains O i k+1 .…”

“…These are recursive relations for the kth time derivative of V s i in terms of derivatives of twists of preceding bodies up to order k − 1 and the time derivatives of q (t), so that the nested summations in (14) and (15) etc. are avoided.…”

“…To this end, loop constraints expressed by the POE were first explored in [50,51] and lead to significant contributions to the higher-order mobility analysis of general linkages [14,65,80,87,99]. The central elements of any such method are the higher-order time derivatives of the loop closure constraints.…”