Reciprocity-based resolution of velocity degeneracies (singularities) for redundant manipulators

A methodology for determining the velocity-degenerate (singular) configurat ions of joint-redundant manipulators is presented. The developed methodolog y uses the properties of reciprocal screws to determine all degenerate conf igurations resulting in a single degree-of-freedom (DOF) motion loss. Six j oint screws ($(sub1),$(sub2),...,$(sub6)) are chosen to form one six-joint sub-group Jacobian, J(sub). Setting the determinant of Jsub to zero (\J(sub )\ = 0) allows all conditions (say n in total) that cause the six-joint sub -group to become velocity degenerate to be identified. Reciprocal screws, W -recip1,W-recip2,...,W-recipn, can be found for each of the n velocity-dege neracy conditions. The reciprocal screw, W-recipi, is reciprocal to the six joints that comprise J(sub) when the ith J(sub) degeneracy condition is tr ue, but will not necessarily be reciprocal to the redundant joints $(r1), $ (r2),...,$(rk-6) (where k is the total number of joints and k > 6). Taking reciprocal products of W-recipi and each redundant joint $(r1),$(r2),...,$( rk-6) and setting the results to zero yields all additional conditions nece ssary for W-recipi to be simultaneously reciprocal to all of the redundant joints. This procedure is repeated for all of the reciprocal screws. The me thod identifies all unique sets of conditions that result in the redundant- manipulator joints $(sub1), $(sub2), ..., $(sub6), $(r1), $(r2), ..., $(rk- 6) becoming degenerate. A by-product of the methodology is that reciprocal screws for all degenerate configurations are derived. Examples are presente d to demonstrate the effectiveness of the methodology at determining the ve locity-degenerate configurations for joint-redundant manipulators. (C) 2001 Elsevier Science Ltd. All rights reserved.