Editing Industrial robot (section)

== Lower mobility parallel manipulators and concomitant motion ==
A full parallel manipulator can move an object with up to 6 [[Degrees of freedom (mechanics)|degrees of freedom]] (DoF), determined by 3 translation ''3T'' and 3 rotation ''3R'' coordinates for full ''3T3R m''obility. However, when a manipulation task requires less than 6 DoF, the use of lower mobility manipulators, with fewer than 6 DoF, may bring advantages in terms of simpler architecture, easier control, faster motion and lower cost.  For example, the 3 DoF Delta   robot has lower ''3T'' mobility and has proven to be very successful for rapid pick-and-place translational positioning applications. The workspace of lower mobility manipulators may be decomposed into 'motion' and 'constraint' subspaces. For example, 3 position coordinates constitute the motion subspace of the 3 DoF Delta robot and the 3 orientation coordinates are in the constraint subspace.  The motion subspace of lower mobility manipulators may be further decomposed into independent (desired) and dependent (concomitant) subspaces: consisting of 'concomitant' or 'parasitic' motion which is undesired motion of the manipulator.<ref>{{Cite book|last1=Nigatu|first1=Hassen|last2=Yihun|first2=Yimesker|title=Proceedings of the 2020 USCToMM Symposium on Mechanical Systems and Robotics |chapter=Algebraic Insight on the Concomitant Motion of 3RPS and 3PRS PKMS |date=2020|editor-last=Larochelle|editor-first=Pierre|editor2-last=McCarthy|editor2-first=J. Michael|chapter-url=https://hal.archives-ouvertes.fr/hal-03233161/file/Nigatu_Yihun___2020___Algebraic_Insight_on_the_Concomitant_Motion_of_3RPS_and_3PRS_PKMs.pdf|series=Mechanisms and Machine Science|volume=83 |language=en|location=Cham|publisher=Springer International Publishing|pages=242–252|doi=10.1007/978-3-030-43929-3_22|isbn=978-3-030-43929-3|s2cid=218789290 }}</ref>  The debilitating effects of concomitant motion should be mitigated or eliminated in the successful design of lower mobility manipulators.  For example, the Delta robot does not have parasitic motion since its end effector does not rotate.