Kinetostatic Synthesis of Coupled Serial Chains

yPro ceedings of DETC'981998 ASME Design Engineering Technical ConferencesSeptemb er 13-16, 1998, Atlanta, Georgia, USADETC98/MECH-5977KINETOSTATIC SYNTHESIS OF COUPLED SERIAL CHAINSVenkat KroviUniversityofPennsylvaniaGRASP Lab oratory,MEAMRo om 326C, 3401 Walnut StreetPhiladelphia, Pennsylvania 19104.E-mail: venkat@grip.cis.up enn.eduhttp://www.cis.up enn.edu/venkatG.K. Ananthasureshyof P, MEAMRo om 334CC, 3401 WE-mail: gksuresh@eniac.seas.up enn .eduhttp://www.seas.up enn.edu/gksureshVijay KumarRo om 301C, 3401 WE-mail: kumar@central.cis.up enn.edukumarABSTRACTSingle Degree-of-frdom Coupled Serial Chain(SDCSC)mechanisms areanovel class of mo dular and compact mechanismswith single degree-of-freedom actuation and control. In this pa-p er, the kinetostatic synthesis of SDCSC mechanisms is addressed.Using the principle of virtual work, the static force equilibriumequations are develop ed for two-link SDCSCs. These are combinedwith the previously develop ed kinematic lo op-closure equations tosolve the kinetostatic precision p ointsynthesis problem. Since theratios of the angular velo cities at the joints are constants by virtueof cable-pulley coupling in SDCSCs, it p ossible to render the kine-tostatic equations linear in terms of the mechanism parameters.As a result, the solution of the precision p ointsynthesis problem ofSDCSCs b ecomes simpler compared to that of the four-bar mech-anism. In order to meet additional criteria such as minimizingthe maximum torque required over the entire range of motion ofthe mechanism, an optimization problem is formulated. The freechoices in the precision p ointsynthesis are used as variables inthe optimal synthesis problem. The pap er also addresses how tor-sional springs at the joints can b e utilized to reduce the requiredinput torque in supp orting a sp eci ed load at the end-e ector.Numerical examples are presented to illustrate the precision p ointand the optimal synthesis of two-link SDCSC mechanism with andwithout torsional springs at the joints.NOMENCLATUREFxExternal force in theXdirectionFyExternal force in theYdirectionMzExternal applied moment at the end-e ectorR1Pulley ratio b etween the rst and second joint ro-tationsTIInput torqueZ0Complex numb er denoting the p osition vector ofthe base jointZ1Complex numb er denoting the p osition vector tothe second joint relative to the base jointZ2Complex numb er denoting the p osition vector tothe end-e ector relative to the second joint Input crank angleZP( )Complex numb er denoting the p osition vector ofthe the end-e ector as a function of the input crankangleAngular deection of thejjth springThe absolute angle of the joinjt where thejthspring is assembled( )Orientation of the end-e ector as a function of theinput crank angleOrienitation of theith link in the rst con guration1INTRODUCTIONIn applications where it is necessary to guide an ende ector through a desired tra jectory, the designer cancho ose either rob otic manipulators or closed-lo op mecha-nisms. While rob ots are very versatile and can b e clearlyused for such applications, the multiple degrees of freedomof the rob otic serial chains are often excessive and uneco-nomical for sp ecialized tasks. In such cases, single degree-of-freedom motion is adequate. While a closed-lo op mech-anism (e.g.the four-bar linkage) is a viable option, weconsider here an alternative con guration called theSingle1Copyrightc1998 by ASME