DYNAMIC MODELLING OF A THREE DEGREE-OF-FREEDOM PLANAR PLATFORM-TYPE MANIPULATOR

摘要

In this paper, tlte dynamictttodelling of a planar threedegree-of-freeduttt platform-typettianipulator is presented. Akinematic analysis is carried outinitially to evaluate the initialcoordinates attd velocities. Thedynatiiic ttiodel of tlte tttatiipulator isformulated usitig a two-steptl.atisfvl-tttatic)n. Initially, thedyttarttic fortttulation is written inlet-tits of the Cartesian coordinatesof a dytiatiiically equivalent systrniof particles. Since there is ttorotational tttotion associated with aparticle, tlien the differentialequations of tttotion are derived byapplying Newton's second law tostudy the tratislatiotial tttolioti of theparticles. T11e cottstraittt forcesbetween the particles are expressedin terms of Lagrange multipliers.Then. the differential equations ofmotion are written itt terms of therelative joint variables. This leadsto ati efficieti t solution aridintegration of tlie equations oftttutiotl. A nutiterical esattiple ispresented and a cotttputet' progratttis developed.