Research On Kinematic And Dynamic Performance Of3-PPR Planar Parallel Mechanism

Parallel mechanisms with few degree of freedom that have less than six degree offreedom not only have the advantages that characterized by all the parallel mechanisms, suchas compact structure, high speed, high accuracy, high load carrying capacity, low moment ofinertia, but also have the low manufacturing cost, easy control and other advanteges. Becauseof these advantages, parallel mechanisms with few degree of freedom attracted wide attentionfrom both industial and academic field.3-DOF parallel mechanisms with their advanteges intype design, control, cost etc. and their stauts as a special combination of planar and spatialmechanisms, become an important part of parallel mechanisms with few degree of freedom.In addtion, generally there is a process from planar (2D) to spatial (3D) in the study ofmechanisms, thus the research of planar3-DOF parallel mechanisms have earned extensiveattention.Currently, researchers had an in-depth study on the3-DOF parallel mechanisms withfull revolute joint (such as3-RRR) or only have a small amount revolute joint (such as3-RPR,3-RRP and3-PRR), but the research on3-DOF parallel mechanisms with multi-prismaticjoint are relatively insufficient. However, due to their special structure, this kind of3-DOFparallel mechanism is the supplement of the former ones, so they played a complementaryrole in planar3-DOF parallel mechanisms. Thus the kinematic and dynamic analysis of the3-DOF parallel mechanism which has only a small amount revolute joint is very necessary.Besides, friction between the joints is an inevitably exist factor in pratical engineering,however, in order to simplify the analysis, always ignore it to build an ideal model to carry onthe analysis in theoretical researchs. This is the difference with the engineering practice, soconsidering the friction in joints to analysis the3-DOF parallel mechanisms are really necessary. This paper selects3-PPR planar parallel mechanism as a research object to carrieson a series of studies about its kinematic and dynamic performance and simulatione.First, an analysis about the kinemtics property of3-PPR planar parallel mechanism iscarried on. The direct and inverse kinematic models accoding to the loop closure theory isestanblished, and the kinmatic simulation which shows that different type drive parameterschange has a significant impact on the displacement, velocity and acceleration of the movingplateform of3-PPR planar parallel mechanism is proceed. Then the workspace about thecenter of moving plateform of3-PPR planar parallel mechanism is gotten, the length of thelinks is the important factor to its workspace is found out. There is a scope of the drive linkslength, over the scope the workspace changed greaty. And the influence on workspace of thelength of middle links changes are more obvious.Second, the dynamic equation of the3-PPR planar parallel mechanism with Lagrangemethod is established. On the basis of kinematic model analysis and the kinematic parametersof the mass center of each part in the3-PPR planar parallel mechanism, to analysis itspotential energy and kinetic energy, obtained the dynamic model. The dynamic modelequation by using the fourth order Rung-Kutta method is solved, so as to acquire theapproximate numerical solution. The consequence indicates that to realize the movingplateform path a reasonable control of the drives is an important measure.Third, considering the influence of the friction, the dynamics of a3-PPR planar parallelmechanism was analyzed and simulated. In this paper, Kane equation of3-PPR planarparallel mechanism with the influence of friction is established, and3-D model of3-PPRplanar parallel mechanism is obtained by using ADAMS software. By means of the dynamicsimulation analysis on the3-PPR planar parallel mechanism, make clear that friction betweenjoints brings a significant effect on mechanisms’ driving force, also find out that frictionbetween prismatic joints significantly increase the driving force and its saltation, this isparticularty evident in the friction between prismatic joints of the middle links, while thefriction between recolute joints only have a certain impact on the numerical size of thedriving force of3-PPR planar parallel mechanism. The results illustrate the necessity of considering the influence of friction between joints in dynamics analysis about the planarparallel mechanism.