Scheme Choice and Inverse Kinematics of a Positioning System Based on a Planar Parallel Mechanism

Recent development of the parallel mechanisms theory has resulted in an increase of the actual machines, which are built using the conceptual schemes of such mechanisms. The advantages of parallel kinematics over conventional open-chain design, such as increased stiffness or lower inertia of moving parts, allow, in theory, higher performance rates in pick-and-place or machining applications. However, the practical usage of parallel mechanisms may be problematic due to their drawbacks, such as restricted workspace area and presence of singularities.The paper discusses a modification of the milling machine “Tetra” developed in “Modular Mechanics”, ltd. (BMSTU), which consists of two identical modules based on planar parallel kinematics mechanism. The loss of module stiffness in certain positions of the end-effector was noticed after experiments on the prototype, thus indicating the presence of singularities. Since this problem is a manifestation of fundamental properties of the chosen kinematic scheme, it was decided to change it.A scheme with three linear rails and three drives, as well as a scheme with a single rail and with four drives were considered as alternative options. The first option was discarded because it requires manufacturing a massive base plate. The second option was selected for future development. In this case, as compared to the previously known design, a configuration of the intermediate links was changed. The use of “lambda”-shaped elements makes it possible to distance the drive supports from the end-effector.For a chosen scheme an inverse kinematics problem was solved. Using constraints associated with the placement of all four drive supports on a single rail and stiffness requirements as well, a one single solution was selected among sixteen possible solutions.The further investigation will include a workspace and singularity analysis and an optimization of geometric parameters of the mechanism.