On Singlarity Of 3-DOF And 4-DOF Parallel Mechanisms

Parallel mechanism has been gradually used in the area of aeronautics, industrial robots and so on, because of the advantages of high structrual stiffness, high load- bearing capacity, and higher control precision. As it is used more and more, the problem that singular configurations has great effects on performances of parallel mechanisms such as the motion ability, forces, control and accuracy etc, has attracted the attention of the robotics researchers in the world. So in order to reduce and eliminate effects of singular configurations, improve performances of parallel mechanisms and promote praticalization and productization of parallel mechanism, it is indispensable that further research on singular configurations of parallel mechanisms. The author studies the singularities of valuable 3-DOF and 4-DOF parallel mechanisms, the main content is as follows:The singularities of five 3-DOF symmetric planar parallel manipulators ,which includes 3-RRR,3-RPR,3-PRR,3-PRP and 3-RRP, are analysed. Then adding an redundant drive on their chain, the singularities of RRR-2RRR,RPR-2RPR,PRR-2PRR,PRP-2PRP and RRP-2RRP are discussed and comparing redundant parallel manipulators with non-redundant parallel manipulators about the effect to the singular configurations.The singularity of the Tricept parallel mechanism is derived.The mechanism is discussed by three different actuator dispositions, which are on prismatic pair and two revolute pairs of the universal joint. The complete Jacobian matrix of three different situations are proposed by the scerws theory. Then the singular conditions of the parallel mechanism are analysed by the theory of Grassman line Gemmetry, and the characters of kinematics are identified in the singular configures. At last the prismatic actuator disposition of the Tricept are presented, the singular-trace equation, which is composed of three independent parametersθ₁ ,θ₂ and z ,is derived, and the singular surfaces ofθ₁-θ₂-z and x-y-z are drawn.4-DOF parallel mechanisms symmetric H4 are widely used at prensent, their singularities are analysed. Based on the character of their structures, two groups of common complete force Jacobian matrix are acquired, and their conditions of limb singularity, plate singularity and actuator singularity are proposed, all the possible configures of actuator singularity and their state of mechanism are indentified. Then a H4 mechanism's three different kinds of singular configures exemplified. In the end, I4R mechanism which is similar with H4 mechannism is discussed. Its inverse kinematics and direct kinematics are illustrated, the singluarity and the numerial example are proposed.