Certified Solving and Synthesis on Modeling of the Kinematics. Problems of Gough-Type Parallel Manipulators with an Exact Algebraic Method

The significant advantages of parallel robots over serial manipulators are now well known. However, they still pose a serious challenge when considering their kinematics. This paper covers the state-of-the-art on modeling issues and certified solving of kinematics problems. Parallel manipulator architectures can be divided into two categories: planar and spatial. Firstly, the typical planar parallel manipulator contains three kinematics chains lying on one plane where the resulting end-effector displacements are restricted. The majority of these mechanisms fall into the category of the 3-RPR generic planar manipulator, [Gosselin 1994, Rolland 2006]. Secondly, the typical spatial parallel manipulator is an hexapod constituted by six kinematics chains and a sensor number corresponding to the actuator number, namely the 6-6 general manipulator, fig. 1.