An algebraic parameterization approach for parallel robots analysis

Abstract In the field of robotic assisted rehabilitation, some parallel mechanisms guide the anatomic limb using a kinematic chain (similar to an exoskeleton), thus, the motion of the moving platform serve no benefit in controlling the rehabilitation exercise. However, the dependency between the active joints of the robot and some intrinsic motion parameters (correlated with the anatomic joints) is required. The authors propose a new algebraic parameterization method based on Study parameters of SE(3), which achieves a direct mathematical description between the desired motion parameters of parallel mechanisms. The moving platform coordinates are eliminated from the constraint equations together with unwanted motion parameters (usually free motion parameters). The approach is first demonstrated on a generic mechanism and thereafter, in a case study, where the constraint equations are derived for a parallel robot (RAISE- designed for lower limb rehabilitation) by eliminating the free motion parameters and obtaining simple input/output equations relating the motion of the active joints of the robot with the motion of the hip and knee joints. The forward and inverse kinematics are presented with numerical examples. The singularities and workspace are also determined for the RAISE parallel robot, showing the particularities and advantages of the proposed approach.