A new method of kinematic analysis and singularity analysis is proposed for a 7-DOF redundant manipulator with three consecutive parallel axes. First, the redundancy angle is described according to the self-motion characteristics of the manipulator, the position and orientation of the end-effector are separated, and the inverse kinematics of this manipulator is analyzed by geometric methods with the redundancy angle as a constraint. Then, the Jacobian matrix is established to derive the conditions for the kinematic singularities of the robotic arm by using the primitive matrix method and the block matrix method. Then, the kinematic singularities conditions in the joint space are mapped to the Cartesian space, and the singular configuration is described using the end poses and redundancy angles of the robotic arm, and a singularity avoidance method based on the redundancy angles and end pose is proposed. Finally, the correctness and feasibility of the inverse kinematics algorithm and the singularity avoidance method are verified by simulation examples.

This paper focuses on a 2R1T 3-UPU (U for universal joint and P for prismatic joint) parallel mechanism (PM) with two rotational and one translational (2R1T) degrees of freedom (DOFs) and the ability of multiple remote centers of motion (M-RCM). The singularity analysis based on the indexes of motion/force transmissibility and constraint shows that this PM has transmission singularity, constraint singularity, mixed singularity and limb singularity. To solve these singularproblems, the quantifiable redundancy transmission index (RTI) and the redundancy constraint index (RCI) are proposed for optimum seeking of redundant actuators for this PM. Then the appropriate redundant actuators are selected and the working scheme for redundant actuators near the corresponding singular configuration are given to help the PM go through the singularity.

Current research on spherical parallel mechanisms (SPMs) mainly focus on surgical robots, exoskeleton robots, entertainment equipment, and other fields. However, compared with the SPM, the structure types and research contents of the SPM are not abundant enough. In this paper, a novel two-degree-of-freedom (2DOF) SPM with symmetrical structure is proposed and analyzed. First, the models of forward kinematics and inverse kinematics are established based on D-H parameters, and the Jacobian matrix of the mechanism is obtained and verified. Second, the workspace of the mechanism is obtained according to inverse kinematics and link interference conditions. Next, rotational characteristics analysis shows that the end effector can achieve continuous rotation about an axis located in the mid-plane and passing through the rotation center of the mechanism. Moreover, the rotational characteristics of the mechanism are proved, and motion planning is carried out. A numerical example is given to verify the kinematics analysis and motion planning. Finally, some variant mechanisms can be synthesized. This work lays the foundation for the motion control and practical application of this 2DOF SPM.

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The singularity problem brings troubles to the design and application for the parallel mechanism. Currently, redundant actuation is one of the useful methods to solve this singularity problem. However, faced to the numerous joints in a parallel mechanism, how to make a quantitative criterion of seeking the most efficient joints added actuators for letting the mechanism passes through singularity is a necessarily open issue. This paper focuses on a 2R1T 3-UPU (U for universal joint and P for prismatic joint) parallel mechanism (PM) with two rotational and one translational (2R1T) degrees of freedom (DOFs) and the ability of multiple remote centers of motion (M-RCM). The singularity analysis based on the indexes of motion/force transmissibility and constraint shows that this PM has transmission singularity, constraint singularity, mixed singularity and limb singularity. To solve these singular problems, the quantifiable redundancy transmission index (RTI) and the redundancy constraint index (RCI) are proposed for optimum seeking of redundant actuators for this PM. Then the appropriate redundant actuators are selected and the working scheme for redundant actuators near the corresponding singular configuration are given to help the PM passes through the singularity. This research proposes a quantitative criterion to optimum seeking of redundant actuators for the parallel mechanism to solve its singularity.