Two rotations and one translation (2R1T) parallel kinematic machines (PKMs) are suitable for the machining of complex curved surfaces, which requires high speed and precision. To further improve rigidity, precision, and avoid singularity, actuation redundancy, and overconstrained PKMs with fixed actuators and limited-degrees of freedom (DOF) limbs are preferred. However, there are few 2R1T PKMs with these features. This paper introduces a new 2R1T overconstrained PKM with actuation redundancy, which is called Tex4. The Tex4 PKM consists of four limited-DOF limbs; that is, two PUR limbs and two 2PRU limbs (where P denotes an actuated prismatic joint, U denotes a universal joint, and R denotes a revolute joint). The kinematic model of the proposed 2PUR-2PRU machine is presented along with the results of mobility, inverse kinematics, and velocity analysis. By considering the motion/force transmissibility, the dimensional parameters of the Tex4 PKM were optimized to obtain an improved satisfactory transmission workspace without singular configurations. Finally, a prototype based on the optimized parameters was fabricated, and its feasibility and accuracy were validated by motion and position error experiments. The Tex4 PKM has the advantages of high rigidity, simple kinematic model, and zero singularity in the workspace, which suggests that it has potential for use in the high-speed machining of curved surfaces.

A general method for the analytical elastostatic stiffness modeling of overconstrained parallel manipulators (PMs) using geometric algebra and strain energy is proposed. First, an analytical solution of the constraint and actuation wrenches exerted on the moving platform is obtained using the outer product and dual operation of geometric algebra, which avoids solving complex symbolic linear equations. Second, considering the compliances of the limbs, an analytical elastostatic model is established using the strain energy to obtain the stiffness matrices of the limbs. Finally, the deformation compatibility equations are added into equilibrium equations to obtain the overall stiffness matrix of the PM, which has a concise expression and a clear physical meaning. The proposed method is applied to the Tex3 overconstrained PM and the Tex4 overconstrained PM with redundant actuation to prove its validity. Comparable results between the theoretical analysis and the finite-element analysis (FEA) show that the former could be used as an effective alternative to the FEA method in the predesign stage. This new approach is universally applicable to the elastostatic stiffness analysis of overconstrained PMs.

Large workpieces are important components of core equipment in aerospace and other fields, where the machining mainly focuses on the surfaces and inner cavities. However, it may be unsuitable for existing machining robots to directly achieve integrated machining, that is, not only the high-precision surface machining but also the machining of different inner cavities in a limited space. To satisfy these machining requirements, a new reconfigurable hybrid robot (RHR) is proposed, called the 3PRR-3PSS-UPU RHR, for machining the surface and inner cavity of large workpieces (where P, P, R, S, and U stand for the actuated prismatic joint, passive prismatic joint, revolute joint, spherical joint, and universal joint, respectively). The proposed RHR consists of two parallel manipulators (PMs), in which one is a spatial 3PRR PM with one translational degree-of-freedom (DOF) and the other is a 3PSS-UPU reconfigurable PM (RPM) with different configurations of two rotational and one translational (2R1T) DOFs using locking equipment, which is the main advantage of the designed robot. The inverse kinematics and singularities of two PMs are analyzed. The stiffness performance of the spatial 3PRR PM is compared with that of a moving slider with one translational DOF. By evaluating the workspace and motion/force transmissibility, the kinematic performance of two PMs is presented using several local and global indices, followed by the dimensional optimization of link parameters. Based on the structural characteristics and excellent performance, it can be inferred that the 3PRR-3PSS-UPU RHR has great potential for machining large workpieces.

This paper presents the type synthesis of 4-DOF non-overconstrained parallel mechanisms (PMs) with symmetrical structures. A special topological structure that includes two intermediate platforms and one moving platform is employed. Constraint conditions for 3R1T, 2R2T, and 1R3T (R: rotation; T: translation) symmetrical PMs are analyzed. Several classes of hybrid limbs that exert a constraint force or a constraint couple are synthesized using screw theory. These limbs are then used to construct 4-DOF PMs, resulting in many novel non-overconstrained 3R1T, 2R2T, and 1R3T PMs with symmetrical structures. The non-overconstrained feature is verified based on the Grübler/Kutzbach criterion.

Forward kinematics-based modeling approaches are capable of constructing complete kinematic error models for parallel robots in a general way. The existing forward kinematics-based modeling methods replace multi-degrees-of-freedom (multi-DOF) joints with several 1DOF joints, allowing each limb of the parallel robot to be modeled like a serial robot. Nonetheless, this substitution complicates the kinematic model and results in additional computation. To overcome this limitation, an efficient kinematic calibration method adopting compact multi-DOF joint models is proposed. First, compact kinematic models for multi-DOF joints are established with the product of exponentials formula and adopted in the forward kinematic formulation of limbs. Error models of limbs are derived by simplifying the forward kinematic formulas' differentials, and the geometric error model for parallel robots is established by further concatenating and reformulating the limb error models. Next, the kinematic model is iteratively updated with the geometric parameter errors identified by the Levenberg–Marquardt algorithm. Error compensation is achieved through the inverse kinematics of the calibrated kinematic model. Finally, simulations and an experiment are implemented for validation. Compared with the existing forward kinematics-based modeling approaches, the error modeling procedures are simplified as the equivalent substitution of multi-DOF joints is avoided. The proposed approach also enhances the error compensation efficiency while maintaining high accuracy improvement.