This paper proposes a kinematic calibration method of a novel 5-degree-of-freedom double-driven parallel mechanism with the sub-closed loop on limbs. At first, considering the introduction of a sub-closed loop significantly increased the complexity and difficulty of kinematic error modeling, an equivalent transformation method is proposed for the limb with a sub-closed loop. Then kinematic error model of the parallel mechanism is established based on the closed-loop vector method and parasitic motion analysis, which is verified by virtual prototype technology. Because the full kinematic error model is generally redundant, error parameter identifiability analysis is carried out by QR decomposition of the identification Jacobian matrix, and the redundant parameters are removed. Additionally, the Sequence Forward Floating Search algorithm is utilized to optimize measurement configurations to reduce the influence of measurement noise. Finally, with a laser tracker as the measuring device, numerical simulations and experiments are implemented to verify the proposed kinematic calibration method. The experiment results show that average position and orientation errors are reduced from 2.778 mm and 1.115° to 0.263 mm and 0.176°, respectively, within the prescribed workspace.

PU- and P*U*-equivalent parallel mechanisms (PMs) are critical families of PMs with one translational and two rotational (1T2R) degree of freedoms and have always been a research hotspot among lower mobility PMs. However, researches on these two families of PMs remain to be inadequate, and existing types are few and uncomprehensive. In this study, first, general wrench systems of PU-equivalent are derived based on virtual-chain approach and screw theory, revealing its constraint characteristics under general configuration. Cause of one parasitic motion is put forward and general wrench systems of P*U*-equivalent PMs with one parasitic motion are obtained. In addition, constraint analysis has been carried out to figure out constraint characteristics of P*U*-equivalent PMs with three parasitic motions. Second, branch chains are divided by generating constraints, and their structures are synthesized based on the presented rules. Then, the process for type synthesis of PU-equivalent PMs and P*U*-equivalent PMs and a series of novel 1T2R PMs are attained based on this. Finally, a novel PU-equivalent PM, 2PRU-PRUPc, and a novel P*U*-equivalent PM with one parasitic motion, 2PRU-PUU PM, are analyzed, demonstrating the effectiveness of the proposed type synthesis method.

A 3-RRPRR variable spherical symmetrical parallel mechanism (PM) with arc-shaped sliding pairs and no parasitic motion is presented, exhibiting two rotational and one translational (2R1T) degrees of freedom. Three limbs are symmetrically distributed between the base and end-effector; upper and lower parts of each limb are mirror symmetrical around the middle. The geometry, mobility, forward/inverse kinematics, workspace, and parasitic motion of the mechanism are analyzed, showing its ability to achieve large rotations around a continuous rotation axis. Finally, a structure synthesis strategy for variable spherical symmetrical PM is proposed, and several limb types meeting the conditions are obtained.

This paper deals with the design of a three-degree-of-freedom (3-DoF) parallel kinematic mechanism (PKM) with high orientational capability. First, a type synthesis method based on Grassmann line geometry and a line-graph method is proposed, and a novel 3-DoF PKM is derived based on this method. Thereafter, the parasitic motions of the derived mechanism are identified under two different orientation description methods, i.e., Tilt-and-Torsion angles (T&T angles) and Roll-Pitch-Yaw angles (RPY angles), and the kinematic optimization considering the motion/force transmissibility is carried out. On this basis, the orientational capability of the discussed mechanism is investigated, and the high orientational capability is demonstrated. The design of the 3-DoF PKM in this paper is very meaningful to the development of the five-axis machine tools with hybrid architectures. The design methods of type synthesis and kinematic optimization can also be used in the design of other PKMs.

In this paper, a new flexure-based micropositioning stage (FMPS) is proposed to achieve decoupled XY translational motions and large travel ranges. The stage consists of four independent kinematic chains, each comprising two flexure-beam prismatic joints. The mechanism with such a special topological structure enables the motions of the platform strictly along XY axes and minimizes the parasitic rotation in theta axis. The kinematics and dynamics analysis of the mechanism are conducted to evaluate the performance of the mechanism in terms of travel range, parasitic motions, linearity, as well as natural frequency. According to the developed models, a parameter optimization of the mechanism is performed under the condition of the maximum travel range. The finite element simulation is carried out to examine the mechanical performance and the theoretical models. The experimental results show that the proposed FMPS possesses a workspace of 600 × 600 μm2, a relative coupling error of 0.6%, and the natural frequencies of 209.7 Hz and 212.4 Hz for the first two modes.