To meet the increasing requirements for precision hybrid machine tools, this paper presents a geometric error propagation model-based accuracy synthesis method for parallel manipulators (PMs) with one translational and two rotational (1T2R) motion abilities. A unified geometric error propagation model of a family of 1T2R PMs is established with the first-order kinematic perturbation method. A set of geometric error propagation intensity indexes is formulated to describe the geometric error propagation characteristics in a quantitative manner. The equivalent effects of specified terminal accuracy are derived to directly determine the allowable values of all geometric source errors. Based on these, a computation algorithm is summarized for designating a tolerance allocation scheme to meet the specified terminal accuracy of a 1T2R PM. To demonstrate the accuracy synthesis method, a novel 1T2R PM with a 2UPR-1RPS (“R,” revolute joint; “U,” universal joint; “S,” spherical joint; “P,” prismatic actuated joint) topology is taken as an example to allocate geometric tolerances under the specified terminal accuracy. Following the tolerance allocation scheme, a laboratory prototype of the exemplary PM is fabricated and further experimentally measured. The measured kinematic results indicate that the prototype possesses an acceptable position error smaller than 0.15 mm, verifying the feasibility of the proposed accuracy synthesis method. Hence, the proposed method can be applied as a forward tolerance design tool to reduce the design iterations and development risks of low-mobility parallel robots.

Redundantly actuated parallel manipulator (RAPM) has been proved to have comparative advantages of higher rigidity and higher payload over other parallel manipulators. This paper is to quantitatively reveal the effect of redundancy on rigidity enhancement of a previously invented 2UPR&1RPS&1RPU RAPM. For this purpose, three critical issues are clarified, i.e., establishing a sufficient accurate stiffness model, constructing a reasonable index frame for evaluating rigidity performance, and quantifying the effect of redundancy on the rigidity enhancement. First, drawing on the screw theory, a hierarchical method is presented to establish a semi-analytic stiffness model at the joint level for the proposed RAPM. Subsequently, based on the stiffness matrix, a set of local and global stiffness indices are constructed to evaluate the rigidity of parallel manipulators. Finally, the stiffness indices of the 2UPR&1RPS&1RPU RAPM and its non-redundantly actuated forms are predicted and compared to reveal the effort of redundancy. The present work is expected to provide a useful frame for quantitatively assessing redundancy-induced rigidity enhancement in redundantly actuated parallel manipulators.

This study presents a comprehensive geometric modeling and error propagation analysis for a 3-degrees-of-freedom spindle head, focusing on an over-constrained parallel mechanism. Four geometric error models are established for the over-constrained spindle head, each considering different combinations of constraint wrenches. A set of sensitivity indices is formulated to evaluate the effectiveness of these models. Comparative sensitivity analysis suggests that a model incorporating all constraint wrenches is suitable for error propagation analysis. Two error propagation indices are introduced to quantify the impact of the geometric source errors on the position and orientation of an individual limb structure. The coupled error propagation indices account for the kinematic interactions among limb structures, allowing for a detailed analysis of the spindle head’s terminal accuracy. The relative deviations of error propagation indices are utilized to assess the quantitative impact of kinematic interactions on the geometric errors of an individual limb structure. Furthermore, this study analyzes the cumulative effects of kinematic errors from three limb structures to reflect the influence of kinematic interactions on the terminal accuracy of the spindle head. The findings indicate that geometric errors of the limbs in such an over-constrained spindle head are mutually compensatory, reducing linear and angular errors and enhancing the spindle head’s terminal accuracy.