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SummaryWhen using parallel manipulators as machine tools, their stiffness is an important factor in the quality of the produced products. This paper presents an overall approximate stiffness model for a heavy-load parallel manipulator, which considers the effects of actuator stiffness, joint clearance, joint contact deformation, and limb deformation. Based on the principle of virtual work and the introduced modified parameters, the proposed overall compliance matrix successfully takes four factors into a unified expression. To obtain the overall compliance matrix, the approximate stiffness models of the joint clearance, joint contact deformation, and limb deformation are given. In addition, by combining the statistical simulation including the random uncertainties and the proposed approximate stiffness models as the basis of the magnitudes for each random variable, an approach based on the expected trajectory and external load is also proposed for stiffness defect identification such that the estimation is more accurate and reliable. Finally, a numerical example of the 1PU+3UPS parallel manipulator and a discussion are presented to demonstrate the practicability of the proposed stiffness model and defect identification approach. After modifying the structure parameters of the defective components, the prototype experiences a significant stiffness improvement.

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In order to extend the type of multi-lobed non-circular bevel gear, some curves such as an Archimedes spiral, a quadratic curve and a Pascal curve are applied to the design of the pitch surface of a multi-lobed non-circular bevel gear. With the aim of studying the design defects of a multi-lobed non-circular bevel gear which has a pitch surface with a concave cusp or a convex cusp, a novel pitch-surface-shaping method is presented to shape the concave cusp or the convex cusp of the pitch surface of a multi-lobed non-circular bevel gear. A section of the pitch surface of the cutter is used to replace the concave or convex pitch surface of the multi-lobed non-circular bevel gear by using the above shaping method. Mathematical models of the pitch surface with multi-stage space curves for a multi-lobed non-circular bevel gear are established. Numerical examples demonstrate that the shaping method is beneficial for improving the machining quality of the teeth profile as well as the transmission performance of a multi-lobed non-circular bevel gear.

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