Zhao Hongzhe

Modeling of a Cartwheel Flexural Pivot

A cartwheel flexural pivot has a small center shift as a function of loading and ease of manufacturing. This paper addresses an accurate model that includes the loading cases of a bending moment combined with both a horizontal force and a vertical force. First, a triangle flexural pivot is modeled as a single beam. Then, the model of cartwheel flexural pivot based on an equivalent model is developed by utilizing the results of the triangle pivot. The expressions for rotational displacement and center shift are derived to evaluate the primary motion and the parasitic motion; the maximum rotational angle is simply formulated to predicate the range of motion. Finally, the model is verified by finite element analysis. The relative error of the primary motion is less than 1.1% for various loading cases even if the rotational angle reaches ±20 deg, and the predicted errors for the two center shift components are less than 15.4% and 7.1%. The result shows that the model is accurate enough for designers to use for initial parametric design studies, such as for conceptual design.

Design of a Family of Ultra-Precision Linear Motion Mechanisms

The parasitic motion of a parallel four-bar mechanism (PFBM) is undesirable for designers. In this paper, the rigid joints in PFBM are replaced with their flexural counterparts, and the center shift of rotational flexural pivots can be made full use of in order to compensate for this parasitic motion. First, three schemes are proposed to design a family of ultraprecision linear-motion mechanisms. Therefore, the generalized cross-spring pivots are utilized as joints, and six configurations are obtained. Then, for parasitic motion of these configurations, the compensation condition is presented, and the design space of geometric parameters is given. Moreover, the characteristic evaluation of these configurations is implemented, and an approach to improve their performances is further proposed. In addition, a model is developed to parametrically predict the parasitic motion and primary motion. Finally, the analytic model is verified by finite element analysis (FEA), so these linear-motion mechanisms can be employed in precision engineering.