Compliant rotational joints have been widely applied in precision mechanisms, where over-constrained sheets are frequently employed to regulate stiffness. However, the effects of the position space of these over-constrained sheets on the stiffness variation remain insufficiently characterized. Furthermore, merely evaluating stiffness along a single direction fails to provide an objective assessment of their kinetostatic performance. To address these limitations, this paper introduces a generalized joint featuring three or five elastic sheets in a polygon arrangement, and two such joints are then combined to form a new generalized polygon-based crossing pivot. The nonlinear spatial analytical models are developed for the generalized triangular and quadrilateral joints based on the Beam Constraint Model and Free Body Diagram. These models are subsequently extended to characterize the polygon-based crossing pivot. A key advantage of the analytical model for the crossing pivot is its explicit incorporation of the position space between the two constituent triangular/quadrilateral joints. Specifically, each generalized triangular/quadrilateral joint can be placed at any position relative to the rotational center of the crossing pivot and oriented at any crossing angle between 0° and 180°. Utilizing the proposed analytical models, the geometric effects (i.e., position space) of the over-constrained sheets on the joint stiffness are systematically investigated using normalized stiffness ratios to ensure an objective comparison across different designs. The normalized twisting stiffness ratios of the triangular and quadrilateral joints are investigated under three types of geometric configurations. Subsequently, the normalized twisting stiffness ratio of the polygon-based crossing pivot comprising two representative quadrilateral joints, also called quadrilateral crossing pivot (QCP), is analyzed with respect to varying crossing positions and crossing angles. The accuracy of the above analysis is validated through nonlinear finite element analysis (FEA), yielding excellent agreement, with errors strictly bounded between 1.6% and 8.5%. Optimization results under three types of loading conditions demonstrate that the QCP can reduce center shift by 75% (or 62%, depending on the loading condition) compared to a conventional crossing pivot when out-of-plane loads exist. Finally, experimental testing on the quadrilateral joint and QCP confirms the accuracy of the analytical and FEA models. Notably, the developed prototype of the QCP enables four basic units to be assembled into 47 distinct configurations, highlighting its exceptional reconfigurability for precision applications.
A method involving cone angle adjustment is proposed to address off-center loading on intersecting-axis beveloid gear teeth caused by installation constraints. Based on the backlash-free involute gear meshing principle, analytical relationships are established among the cone angle, transverse pressure angle, helix angle, and imaginary rack parameters. Using scale factor λ and translation factor η, a meshing geometry model for cone angle adjustment is developed, where the minimum mesh gap distribution is controlled by λ and the contact position by η. Loaded tooth contact analysis is performed on a typical intersecting-axis beveloid gear pair under heavy loads with multiple adjustment factor sets. Results show that, after optimization, the contact pattern expands along the tooth width, peak contact pressure decreases, and transmission error fluctuation reduces. Even with small cone angle errors, performance exceeds that of the original toe-loaded gear pair considered in this study. Parameter analysis indicates that, with proper η, the adjusted cone angle can accommodate small shaft angle errors. This method requires no additional tooth modification and effectively suppresses off-center loading, providing theoretical support for high-performance beveloid gear applications.
This paper contains the derivation of the equations of motion for a single railway wheelset using exact linearisation. It can be shown that there is a quantitatively small, but existing deviation between the precisely derived equations and the usual equations in the literature obtained by conventional approximate linearisation. The assumptions of the different derivation methods are carefully analysed and compared. We analyse the effects of the improved equations on the dynamics and stability of the vibrations.
Bearings play a critical role in mechanical and mechatronic systems. Flexure bearings enable high-precision rotational motion, and their wear-free properties have the potential to enable substantially more longevity than conventional bearings. However, flexure bearings are typically only able to operate over a limited range of motion, precluding their use in applications requiring larger displacements. To address this, we previously introduced the metamorphic flexure bearing (MFB), which primarily operates as a flexure bearing but transitions automatically to a conventional bearing to accommodate greater displacement. The transition between bearing modes is enforced mechanically by a retention mechanism, which produces a displacement-dependent resistive force to selectively activate one bearing at a time. Herein, we present a rotary-motion MFB and demonstrate key performance characteristics during quasi-static operation for two types of retention mechanisms (retention-handoff and constant-stiffness). We also investigate the occurrence of a “combined mode”, in which both bearings are simultaneously engaged during dynamic operation, and define the acceleration thresholds that govern this behavior. Our results provide a starting point for design and implementation of rotary MFBs across applications.
