Nonlinear Finite Element Load-Displacement Model and Analysis of Circular-Axis Hinge, Self-Similar Mechanism with Large Out-of-Plane Motion

This research studies the large-displacement response of a fractal-architecture mechanism with circular-axis flexible hinges, which was introduced in [1], by formulating an efficient and accurate nonlinear finite element model. Two three-dimensional line elements are proposed whose nodal degrees of freedom include the three spatial Tait-Bryan angles. The nonlinear finite element is generated using the minimum potential energy condition for the entire deformed structure in a non-incremental approach. The error does not depend on the number of load steps since one step is sufficient to achieve the final, deformed state. The method is applied to predict the nonlinear, large, out-of-plane displacement of the fractal-hinge compliant mechanism. The model predictions are validated by finite element code simulation and experimental testing. The nonlinear finite element force-displacement data coincide with the linear compliance model predictions of [1] for approximately ¼ lower portion of the load range and display the expected hardening-spring features for the load range remainder.

Plane Tangent to Quasi-Rotation Surface

The analysis of a surface generated by quasi-rotation of a straight line around a circle is provided in the present paper. The considered case features a straight generatrix belonging to the plane of a circular axis of quasi-rotation and intersecting it in two points. A geometric method of determination of a point belonging to a surface given its projection on the axis plane is demonstrated. Geometric construction of the curves of intersection between the considered surface and a conic surface is presented. A method of determination of points belonging to the considered surface as points belonging to the curve of intersection of two conic surfaces is acquired. Step-by-step constructions illustrating the solution of the problem of determination of a plane tangent to the considered surface in a given point are provided. The problem is solved through the methods of descriptive geometry. Every construction is performed according to an analytic algorithm, not involving approximate methods of determination of the sought points. The construction is carried out in a CAD system through the use of tools “straight line by two points” and “circle by center and point”. The presented solution to the defined problem is connected to the solution to the problem of determination of the rays reflected from the considered surface. The results of the paper expose the geometric properties of surfaces of quasi-rotation. The provided constructions can serve as the basis for the research of optical properties of the considered surfaces.