Automatic and interactive design of compliant mechanisms

A compliant mechanism is a single or multiple piece flexures that transfer force or motion through deflection of its flexible members. Compared with traditional rigid body mechanisms, compliant mechanisms or flexures have many advantages such as high precision and a simplified manufacturing and assembly process. Because its relatively low number of links, compliant mechanisms are especially suitable for micro fabrication process. However the design and analysis of compliant mechanisms possesses a significant due to the non linearity of deformation of the flexible members.

This research focuses on developing mathematical models and computational techniques to analyze and synthesize a compliant mechanism for a specified design task.

  • Inverse static analysis

    • The goal inverse static analysis is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. A compliant mechanism is first simplified as a Pseudo-Rigid-Body-Model. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential energy function. If there are torsional springs, we approximate the linear torsion spring torque at each joint by using sine and cosine functions in order to apply homotopy continuation method to these equations. One advantage of this approach is that it can find all equilibrium configurations.

    Publication: Su, H.-J. , and McCarthy J.M., "A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Complaint Mechanisms", ASME Journal of Mechanical Design , 128(4):776-786, 2006. (PDF)

    		Linear torsional spring can be simplified by using sine and cosine functions.

    The four equilibrium configurations of a compliant platform mechanism (above) with three flexible limbs. Red lines are linear springs. The triangle is the stage.

    This compliant 4-bar has two stable and two unstable equilibriums. They are obtained by simultaneously solving kinematic and static equations using homotopy continuation method.

  • Synthesis of bi-stable and multi-stable compliant mechanisms

Bi-stable or multi-stable compliant mechanisms have two or more stable equilibrium positions or configurations and find applications in devices such as switches, valves. Our synthesis problem begins with specifying a set of equilibrium positions for a compliant mechanism. And the goal is to determine dimensions and the spring constants of flexural joints such that the mechanism achieves static equilibrium at specified positions in the absence of external forces. We assume that Pseudo-Rigid-Body-Model of a compliant mechanism has been identified and the focus is on finding the dimensions and spring constants. This problem evolutes from ``rigid body guidance'' problem which was introduced by Burmester (1886) who used a graphical approach to seek a planar four bar to reach five specified planar positions.

Our design equations are formed by combining geometric constraints and equilibrium constraints. As in static analysis, equilibrium equations are transformed into polynomial form through an approximation of flexural joints. As a result, we can apply polynomial solution techniques to solve the design equations. This method is especially beneficial when a compliant mechanism undergoes large deflections.

Publication: Su, H.-J. , and McCarthy J.M., " Synthesis of Bistable Compliant Four-bar Mechanisms using Polynomial Homotopy," accepted by ASME Journal of Mechanical Design , May 2006. (PDF)

Planar Burmester problem or rigid body guidance problem

 

Synthesis of a compliant four-bar to reach n specified equilibrium positions

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