Larry L. Howell

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

Geometric nonlinearities often complicate the analysis of systems containing largedeflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closedform elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms

A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms

Compliant mechanisms gain at least some of their motion from flexible members. The combination of large-deflection beam analysis, kinematic motion analysis, and energy storage makes the analysis of compliant mechanisms difficult. The design of mechanisms often requires iteration between synthesis and analysis procedures. In general, the difficulty in analysis has limited the use of compliant mechanisms to applications where only simple functions and motions are required. The pseudo-rigid-body model concept promises to be the key to unifying the compliant and rigid-body mechanism theories. It simplifies compliant mechanism analysis by determining an equivalent rigid-body mechanism that accurately models the kinematic characteristics of a compliant mechanism. Once this model is obtained, many well known concepts from rigid-body mechanism theory become amenable for use to analyze and design compliant mechanisms. The pseudo-rigid-body-model concept is used to develop a loop-closure method for the analysis and synthesis of compliant mechanisms. The method allows compliant mechanisms to be designed for tasks that would have earlier been assumed to be unlikely, if not impossible, applications of compliant mechanisms.

Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms

Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.

Modeling the thermal behavior of a surface-micromachined linear-displacement thermomechanical microactuator

Thermomechanical microactuators possess a number of desirable attributes including ease of fabrication and large force and displacement capabilities relative to other types of microactuators. These advantages provide motivation for improving thermomechanical microactuator designs that are more energy efficient and thus better suited for low-power applications. To this end, this paper describes the development and experimental validation of a finite-difference thermal model of a thermomechanical in-plane microactuator (TIM). Comparisons between the model and experimental results demonstrate the importance of including the temperature dependence of several parameters in the model. Strategies for reducing the power and energy requirements of the TIM were investigated using model simulations as a guide. Based on design insights gained from the model, the energy efficiency of the TIM has been improved significantly by operating in a vacuum environment and providing short-duration, high-current pulse inputs. These improvements have been validated experimentally.

A self-retracting fully compliant bistable micromechanism

A new class of fully compliant bistable mechanisms with the added benefit of integrated self-retraction has been developed (hereafter identified as Self-Retracting Fully compliant Bistable Mechanism or SRFBM). A technique using tensural pivots to manage compressive loading in compliant mechanisms is introduced and implemented in the SRFBM. The elimination of traditional kinematic joints and their associated clearance allows a total displacement between stable positions of 8.5 /spl mu/m, and the mechanism size is less than 300 /spl mu/m square when using 2.0 /spl mu/m minimum line widths. Maximum actuation force is approximately 500 /spl mu/N. The SRFBMs small linear displacement and reasonable actuation force facilitate integration with efficient thermal actuators. Furthermore, fully compliant mechanisms allow greater freedom in fabrication as only one mechanical layer is needed. Systems with on-chip actuation have been fabricated and tested, demonstrating bistability and on-chip actuation, which requires approximately 150 mW. A single fatigue test has been completed, during which the SRFBM endured approximately 2 million duty cycles without failure.

Accommodating Thickness in Origami-Based Deployable Arrays

The purpose of this work is to create deployment systems with a large ratio of stowed-to-deployed diameter. Deployment from a compact form to a final flat state can be achieved through origami-inspired folding of panels. There are many models capable of this motion when folded in a material with negligible thickness; however, when the application requires the folding of thick, rigid panels, attention must be paid to the effect of material thickness not only on the final folded state, but also during the folding motion (i.e., the panels must not be required to flex to attain the final folded form). The objective is to develop new methods for deployment from a compact folded form to a large circular array (or other final form). This paper describes a mathematical model for modifying the pattern to accommodate material thickness in the context of the design, modeling, and testing of a deployable system inspired by an origami six-sided flasher model. The model is demonstrated in hardware as a 1/20th scale prototype of a deployable solar array for space applications. The resulting prototype has a ratio of stowed-to-deployed diameter of 9.2 (or 1.25 m deployed outer diameter to 0.136 m stowed outer diameter). INTRODUCTION The purpose of this work is to develop deployment systems that unfold from a compact form to a large array. This work ∗Corresponding author: lhowell@byu.edu is motivated by the need for compactly folded solar arrays for space applications. A large ratio of stowed-to-deployed diameter enables large solar arrays to be launched in their compact, folded configuration and then deployed in space to a much larger surface area. For our objectives, a design with synchronous deployment was desired to simplify actuation and deployment. Deployment from a compact form to a final flat state can be achieved through origami-inspired folding of panels. There are many models capable of this motion when folded in paper or other materials with negligible thickness; however, when the application requires the folding of thick, rigid panels, material thickness can inhibit the folding motion. To be rigid-foldable, the panels must not be required to flex to attain the final folded form. This paper describes the approach for modifying the design of an origami six-sided flasher model to accommodate material thickness. This work builds on existing models to present a unique design that is rigid-foldable through two different methods. In the first method, the panels are allowed to flex along their diagonals. In the second method, the panels are affixed to a flexible membrane with discrete gap spacing between the panels. Both folding solutions enable the model to be rigid-foldable.

Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model

Based on the principle of dynamic equivalence, a new dynamic model of compliant mechanisms is developed using the pseudo-rigid-body model. The dynamic equation of general planar compliant mechanisms is derived. The natural frequency of a compliant mechanism is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the effectiveness and advantage of the proposed method compared with the methods of FEA and flexible mechanisms.

Design of Two-Link, In-Plane, Bistable Compliant Micro-Mechanisms

A bistable mechanism has two stable states within its range of motion. Its advantages include the ability to stay in two positions without power input and despite small external disturbances. Therefore, bistable micro-mechanisms could allow the creation of MEMS with improved energy efficiency and positioning accuracy. This paper presents bistable micro-mechanisms which function within the plane of fabrication. These bistable mechanisms, called Young bistable mechanisms, obtain their energy storage characteristics from the deflection of two compliant members. They have two pin joints connected to the substrate, and can be constructed of two layers of polysilicon. The pseudo-rigid-body model is used to analyze and design these mechanisms. This approach allows greater freedom and flexibility in the design process. The mechanisms were fabricated and tested to demonstrate their bistable behavior and to determine the repeatability of their stable positions.

The modeling of cross-axis flexural pivots

Abstract Cross-axis flexural pivots, formed by crossing two flexible beams at their midpoints, have been used in compliant mechanisms for many years. However, their load–deflection behavior has yet to be appropriately modeled to allow easy analysis and synthesis of mechanisms containing them. This paper uses results of non-linear finite element analysis to investigate this behavior. Based on the analysis, two models for the pivots are presented – one simple and one more complex. The accuracy of the models is demonstrated by comparing results to those measured for pivots made from polypropylene and steel.

Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior

Bistable mechanisms, which have two stable equilibria within their range of motion, are important parts of a wide variety of systems, such as closures, valves, switches, and clasps. Compliant bistable mechanisms present design challenges because the mechanism’s energy storage and motion characteristics are strongly coupled and must be considered simultaneously. This paper studies compliant bistable mechanisms which may be modeled as four-link mechanisms with a torsional spring at one joint. Theory is developed to predict compliant and rigid-body mechanism configurations which guarantee bistable behavior. With this knowledge, designers can largely uncouple the motion and energy storage requirements of a bistable mechanism design problem. Examples demonstrate the power of the theory in bistable mechanism design.