An Objective Evaluation of Displacement-Amplifying Compliant Mechanisms for Sensor Applications

Displacement-amplifying compliant mechanisms (DaCMs) reported in literature are mostly used for actuator applications. This paper considers them for sensor applications that rely on displacement measurement, and evaluates them objectively. The main goal is to increase the sensitivity under constraints imposed by several secondary requirements and practical constraints. A spring-mass-lever model that effectively captures the addition of a DaCM to a sensor is used in comparing eight DaCMs. We observe that they significantly differ in performance criteria such as geometric advantage, stiffness, natural frequency, mode amplification, factor of safety against failure, cross-axis stiffness, etc., but none excel in all. Thus, a combined figure of merit is proposed using which the most suitable DaCM could be selected for a sensor application. A case-study of a micro machined capacitive accelerometer and another case-study of a vision-based force sensor are included to illustrate the general evaluation and selection procedure of DaCMs with specific applications. Some other insights gained with the analysis presented here were the optimum size-scale for a DaCM, the effect on its natural frequency, limits on its stiffness, and working range of the sensor.

Design and Fabrication of an Elastic Knee Orthosis: Preliminary Results

When humans hop or run on compliant surfaces they alter the stiffness of their legs so that the overall stiffness of the leg-surface system remains the same. Adding a spring in parallel to the ankle joint incites a similar neuromuscular response; humans decrease their biological ankle stiffness such that the overall ankle stiffness remains unchanged. These results suggest that an elastic exoskeleton could be effective at reducing the metabolic cost of locomotion. To further increase our understanding of human response we have developed an elastic knee brace that adds a stiff spring in parallel to the knee. It will be used as a test platform in ascertaining the neuromuscular effects of adding a parallel knee spring while hopping on one leg. This paper focuses primarily on the mechanical design and implementation of our elastic knee orthosis. Results of the forthcoming studies of human subjects wearing this knee orthosis will be presented in a separate article that will focus on the biomechanics and the neuromuscular adaptations of the human body. Prior research found that the neuromuscular response to hopping on compliant surfaces was the same when running on compliant surfaces. We expect that our results from hopping with springs in parallel with the knee will also be applicable to running. This elastic knee brace represents the first phase of an ongoing research project to develop a passive compliant lower-body exoskeleton to assist in human running. It is expected that this research will benefit healthy individuals as well as those with disabilities causing decreased muscle function.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

Bistable Compliant Four-Bar Mechanisms With a Single Torsional Spring

Significant reduction in cost and time of bistable mechanism design can be achieved by understanding their bistable behavior. This paper presents bistable compliant mechanisms whose pseudo-rigid-body models (PRBM) are four-bar mechanisms with a torsional spring. Stable and unstable equilibrium positions are calculated for such four-bar mechanisms, defining their bistable behavior for all possible permutations of torsional spring locations. Finite Element Analysis (FEA) and simulation is used to illustrate the bistable behavior of a compliant mechanism with a straight compliant member, using stored energy plots. These results, along with the four-bar and the compliant mechanism information, can then be used to design a bistable compliant mechanism to meet specified requirements.

Elastic Averaging in Flexure Mechanisms: A Muliti-Beam Parallelogram Flexure Case-Study

Over-constraint is an important concern in mechanism design because it can lead to a loss in desired mobility. In distributed-compliance flexure mechanisms, this problem is alleviated due to the phenomenon of elastic averaging, thus enabling performance-enhancing geometric arrangements that are otherwise unrealizable. The principle of elastic averaging is illustrated in this paper by means of a multi-beam parallelogram flexure mechanism. In a lumped-compliance configuration, this mechanism is prone to over-constraint in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear load-stiffening and elasto-kinematic effects in the constituent beams have an important role to play in the over-constraint and elastic averaging characteristics of this mechanism. Therefore, a parametric model that incorporates these nonlinearities is utilized in predicting the influence of a representative geometric imperfection on the primary motion stiffness of the mechanism. The proposed model utilizes a beam generalization so that varying degrees of distributed compliance are captured using a single geometric parameter.

Topology Optimization of Electrostatically Actuated Micromechanical Structures With Accurate Electrostatic Modeling of the Interpolated Material Model

In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.

Assembly Configuration Synthesis Method for Discretely-Actuated Manipulators

Discretely-actuated manipulators are defined in this paper as serial planar chains of many links where the actuation of one link with respect to the previous link occurs in one of three discrete positions. Because of the limited end-effector workspace, a link may be manually connected to the previous link in one of four 90° orientations to assist in generating a workspace corresponding to specific applications. Given an application workspace, the assembly configuration synthesis strategy presented here is a novel approach to determine the nominal configuration (all actuators in their 0° position) of the serial chain. The solved configuration will cover an application grid area using its discrete actuation with no change in nominal configuration. The unique application workspace, defined as a planar grid area, requires the end effector to be positioned somewhere within each specific element of the grid. The synthesis strategy is made up of three stages with each stage having tests that increase in computation and difficulty that a potential configuration must pass or be eliminated. Critical to the tests is the ability to quickly model and approximate the end-effector workspace of a configuration and a new method for this approximation is described.

Pseudo-Rigid-Body Model Chain Algorithm: Part 2 — Equivalent Representations for Combined Load Boundary Conditions

Pseudo-rigid-body models help expedite the compliant mechanism design process by aiding the analysis and synthesis of candidate design solutions, using loop-closure techniques for rigid-body mechanisms. Presently, these models are available only for relatively simple compliant beam geometries and loading situations. The pseudo-rigid-body model chain algorithm provides reasonable approximations of the deformed shape of complex compliant members; however, it has one major limitation. The elastic deformation of each compliant segment under combined load boundary conditions is obtained by superposing the pseudo-rigid-body model displacements due to i) the force and ii) the moment loads, respectively. Hence, each segment needs to be characterized by two separate pseudo-rigid-body models in order to accurately determine its deformation kinematics. Such an idealization of compliant segments would present significant challenges when attempting to represent the pseudo-rigid-body model chain in vectorial form, as in planar vector loop-closure methods. Vectorial modeling would be possible if each flexible segment in the chain could be represented by an “equivalent pseudo-rigid-body model.” This paper proposes the concept of a rudimentary equivalent pseudo-rigid-body model to represent compliant segments with combined load boundary conditions in the pseudo-rigid-body model chain algorithm. Such a model may help overcome the difficulties confronted in the potential implementation of the pseudo-rigid-body model chain in planar vector loop-closure solution techniques.

Representation of the Variable Chain Mechanisms With Sequential Movement

A mechanism that encounters a certain change in the number of links or degree of freedom during operation will also result the variation of the topological structure in every stage. Since the mechanisms with variable chain in different stages during operation have different topologies, but the applications of this kind of mechanisms are very extensively. And this also result the complications of representation of the topology thoroughly. Mechanisms with variable chain now always been represented by graph according to the topology of each stage, but hardly represent by using a formula. We would like to propose an approach to develop the function for representing the mechanism with variable chain that focus on the sequential movement, and help the representation of the operation not only by the graph but also by the function. According to the operation of the mechanisms with variable chain, the movement of the mechanisms can be classified into parallel system movement and sequential system movement. Parallel movement mechanisms are the mechanisms operate more than one links in the same time when giving an input; and when we give an input that can operate just only one link and effect and transfer the movement of the next one step by step, we can call this kind of mechanisms as sequential mechanisms. In this work we apply composite function for represent the movement of each stage, and also verified the representation by applying it on the existed examples.

Spherical Bistable Micromechanism

A new micromechanism, the Spherical Bistable Micromechanism (SBM), is described. The SBM has several advantageous features, which include: two stable positions that require power only in transitioning from one to the other; robustness against small disturbances; and an output link with a stable out-of-plane orientation. The SBM may be useful in applications such as 2-D optical mirror arrays or in erecting out-of-plane structures.