Design of compliant mechanisms using continuum topology optimization: A review

Kinematic analysis of mechanisms kinematic synthesis of mechanisms simple mechanisms and coupler curves cams spur gears helical, spiral, worm and bevel gears gear trains hydrodynamic lubrication static force analysis inertia force analysis combined static and inertia force analysis turning moment diagram and flywheel balancing of rotating components balancing of reciprocating components gear forces.

Mechanism and machine theory

A review of modelling and analysis of morphing wings

In recent years, the robotic research area has become extremely prolific in terms of wearable active exoskeletons for human body motion assistance, with the presentation of many novel devices, for upper limbs, lower limbs, and the hand. The hand shows a complex morphology, a high intersubject variability, and offers limited space for physical interaction with a robot: as a result, hand exoskeletons usually are heavy, cumbersome, and poorly usable. This paper introduces a novel device designed on the basis of human kinematic compatibility, wearability, and portability criteria. This hand exoskeleton, briefly HX, embeds several features as underactuated joints, passive degrees of freedom ensuring adaptability and compliance toward the hand anthropometric variability, and an ad hoc design of self-alignment mechanisms to absorb human/robot joint axes misplacement, and proposes a novel mechanism for the thumb opposition. The HX kinematic design and actuation are discussed together with theoretical and experimental data validating its adaptability performances. Results suggest that HX matches the self-alignment design goal and is then suited for close human-robot interaction.

A Powered Finger–Thumb Wearable Hand Exoskeleton With Self-Aligning Joint Axes

A piezoelectric-driven actuator based on coupling motion has been proposed and tested to achieve a large linear working stroke with high resolution. “Z-shaped” flexure hinges are exploited for the symmetric flexure hinge mechanism to reduce the structural stress. Coupling motion is obtained by placing this symmetric flexure hinge mechanism with an angle of $\theta =20^\circ $ to the slider. Experimental results indicate that linear motion with a large working stroke is effectively obtained by this coupling motion; the maximum motion speed is $V_{s}=$ 6057 μm/s and the maximum output force is $F_{g}=$ 350 g. Additionally, the influences of input frequency $f$ and input voltage $U_{e}$ are investigated, and the system kinetic model is established to better analyze the performance of this designed piezoelectric-driven linear actuator.

A Piezoelectric-Driven Linear Actuator by Means of Coupling Motion

Classification and type synthesis of 1-DOF remote center of motion mechanisms

Flexure mechanism synthesis, however, is still a comparably difficult task. This paper aims at exploring a simple but systematic type synthesis methodology for general flexure mechanisms. The applied mathematical tool is reciprocal screw system theory in geometric form, and the proposed approach is an improvement of freedom and constraint topology (FACT), which is based on the FACT approach, combining with other methods including equivalent compliance mapping, set operation on building blocks, etc. As a result, it enables the type synthesis of flexure mechanisms simple, complete, and effective. What is more significant is that the proposed approach makes the unified type synthesis of both constraint-based and kinematics-based flexure mechanisms available. That is also the new contribution to the flexure de-sign.

Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms

This paper presents a symbolic formulation for analytical compliance analysis and synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. Our approach is based on the screw theory that characterizes flexure deformations with motion twists and loadings with force wrenches. In this work, we first derive a symbolic formulation of the compliance and stiffness matrices for commonly used flexure elements, flexure joints, and simple chains. Elements of these matrices are all explicit functions of flexure parameters. To analyze a general flexure mechanism, we subdivide it into multiple structural modules, which we identify as serial, parallel, or hybrid chains. We then analyze each module with the known flexure structures in the library. At last, we use a bottom-up approach to obtain the compliance/stiffness matrix for the overall mechanism. This is done by taking appropriate coordinate transformation of twists and wrenches in space. Four practical examples are provided to demonstrate the approach. A numerical example is employed to compare analytical compliance models against a finite element model. The results show that the errors are sufficiently small (2%, compared with finite element (FE) model), if the range of motion is limited to linear deformations. This work provides a systematical approach for compliance analysis and synthesis of general flexure mechanisms. The symbolic formulation enables subsequent design tasks, such as compliance synthesis or sensitivity analysis. [DOI: 10.1115/1.4006441] 1 Introduction and Motivations Flexure mechanisms [1] are formed by multiple (often identical) flexure pivots or simple chains that are designed to produce a defined motion upon application of an appropriate loading. They are widely used in various precision instruments and machines [2] from nanomanipulators [3], nanopositioners [4], and optical scanning mirrors [5] to scanning transmission X-ray microscopy [6]. One important step toward the control and design of flexure mechanisms is the compliance analysis or mapping; the goal of which is to determine the relationship between the deformation and the loading applied to the device. Dimentberg [7] applied the screw calculus [8] to study the statics and vibration of an elastic suspension system. Loncaric [9] applied Lie algebra to the stiffness and compliance analysis of robotic devices and showed that the stiffness and compliance matrices can be reduced to a normal form by a particular choice of the coordinate frame. Lipkin and Patterson [10‐12] studied the structure of compliance matrices via eigenvalue decomposition. Selig and Ding [13,14] applied the screw theory [15,16] to the compliance analysis of static beams. In their work, a general loading is represented by a wrench, while a general deformation is represented by a motion screw. They derived the compliance matrix for a cantilever beam subject to an end loading, and showed that the result was consistent with the

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A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms.

Beam-based compliant mechanisms have been widely used in many precision applications due to their large-displacement characteristic Meanwhile, a simple and accurate analytical tool is no doubt useful to assist design and optimize these mechanisms The pseudo-rigid-body (PRB) model is such a good alternative The PRB model in a traditional sense, however, is too approximate to calculate some precise characteristics such as center-shift of a flexural joint In this paper, a new method is proposed to easily establish simple and accurate PRB models for a variety of beam-based compliant mechanisms As is well known, for most of the beam-based compliant mechanisms, there is usually an instantaneous center of rotation (ICR) on each beam, and the beam can be considered as a fixed-guided beam with one end fixed while the other end moves along a certain curve that usually is an approximate arc around the ICR In this case, the behavior of beams can be imitated by a rigid bar with two pin-joints One of the pin-joints is directly added at the end of the rigid bar The position of the other is determined by the characteristic radius factor, and a torsional spring is added at the position to represent the beam's stiffness The modeling method is used to analyze two commonly used beam-based compliant mechanisms as examples, ie a parallel linear spring stage and a cross strip pivot The performances of precision, stiffness and stroke for the two mechanisms are investigated, and the method is validated by comparing the results with other research work presented in the literatures Both cases show the method is intuitive and accurate, and it will be useful in the early phases of the design for beam-based compliant mechanisms

Jingjun Yu

Papers

Classification and type synthesis of 1-DOF remote center of motion mechanisms

Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms

A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms.

An effective pseudo-rigid-body method for beam-based compliant mechanisms

The modeling of cartwheel flexural hinges