Jingjun Yu

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

A Symbolic Formulation for Analytical Compliance Analysis and 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.

Design and Experimental Testing of an Improved Large-Range Decoupled XY Compliant Parallel Micromanipulator

There is an increasing need for XY compliant parallel micromani-pulators (CPMs) providing good performance characteristicssuch as large motion range, well-constrained cross-axis coupling,and parasitic rotation. Decoupled topology design of the CPMscan easily realize these merits without increasing the difficulty ofcontrolling. This paper proposes an improved 4-PP model on thebasis of a classical 4-PP model and both of them are selected formanufacturing and testing to verify the effectiveness of theimprovement. It has shown from experimental results that there isa large improvement on the performances of improved 4-PP com-pliant parallel manipulator (CPM): large range of motion up to5mm 5 mm in the unidirection in the dimension of311 mm 311 mm from their own shortages, such as smaller motion range [24 mm, smaller compliance fluctuation (only36.63% of that of the initial 4-PP model), smaller cross-axis cou-pling (only 28.10% of that of the initial 4-PP model generated bya single-axis 5 mm actuation), smaller in-plane parasitic yaw(only 57.14% of that of the initial 4-PP model generated bydouble-axis 5 mm actuation). [DOI: 10.1115/1.4030467]

A Novel Family of Leaf-Type Compliant Joints : Combination of Two Isosceles-Trapezoidal Flexural Pivots

The leaf-type isosceles-trapezoidal flexural (LITF) pivot consists of two compliant beams and two rigid bodies. For a single LITF pivot, the range of motion is small while the center-shift is relatively large. The capability of performance can be improved greatly by the combination of two LITF pivots. Base on the pseudorigid-body (PRB) model of a LITF pivot, a method to construct the double-LITF pivots is presented by regarding a single LITF pivot as a the configurable flexure module. The trends of the center-shift are mainly considered by using this method with the combination of two LIFT pivots. Eight types of double-LITF pivots are synthesized. Compared with the single LIFT pivot, the stroke becomes larger, and stiffness becomes smaller. Four of them have the increased center-shift. The other four have the decreased center-shift. Two of the double-LITF pivots are selected as the examples to explain the proposed method. The comparison between PRB model and finite element analysis result shows the validity and effectiveness of the method. DOI: 10.1115/1.3046140

Mobility analysis of complex joints by means of screw theory

In structural design of current complex mechanisms or robots like parallel kinematic machines (PKMs), surgical robots, and reconfigurable robots, there commonly exist some functional modules called complex joints (CJs). Each of them, consisting of several simple pairs and essentially a mechanism, plays the same and more important roles as simple joints in kinematics and dynamics. However, as the primarily important aspect in mechanism analysis, the type and mobility of these CJs are far from familiarity. Therefore, this paper aims at addressing the type and mobility of CJs. For this purpose, the concept and classification of CJs are first discussed, an effective method to analyze the mobility characteristics of these CJs is then developed based on the equivalent screw system. The advantage of this method is that it reveals mobility characteristics by using equivalent transformations of kinematic pair screw (KP-screw) and constraint screw (C-screw) systems. With this method, the mobility characteristics of some concrete CJs are obtained correspondingly.

Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part I—General Methodology

The systematic methodologies involved in type synthesis of flexure systems are no doubt helpful to generate one and more high-performance precision machine designs at the stage of conceptual design with a rapid and effective way. This paper provides a systematic formulation of the type synthesis of parallel, serial, and hybrid flexure systems via a mapping from a geometric concept to physical entity. The whole type synthesis principle is built upon screw system theory and the geometric Freedom and Constraint Topology (FACT) approach, also combining with other concepts and methods including equivalent compliance mapping, building block etc, which enables the type synthesis of flexure systems deterministic, simple and practical. After that, Type synthesis procedure for various flexure systems are elaborated with examples. As a result, as many specified-DOF (Degree of Freedom) flexure systems as possible can be found and therefore pave the way for obtaining an optimal configuration.Copyright

Design of Compliant Straight-line Mechanisms Using Flexural Joints

Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanisms are applicable. To construct more kinds of them, an approach to design large-displacement straight-line flexural mechanisms with rotational flexural joints is proposed, which is based on a viewpoint that the straight-line motion is regarded as a compromise of rigid and compliant parasitic motion of a rotational flexural joint. An analytical design method based on the Taylor series expansion is proposed to quickly obtain an approximate solution. To illustrate and verify the proposed method, two kinds of flexural joints, cross-axis hinge and leaf-type isosceles-trapezoidal flexural(LITF) pivot are used to reconstruct straight-line flexural mechanisms. Their performances are obtained by analytic and FEA method respectively. The comparisons of the results show the accuracy of the approach. Both examples show that the proposed approach can convert a large-deflection flexural joint into approximate straight-line mechanism with a high linearity that is higher than 5 000 within 5 mm displacement. This can lead to a new way to design, analyze or optimize straight-line flexure mechanisms.

A Family of Rotational Parallel Manipulators With Equal-Diameter Spherical Pure Rotation

In this work, a family of two degrees of freedom (2-DOF) rotational parallel manipulators (RPMs) with an equal-diameter spherical pure rotation (ESPR) is presented and discussed systematically. The theoretical models of both kinematics and constraints inherited in the manipulators are analyzed through a graphical approach. Based on the established constraint model, these 2-DOF ESPR RPMs are classified into three types according to their compositions of constraint spaces and several novel parallel manipulators are illustrated correspondingly. Finally, two common necessary geometric conditions satisfied for these manipulators are discussed in details with examples. The two conditions will be helpful for engineers with designing ESPR RPMs. Moreover, as one characteristic existing in the ESPR RPMs, two cases of self-rotations accompanying revolutions around fixed axes are revealed. As a result, the corresponding loci of points in the moving platform are proved to be compositions of two subrotations, which are spatial curves and surfaces rather than spherical curves and surfaces. [DOI: 10.1115/1.4025860]

Reconfiguration Analysis of a Two Degrees-of-Freedom 3-4R Parallel Manipulator With Planar Base and Platform

This paper deals with a 2-DOF (degrees-of-freedom) 3-4R parallel manipulator (PM) with planar base and platform—a novel PM with multiple operation modes (or disassembly free reconfigurable PM) that can use the minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM are derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler–Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace-based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R PM with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

Analytical Compliance Analysis and 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.