Automatic Synthesis of a Planar Linkage With a Stiffness-Varying Spring Connected Rigid Block Model

2007 ◽  
Author(s):  
Sang Jun Nam ◽  
Gang-Won Jang ◽  
Jung Hun Park ◽  
Jin Sub Hun ◽  
Yong Sub Yi ◽  
...  
Keyword(s):  
Minimization Problem ◽  
Variable Stiffness ◽  
Synthesis Process ◽  
Rigid Block ◽  
Linkage Mechanism ◽  
Block Model ◽  
Revolute Joints ◽  
Gradient Based ◽  
Input Motion ◽  
Linkage Model

A linkage mechanism is a device to convert an input motion into a desired motion in a machine or a robot. The traditional linkage synthesis practice is depended on the experience and intuition of the skilled designer. This practice based on trial and error approach or only size/shape changes of already-available mechanism often results in improper design. This observation has motivated us to develop a so-called “automatic” design methodology that determines the linkage type and dimensions during synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer. The main contribution of this research is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. This work shows how new idea works and verifies this new approach on the synthesis of the planar linkages consisting of links and revolute joints.

Automatic Synthesis of a Planar Linkage Mechanism With Revolute Joints by Using Spring-Connected Rigid Block Models

2006 ◽  
Vol 129 (9) ◽  
pp. 930-940 ◽  
Author(s):  
Yoon Young Kim ◽  
Gang-Won Jang ◽  
Jung Hun Park ◽  
Jin Sub Hyun ◽  
Sang Jun Nam
Keyword(s):  
Minimization Problem ◽  
Synthesis Method ◽  
Synthesis Process ◽  
Rigid Block ◽  
Linkage Mechanism ◽  
Block Model ◽  
Mechanism Synthesis ◽  
Revolute Joints ◽  
Planar Linkage Mechanism ◽  
Linkage Model

In traditional linkage design practice, a designer first decides the specific linkage type, such as a four- or six-bar linkage, and then varies the joint locations and link lengths until the designer finds the desired linkage. The objective of this research is to establish an automatic mechanism synthesis method that determines the linkage type and dimensions during the synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer. The main contribution of this investigation is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. Though mechanisms involving only revolute joints are investigated and the solved problems are relatively simple, the notion of the block model and the synthesis formulation in real variables are expected to give a different perspective on mechanism synthesis.

The Spring-Connected Rigid Block Model Based Automatic Synthesis of Planar Linkage Mechanisms: Numerical Issues and Remedies

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Sang Jun Nam ◽  
Gang-Won Jang ◽  
Yoon Young Kim
Keyword(s):  
Closed Loop ◽  
Synthesis Method ◽  
Direct Application ◽  
Rigid Block ◽  
Block Model ◽  
Automatic Synthesis ◽  
Open Path ◽  
Synthesis Of Mechanisms ◽  
Input Motion ◽  
Linkage Synthesis

Because it is difficult to select in advance an appropriate linkage for converting an input motion to a desired output motion, a linkage synthesis method that does not require any baseline linkage would be preferred. To this end, an optimization-based linkage synthesis method that employs a spring-connected rigid block model has recently been suggested and applied for open-path problems. The objective of this study is to expand the method for the synthesis of more complex linkage mechanisms such as closed-loop linkages. Because the direct application of the method originally developed for open-path problems causes several numerical difficulties for closed-loop problems, an alternative optimization-based synthesis formulation is proposed in this investigation. The effectiveness of the suggested formulation is verified through several case studies including the synthesis of mechanisms generating closed paths.

Design of a Two-Input Linkage-Based Motor

1996 ◽  
Author(s):  
Yassir Shanshal ◽  
Kambiz Farhang
Keyword(s):  
Design Methodology ◽  
Angular Motion ◽  
Dimensional Synthesis ◽  
Reciprocating Motion ◽  
Linkage Mechanism ◽  
Motion Synthesis ◽  
Small Motion ◽  
Motor Design ◽  
Input Motion ◽  
Approximate Equations

Abstract This paper proposes the use of a seven-bar linkage mechanism to obtain a multiply actuated motor. Design of two input mechanisms is presented involving two synthesis sub-tasks of input motion synthesis and dimensional synthesis. To this end a design methodology is presented based on the theory of small crank mechanisms. For the case of small motion, approximate equations are developed with the premise that as a result of small reciprocating motion of the input actuators, the motion of every link, with the exception of the output, is small. The motion, in turn, is expressed as a sum of an average and a small oscillatory angular motion about the average. A set of design equations are obtained from the approximate kinematic equations. The design methodology is exemplified using the synthesis of a seven-link mechanism with two translating inputs.

Simultaneous Shape and Topology Optimization of Planar Linkage Mechanisms Based on the Spring-Connected Rigid Block Model

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jeonghan Yu ◽  
Sang Min Han ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Simultaneous Optimization ◽  
Optimization Process ◽  
Rigid Block ◽  
Low Resolution ◽  
Block Model ◽  
Shape And Topology Optimization ◽  
Fixed Grid ◽  
Computation Efficiency ◽  
And Topology

Abstract Using the topology optimization can be an effective means of synthesizing planar rigid-body linkage mechanisms to generate desired motion, as it does not require a baseline mechanism for a specific topology. While most earlier studies were mainly concerned with the formulation and implementation of topology optimization-based synthesis in a fixed grid, this study aims to realize the simultaneous shape and topology optimization of planar linkage mechanisms using a low-resolution spring-connected rigid block model. Here, we demonstrate the effectiveness of simultaneous optimization over a higher-resolution fixed-grid rigid block-based topology optimization process. When shape optimization to change the block shapes is combined with topology optimization to synthesize the mechanism, the use of low-resolution discretized models improves the computation efficiency considerably and helps to yield compact mechanisms with less complexity, making them more amenable to fabrication. After verifying the effectiveness of the simultaneous shape and topology optimization process with several benchmark problems, we apply the method to synthesize a mechanism which guides a planar version of a human's gait trajectory.

Topology optimization of linkage mechanisms simultaneously considering both kinematic and compliance characteristics

2020 ◽  
pp. 1-51
Author(s):  
Sang Min Han ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Kinematic Chain ◽  
Variable Stiffness ◽  
Optimization Method ◽  
Vehicle Suspension ◽  
Linkage Mechanism ◽  
Mechanism Synthesis ◽  
Kinematic Characteristics ◽  
Mechanism Kinematic ◽  
Topology Optimization Method

Abstract Studies on the topology optimization of linkage mechanisms have thus far focused mainly on mechanism synthesis considering only kinematic characteristics describing a desired path or motion. Here, we propose a new topology optimization method that synthesizes a linkage mechanism considering not only kinematic but also compliance (K&C) characteristics simultaneously, as compliance characteristics can also significantly affect the linkage mechanism performance; compliance characteristics dictate how elastic components, such as bushings in a vehicle suspension, are deformed by external forces. To achieve our objective, we use the spring-connected rigid block model (SBM) developed earlier for mechanism synthesis considering only kinematic characteristics, but we make it suitable for the simultaneous consideration of K&C characteristics during mechanism synthesis by making its zero-length springs multifunctional. Variable-stiffness springs were used to identify the mechanism kinematic configuration only, but now in the proposed approach, they serve to determine not only the mechanism kinematic configuration but also the compliance element distribution. In particular, the ground-anchoring springs used to anchor a linkage mechanism to the ground are functionalized to simulate actual bushings as well as to identify the desired linkage kinematic chain. After the proposed formulation and numerical implementation are presented, case studies are considered. In particular, the effectiveness of the proposed method is demonstrated with a simplified two-dimensional vehicle suspension design problem. This study is expected to pave the way to advance the topology optimization method for general linkage mechanisms whenever K&C characteristics must be simultaneously considered for mechanism synthesis.

Application of the Exact Gradient Approach in Optimal Synthesis of Mechanisms

1993 ◽  
Author(s):  
Jawaharlal Mariappan ◽  
Sundar Krishnamurty
Keyword(s):  
Generalized Solution ◽  
Optimization Method ◽  
Solution Procedure ◽  
Optimal Synthesis ◽  
Synthesis Process ◽  
Mechanism Synthesis ◽  
Approximate Methods ◽  
Synthesis Of Mechanisms ◽  
Gradient Based ◽  
Gradient Approach

Abstract This paper presents the application of the unified exact gradient approach to optimal synthesis of mechanisms. The exact gradient approach is a systematic and efficient solution procedure that is applicable for any type of mechanism synthesis problem. In this approach, the exact gradients necessary for optimization are developed using a generalized solution procedure based on matrix methods. Availability of exact gradients in this approach enables the utilization of any gradient-based optimization method in mechanism synthesis process. As a result, this approach will be computationally most efficient, since it will not require direct search methods, or, finite difference approximate methods to find optimal solutions. These salient features of this approach are demonstrated with the aid of several mechanism problems and the results discussed.

scholarly journals Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part II—Numerations and Synthesis of Complex Flexible Joints

2010 ◽  
Author(s):  
J. J. Yu ◽  
X. Pei ◽  
S. Z. Li ◽  
Hai-jun Su ◽  
J. B. Hopkins ◽  
...  
Keyword(s):  
High Performance ◽  
Screw Theory ◽  
Companion Paper ◽  
Synthesis Process ◽  
Type Synthesis ◽  
Flexible Joints ◽  
Flexible Joint ◽  
Modeling And Analysis ◽  
Revolute Joints ◽  
Application Requirements

In recent years, the increasing of application requirements call for development of a variety of high-performance (e.g. large-displacement, high-precision) flexible joints. In this paper we demonstrate how to use the proposed methodology for the type synthesis of flexure systems given in the companion paper to synthesize concepts for complex flexible joints. According to the joint characteristics other than other flexure systems, a basic design philosophy and a general type synthesis process for flexible joints are presented firstly. The numerations and type synthesis for four commonly used flexible joint types, i.e. flexible revolute joints (FRJs), flexible translational joints (FTJs), flexible universal joints (FUJs), and flexible spherical joints (FSJs) are investigated in detail. As a result, not only a variety of known flexible joints are systematically surveyed and classified, but also are some new flexible joints developed. The output of this process is the derivation of a multiple of flexible joint concepts that would then be modeled and optimized by existing modeling and analysis methods.

scholarly journals Initiation, movement, and run-out of the giant Tsaoling landslide — What can we learn from a simple rigid block model and a velocity–displacement dependent friction law?

2014 ◽  
Vol 182 ◽  
pp. 158-181 ◽  
Author(s):  
Che-Ming Yang ◽  
Wei-Lun Yu ◽  
Jia-Jyun Dong ◽  
Chih-Yu Kuo ◽  
Toshihiko Shimamoto ◽  
...  
Keyword(s):  
Rigid Block ◽  
Block Model ◽  
Friction Law

Designing Variable-Geometry Extrusion Dies That Utilize Planar Shape-Changing Rigid-Body Mechanisms

2015 ◽  
Author(s):  
Bingjue Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Rigid Body ◽  
Cross Sections ◽  
Synthesis Process ◽  
Variable Geometry ◽  
Extrusion Dies ◽  
Geometry Design ◽  
Revolute Joints ◽  
Planar Shape ◽  
Fixed Line ◽  
Synthesis Methodology

This paper presents a kinematic synthesis methodology for planar shape-changing rigid-body mechanisms that addresses constraints arising in the design of variable-geometry polymer extrusion dies. Such a die is capable of morphing its orifice in order to create extrusions of non-constant cross section. A variable-geometry shape-changing die problem is defined by a set of design profiles of different shapes and arc lengths, which approximate various cross sections of the extrusion. The primary advantage of the presented methodology is addressing the need for bodies in the mechanism formed by fusing links in the shape-changing portion of the chain. Previous methodologies included such fused links, but only at the end of the synthesis process where revolute joints were seen to be underutilized. A new method is needed to control, or even eliminate the use of revolute joints in the shape-changing chain of rigid links. The result of this new work is an iterative method which generates an optimized morphing chain to best match the design profiles while minimizing the number of prismatic and revolute joints needed to do so. The additional variable-geometry design constraints also require a generalization to the definition of fixed-end profiles previously proposed, also allowing chain ends to be defined by prismatic joints on a fixed line of slide. A virtual-chain method is also proposed to solve closure problems caused by the reduction in the number of revolute joints.

A Rolling 8-Bar Linkage Mechanism

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Yaobin Tian ◽  
Yan-An Yao ◽  
Jieyu Wang
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Rolling Direction ◽  
Linkage Mechanism ◽  
Zero Moment Point ◽  
Revolute Joints ◽  
Straight Line ◽  
Polygonal Region ◽  
Zero Moment

In this paper, a rolling mechanism constructed by a spatial 8-bar linkage is proposed. The eight links are connected with eight revolute joints, forming a single closed-loop with two degrees of freedom (DOF). By kinematic analysis, the mechanism can be deformed into planar parallelogram or spherical 4-bar mechanism (SFM) configuration. Furthermore, this mechanism can be folded onto a plane at its singularity positions. The rolling capability is analyzed based on the zero-moment-point (ZMP) theory. In the first configuration, the mechanism can roll along a straight line. In the second configuration, it can roll along a polygonal region and change its rolling direction. By alternatively choosing one of the two configurations, the mechanism has the capability to roll along any direction on the ground. Finally, a prototype was manufactured and some experiments were carried out to verify the functions of the mechanism.

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