Initial Estimates in the Design of Rack-and-Pinion Steering Linkages

2000 ◽  
Vol 122 (2) ◽  
pp. 194-200 ◽  
Author(s):  
P. A. Simionescu ◽  
M. R. Smith
Keyword(s):  
Synthesis Method ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Minimum Pressure ◽  
Pressure Angle ◽  
Early Stages ◽  
Design Charts

Based on recent results concerning the occurrence of function cognates in Watt II linkages, it is shown that only 3 geometric parameters are sufficient for defining the kinematic function of simplified planar rack-and-pinion steering linkages. The steering performances of the mechanisms are analytically expressed in terms of these parameters and, by employing an optimization-based synthesis method involving increasing the degree of freedom of the mechanism, the optimum domains are determined. The parameter sets corresponding to these minimum steering error domains are displayed in design charts. These charts aid the automotive engineer in the early stages of conceiving a new steering linkage by providing initial estimates of the basic geometry of the mechanism. They also provide information on two other characteristics of concern, i.e. the minimum pressure angle occurring in the joints and the rack stroke required for maximum turn of the wheels. [S1050-0472(00)00402-5]

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

A Novel Synthesis Method of Polygon-Scaling Mechanisms

2014 ◽  
Author(s):  
Guochao Bai ◽  
Shimin Wei ◽  
Duanling Li ◽  
Qizheng Liao ◽  
Xianwen Kong
Keyword(s):  
Synthesis Method ◽  
3D Models ◽  
Degree Of Freedom ◽  
Straightforward Manner ◽  
Novel Synthesis

A polygon-scaling mechanism is a single DOF (degree-of-freedom) mechanism for scaling a polygon. This paper presents a tetragon-elements based synthesis method of polygon-scaling mechanisms. According to movable conditions of radial scaling elements, four basic tetragon elements (rhombus element, parallelogram element, kite element and general tetragon element) are proposed. For a given polygon, these four types of elements can be selected based on the characteristics of target polygons to construct polygon-scaling mechanisms in a straightforward manner. Using this synthesis method, some planar 1-DOF scaling mechanisms are obtained with the characteristics of retracting and deploying. Their 3D models are also presented to proof the validity of the proposed method. Finally, a table of tetragon elements with the characteristics of their associated polygon-scaling mechanisms is summarized using which polygon-scaling mechanisms can be easily constructed.

Synthesis of multi-input multi-degree-of-freedom fixed shaft gear transmission configuration for vehicles

2021 ◽  
pp. 095440702110652
Author(s):  
Xueliang Li ◽  
Zhihang Wu ◽  
Shujun Yang ◽  
Jibin Hu ◽  
Zengxiong Peng
Keyword(s):  
Electric Vehicles ◽  
Rapid Development ◽  
Synthesis Method ◽  
Theory Model ◽  
Gear Transmission ◽  
Degree Of Freedom ◽  
Speed Ratio ◽  
Multiple Parameters ◽  
Transmission Mechanisms ◽  
Derivation Method

The rapid development of dual-clutch transmission (DCT) and hybrid and purely electric vehicles stimulate the researches on multi-input fixed shaft gear transmission mechanisms. The multiple degree-of-freedom (DOF) transmission mechanism can achieve a wider range of speed ratio adjustment and more modes under certain space and weight constraints, which is an ideal choice for multi gear transmission. In this paper, a synthesis method of fixed shaft gear transmission configuration is proposed. Based on the established graph theory model, kinematic characteristics of the fixed shaft gear transmission configuration are studied and the shift sequence is determined. Using these characteristics, a derivation method from the basic configuration to the comprehensive gears and shafts configuration is proposed. Multiple parameters such as the synchronizer arrangement and speed ratios are optimized. Finally, the proposed method is vigorously verified by a seven-speed DCT with four DOFs. This method is comprehensive and systematic in designing fixed shaft gear transmission configurations, which can be applied to DCT, transmissions for parallel hybrid electric vehicles, and to some novel multi-input transmissions.

Solution Region Synthesis Method for Six Positions Synthesis of 5-SS Spatial Linkage

2016 ◽  
Author(s):  
Jianyou Han ◽  
Guangzhen Cui ◽  
Junjie Hu
Keyword(s):  
Systematic Approach ◽  
Synthesis Method ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Region Method ◽  
Solution Region ◽  
The One

This paper presents a systematic approach to perform the dimensional synthesis of spatial 5-SS (spherical-spherical) link-ages for six specified positions of the end-effector. The dimensional synthesis equations for a SS link are formulated and solved. We synthesize five SS links to connect the base and end-effector, and then obtain the one-degree-of-freedom spatial 5-SS linkage, which can move through six specified positions. We use the solution region method to build the planar solution region expressing the linkages, due to there are infinite linkages for six positions synthesis. It is convenient to select the linkages from the solution region for designers. The applicability of the proposed approach is illustrated by the example.

Geometric Design of a Bio-Inspired Flapping Wing Mechanism Based on Bennett-Derived 6R Deployable Mechanisms

2014 ◽  
Author(s):  
Huang Hailin ◽  
Li Bing
Keyword(s):  
Flapping Wing ◽  
Geometric Design ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Flapping Motion ◽  
Single Degree ◽  
Revolute Joints ◽  
Air Vehicle ◽  
Deployable Mechanism

In this paper, we present the concept of designing flapping wing air vehicle by using the deployable mechanisms. A novel deployable 6R mechanism, with the deploying/folding motion of which similar to the flapping motion of the vehicle, is first designed by adding two revolute joints in the adjacent two links of the deployable Bennett linkage. The mobility of this mechanism is analyzed based on a coplanar 2-twist screw system. An intuitive projective approach for the geometric design of the 6R deployable mechanism is proposed by projecting the joint axes on the deployed plane. Then the geometric parameters of the deployable mechanism can be determined. By using another 4R deployable Bennett connector, the two 6R deployable wing mechanisms can be connected together such that the whole flapping wing mechanism has a single degree of freedom (DOF).

Research on the Configurations and Singularity of Serial-Parallel Mechanism

2011 ◽  
Vol 393-395 ◽  
pp. 265-268
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Synthesis Method ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Spatial Mobility

Methods to analysis the DOF(degree of freedom) and singularity of pure serial and pure parallel manipulator, which can not be used to the serial-parallel manipulator directly, three type of practical topological units and one type of virtual topological unit adopted, Synthesis method of topological dimensionality of the spatial mobility of each topological unit integrated together, architectures of serial-paralle mechanism discussed, also the formula and process of its topological dimensionality of spatial mobility presented, singularity analysis of serial-parallel mechanism can be carried out based on the forgoing results.

scholarly journals Configuration synthesis of electric-drive transmissions for tracked vehicles

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774966
Author(s):  
Ming-Fei Gao ◽  
Ji-Bin Hu ◽  
Zeng-Xiong Peng
Keyword(s):  
Graph Theory ◽  
Electric Drive ◽  
Synthesis Method ◽  
Theory Model ◽  
Degree Of Freedom ◽  
Transmission Mechanism ◽  
Necessary Condition ◽  
Tracked Vehicles ◽  
Configuration Synthesis ◽  
Complex Transmission

This article focus on the configuration synthesis of electric-drive transmissions for tracked vehicles. First, a new graph theory model is proposed to represent the transmission mechanism, which makes the complex transmission system easier to understand. Second, a configuration synthesis method is proposed based on kinematics and statics, in which the speed degree of freedom and torque degree of freedom are considered as the constraints of configuration synthesis. Also, the expressions for speed degree of freedom and torque degree of freedom are derived. Third, based on the graph theory model, the necessary condition to achieve skid steering in the transmission of tracked vehicles is obtained. The results of this article can provides a theoretical basis for the design and analysis of transmission mechanism of tracked vehicles.

Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 232-241 ◽  
Author(s):  
Xichun Nie ◽  
Venkat Krovi
Keyword(s):  
Low Cost ◽  
Synthesis Method ◽  
Path Following ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Serial Chain ◽  
End Effectors ◽  
Serial Chains

Single degree-of-freedom coupled serial chain (SDCSC) mechanisms are a class of mechanisms that can be realized by coupling successive joint rotations of a serial chain linkage, by way of gears or cable-pulley drives. Such mechanisms combine the benefits of single degree-of-freedom design and control with the anthropomorphic workspace of serial chains. Our interest is in creating articulated manipulation-assistive aids based on the SDCSC configuration to work passively in cooperation with the human operator or to serve as a low-cost automation solution. However, as single-degree-of-freedom systems, such SDCSC-configuration manipulators need to be designed specific to a given task. In this paper, we investigate the development of a synthesis scheme, leveraging tools from Fourier analysis and optimization, to permit the end-effectors of such manipulators to closely approximate desired closed planar paths. In particular, we note that the forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. The proposed Fourier-based synthesis method exploits this special structure to achieve the combined number and dimensional synthesis of SDCSC-configuration manipulators for closed-loop planar path-following tasks. Representative examples illustrate the application of this method for tracing candidate square and rectangular paths. Emphasis is also placed on conversion of computational results into physically realizable mechanism designs.

Rigid Foldability of Triangle-Twist Origami Pattern and its Derived 6R Linkage

2017 ◽  
Author(s):  
Rui Peng ◽  
Jiayao Ma ◽  
Yan Chen
Keyword(s):  
Theoretical Method ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Space Structures ◽  
Engineering Applications ◽  
Systematic Method ◽  
Mountain Valley ◽  
Folding Pattern ◽  
Spatial Linkages ◽  
Spherical Linkages

Rigid origami is an important subset of origami with broad engineering applications from space structures to metamaterials. The rigid foldability of an origami pattern is determined by both the geometric parameters and the mountain-valley crease assignment. In this paper, by using the equivalent relationships between origami vertices and spherical linkages, a systematic method was proposed to analyze the motion of the triangle-twist pattern with varying distribution of mountain and valley creases, and its rigid folding types were identified. Moreover, kirigami technology was applied to the rigid folding pattern without changing its degree of freedom, from which a new kind of overconstrained 6R linkage was developed. The theoretical method proposed in this paper can be readily extended to study other types of origami patterns, which will in turn help to design structures with large deployable ratio as well as some new spatial linkages.

Research on Minimum Pressure Angle of Bennett Linkage

2019 ◽  
Author(s):  
Lele Bai ◽  
Lubin Hang ◽  
Xiaobo Huang ◽  
Mingyuan Wang ◽  
Ziyu Liu
Keyword(s):  
Twist Angle ◽  
Kinematic Model ◽  
Analytic Formula ◽  
Geometric Meaning ◽  
Output Link ◽  
Deployable Structures ◽  
Minimum Pressure ◽  
Pressure Angle ◽  
Important Index ◽  
Space Deployable Structures

Abstract Space deployable structures that are constructed by the single loop over-constrained linkages have been extensively applied in the fields of aerospace and construction. The pressure angle regarded as an important index to measure the performance of the basic units has attracted more and more attention. The kinematic model of the Bennett linkage is studied by the D-H matrix and the analytic formula of the pressure angle has been deducted through kinematic equations. The rule of the Bennett linkage has been discovered that the minimum pressure angle occurs while the input angle equals nπ + π / 2(n ∈ N). According to the linkage configuration at the input angle of π / 2, the geometric meaning is revealed that the minimum pressure angle of the linkage is the same as the twist angle of the joint axes of the output link. Finally, conclusions can also be drawn that the smaller the twist angle of the output link is, the smaller the minimum pressure angle will be. The research enriches the kinematics of Bennett linkage and provides a reference for its engineering applications.

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