Finite Position Synthesis of 5-SS Platform Linkages Including Partially Specified Joint Locations

2017 ◽  
Author(s):  
Xin Ge ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Linear Structure ◽  
Motion Generation ◽  
Numerical Examples ◽  
Moving Points ◽  
Unified Algorithm ◽  
Moving Platform ◽  
Position Synthesis ◽  
Partial Specification ◽  
Generation Problem ◽  
Novel Algorithm

A 5-SS platform linkage generates a one-degree-of-freedom motion of a moving platform such that each of five moving points on the platform is constrained on a sphere, or in its degenerated case, on a plane. It has been well established a 5-SS platform linkage can be made to guide though seven positions exactly. This paper investigates the cases when the number of given positions are less than seven that allows for partial specification of locations of the moving points. A recently developed novel algorithm with linear structure in the design equations has been extended for the solution of the problem. The formulation of this expanded motion generation problem unifies the treatment of the input positions and constraints on the moving and fixed joints associated with the 5-SS platform linkage. Numerical examples are provided to show the effectiveness of the unified algorithm.

From 5-SS Platform Linkage to Four-Revolute Jointed Planar, Spherical and Bennett Mechanisms

2016 ◽  
Author(s):  
Xin Ge ◽  
A. Purwar ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Examples ◽  
Revolute Joints ◽  
Novel Approach ◽  
Design Variables ◽  
Moving Points ◽  
Unified Algorithm ◽  
Three Dimensional Space

Recently, we developed a novel approach to the problem of geometric design of 5-SS platform linkages such that its moving points are constrained on a sphere or a plane. Dual quaternions are used to obtain the bilinear design equations with seven design variables, which can be further recast into a linear equation with 16 design variables with a set of simple proportional relationships. This leads to a novel algorithm that reduces the kinematic design problem to that of null space analysis followed by a generalized eigenvalue problem. In this paper, we show that the same approach leads to a unified algorithm for synthesizing planar, spherical and spatial Bennet mechanisms with four revolute joints as over-constrained four-revolute jointed mechanisms in three dimensional space. Numerical examples are given in the end.

MotionGen: An iOS and Android App for Planar Four-Bar Motion Generation

2016 ◽  
Author(s):  
Anurag Purwar ◽  
Shrinath Deshpande ◽  
Q. J. Ge
Keyword(s):  
Rigid Bodies ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Unified Framework ◽  
Approximate Synthesis ◽  
Unified Algorithm ◽  
Android App ◽  
Google Android ◽  
High Utility ◽  
Generation Problem

MotionGen is an indigenously developed app for Apple iOS and Google Android platforms to help mechanism designers solve planar four-bar motion generation problem. The app is a computer implementation of authors’ recent work in developing a unified framework for the synthesis and simulation of planar four-bar mechanisms for the motion generation problem. Simplicity, high-utility, and wide-spread adoption of planar four-bar linkages have made them one of the most studied topics in Kinematics leading to development of algorithms and theories that deal with path-, function-, and motion generation-problems. Yet to date, there have been no attempts to develop efficient computational algorithms amenable to real-time computation of both type and dimensions of planar four-bar mechanisms for a given motion. MotionGen solves this problem effectively by extracting the geometric constraints of a given motion to provide the best dyad-types as well as dimensions of a total of up to six four-bar linkages. The unified algorithm also admits additional practical constraints, such as imposition of fixed- and moving-pivot and -line locations along with mixed exact- and approximate-synthesis scenarios. In that regard, its synthesis capabilities set it apart from other softwares of its ilk. However, its simulation approach also departs from more traditional methods, which typically involves assembling four rigid bodies and then designating fixed and moving links. Instead, the MotionGen requires users to assemble only two of the geometric constraints of mechanical dyads for quick prototyping of planar four-bar linkages. The app is equipped with an intuitive graphical user interface that allows a fluid dialog with the user to facilitate rapid manipulation and visualization of linkages.

Patterned Bootstrap: A New Method That Gives Efficiency for Some Precision Position Synthesis Problems

2006 ◽  
Vol 129 (2) ◽  
pp. 173-183 ◽  
Author(s):  
Zhenjun Luo ◽  
Jian S. Dai
Keyword(s):  
Complete Solution ◽  
Systems Of Equations ◽  
Motion Generation ◽  
Underdetermined Systems ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Convergence Method ◽  
Position Synthesis ◽  
Generation Problem ◽  
Methods Numerical

This paper presents a heuristic global convergence method, termed as patterned bootstrap (PB), for solving systems of equations. In the PB method, multiple directions starting from a given point are searched. A number of intermediate underdetermined systems are selected and solved sequentially using classic globally convergence methods. Numerical experiments demonstrate that the PB method outperforms Levenberg-Marquardt method on solving a number of challenging synthesis problems in no more than 18 variables. On the other hand, Levenberg-Marquardt method normally outperforms the PB method on solving several systems of equations in 30 variables which are derived from the five precision-position motion generation problem of spatial RRR manipulators. In the paper, tunneling functions are also introduced to exclude degenerated solution sets in several synthesis problems. The research reveals that appropriate numerical methods and synthesis equations can be chosen for obtaining most solutions efficiently and provide a complete solution set of a precision position synthesis problem within a domain of interest.

A Novel Synthesis Method for Three-Position Motion Generation With Planar Four-Bar Mechanisms

2012 ◽  
Author(s):  
Jianyou Han ◽  
Tong Yang
Keyword(s):  
Synthesis Method ◽  
Solution Space ◽  
The Other ◽  
Motion Generation ◽  
Numerical Examples ◽  
Novel Synthesis ◽  
Generation Problem

This paper deals with the three-position motion generation problem with two specific grounded link lengths. There are two infinities of solutions for selecting the two links on the derived contours of the link lengths. These points on the contours are circle points or center points. After one half of the basic four bar had been selected on the contour, two infinities of solutions remained. These solutions can be mapped in a plane to determine where the particular types of mechanisms occur. Furthermore after one half of the basic four bar had been selected on the contour, one infinity of solutions still remained on the other contour. This indicates two infinities of solutions are still remained for the two given link lengths. These contours can be displayed in the solution space in which the motion generation is defined. With these significant useful information the better mechanism can be obtained, which satisfies more design conditions. Expressions of the contours are derived. Two numerical examples are used for illustration, but the results can be applied to any three-position motion generation problem.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

Synthesis of Linkages to Generate Specified Histories of Forces and Torques: The Planar 4R Four-Bar Mechanism

1987 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Return Time ◽  
Synthesis Process ◽  
Synthesis Methods ◽  
Multiplication Factor ◽  
Optimum Synthesis ◽  
Torque Generation ◽  
Gear Drives ◽  
Position Synthesis ◽  
Internal Gear ◽  
Generation Problem

Abstract Analytical precision position and optimum synthesis methods for linkages to generate specified force and torque histories are presented and applied to the planar four-bar mechanism. Mechanical advantage method (MAM) and integration of power equilibrium method (IPEM) are used to develop design equations. MAM yields design equations to use when the torque multiplication factor is defined at discrete number of design positions, as well as in continuous forms. IPEM requires continuous forms, but it reduces the torque generation problem into a function generation problem. Design equations with one, two, three, and four unknowns are developed for precision position synthesis; and they are used to formulate optimum synthesis process using many design positions that requires no iteration. Generation of infinite torque multiplication factor and synthesis of quick-return four-bar mechanism to generate specified advance-to-return time ratio are also considered. The synthesized four-bar mechanisms replace circular and non-circular external and internal gear drives. Several industrial application examples are included. The second part of the article considers the slider-crank mechanism.

Elimination of Branch, Grashof, and Order Defects in Path-Angle Generation and Function Generation Synthesis

1979 ◽  
Vol 101 (3) ◽  
pp. 428-437 ◽  
Author(s):  
K. J. Waldron ◽  
E. N. Stevensen
Keyword(s):  
Motion Generation ◽  
Function Generation ◽  
And Function ◽  
Generation Problem

Path-Angle Generation and Function Generation synthesis problems are restated as Plane-Position (or Motion Generation) problems, enabling the use of the classical Burmester technique and recent extensions that permit the avoidance of Branch, Grashof, and Order defects. An example of the solution of a Path-Angle Generation problem is given.

Approximate Velocities in Mixed Exact-Approximate Position Synthesis of Planar Mechanisms

1999 ◽  
Vol 123 (3) ◽  
pp. 388-394 ◽  
Author(s):  
Jennifer E. Holte ◽  
Thomas R. Chase ◽  
Arthur G. Erdman
Keyword(s):  
Two Dimensional ◽  
Computer Implementation ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Form Complex ◽  
New Approach ◽  
Realistic Representation ◽  
Velocity Constraints ◽  
Position Synthesis ◽  
Exact Positions

A new approach to the synthesis of planar linkage mechanisms with approximate velocity constraints is proposed. The paper presents the first closed-form complex-number dyad solution to the ground pivot specification problem for two precision positions with velocity specified at one of the positions. The solution is then manipulated in order to add approximate velocity constraints to design methods for two exact positions and an unlimited number of approximate positions. The approximate position and velocity constraints facilitate more realistic representation of design objectives. Solution spaces are presented using two-dimensional ground-pivot maps. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation.

Synthesis and analysis of spatial CS-3SS mechanism for body guidance

2015 ◽  
Vol 229 (13) ◽  
pp. 2455-2466
Author(s):  
Wen-Yeuan Chung
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Kinematic Chain ◽  
Spherical Joint ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Cylindrical Joint ◽  
Input Parameters ◽  
Three Stages ◽  
Moving Platform

This work presents a new spatial mechanism for three-dimensional body guidance. The moving platform of this mechanism is supported by a C–S leg and three S–S legs. Driving unit is the cylindrical joint and has two input parameters. The strategy for synthesizing the C–S leg is proposed and at most eight positions of the spherical joint can be prescribed, while at most seven positions can be prescribed in designing each S–S leg. This CS-3SS mechanism can thus be synthesized by prescribing at most seven precision poses. For this multi-loop spatial mechanism, both noticeable works that are the analysis of configurations and strategy for evaluating branch defects are carried out. The mechanism by giving two inputs has zero degrees of freedom and is analogous to a spherical kinematic chain with five links. At most eight configurations can be obtained and the criterion of double configurations is derived successfully. These results are based on to develop the strategy for evaluating branch defects. This strategy has three stages which are calculating the values of criteria, checking properties of other branches and final verification. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the proposed mechanism.

Sign in / Sign up

Export Citation Format

Share Document