Synthesis of Watt II Mechanisms for Four Simultaneous Positions

2015 ◽  
Author(s):  
Pierre Larochelle ◽  
Jugesh Sundram ◽  
Ronald A. Zimmerman
Keyword(s):  
Algebraic Geometry ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Generation Task ◽  
Kinematic Synthesis ◽  
Synthesis Algorithm ◽  
Relative Angle ◽  
Synthesis Technique ◽  
Two Bodies

This article presents the kinematic synthesis of Watt II six-bar mechanisms for simultaneously guiding two bodies through four prescribed positions. The two bodies to be moved are connected by a revolute joint and the motion generation task is defined by the four desired positions of one body and the relative angle of the second body with respect to the first body. The methodology uses an algebraic geometry formulation of the exact synthesis of planar RR dyads for four prescribed positions from classical Burmester theory. The result is a dimensional synthesis technique for designing Watt II mechanisms for four simultaneous positions. A case study illustrating the application of the synthesis algorithm is included.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Locations

2013 ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyads rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed locations to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain; also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. An example that demonstrates the synthesis technique is included.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Positions

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Pick And Place ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyad's rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed positions to yield designs that exactly reach the prescribed pick and place positions while approximating an arbitrary number of guiding positions. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain, also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on elements of SE(2); the group of planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. Two examples that demonstrate the synthesis technique are included.

Design of Graphical User Interfaces for the Synthesis of Planar RR Dyads

2014 ◽  
Author(s):  
Jugesh Sundram ◽  
Venkatesh Venkataramanujam ◽  
Pierre Larochelle
Keyword(s):  
Case Studies ◽  
User Interfaces ◽  
Graphical User Interfaces ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Mechanism Synthesis ◽  
Generation Task ◽  
Design And Implementation ◽  
Design Case ◽  
Hybrid Motion

This article discusses the design and implementation of two Matlab graphical user interfaces (GUIs) for mechanism synthesis. The first GUI addresses the four location Burmester synthesis problem. The designer specifies the 4 locations that are used to generate the Burmester curves for these prescribed locations. The GUI enables the designer to interact with these curves and choose a pair of moving and fixed pivots forming an RR dyad. The second GUI addresses dimensional synthesis of RR dyads for hybrid motion generation tasks. Given a hybrid motion generation task, the designer can either pick the fixed or moving pivots and the corresponding pivots of an RR dyad is determined. In both the interfaces, the designer is provided with tools to specify tasks. The GUIs were designed with an objective to provide the designer with a simple workflow. Design case studies that illustrate the features and capabilities of each GUI are included.

MotionGen: Interactive Design and Editing of Planar Four-Bar Motions for Generating Pose and Geometric Constraints

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Anurag Purwar ◽  
Shrinath Deshpande ◽  
Q. J. Ge
Keyword(s):  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Unified Framework ◽  
Synthesis Algorithm ◽  
Approximate Synthesis ◽  
High Utility ◽  
High Level ◽  
Generation Problem ◽  
Practical Constraints

In this paper, we have presented a unified framework for generating planar four-bar motions for a combination of poses and practical geometric constraints and its implementation in MotionGen app for Apple's iOS and Google's Android platforms. The framework is based on a unified type- and dimensional-synthesis algorithm for planar four-bar linkages 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 in an intuitive fashion while providing high-level, rich options to enforce practical constraints. It is done 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 framework also admits a plurality of practical geometric constraints, such as imposition of fixed and moving pivot and line locations along with mixed exact and approximate synthesis scenarios.

A New Method of Task Specification for Spherical Mechanism Design

1998 ◽  
Author(s):  
David M. Tse ◽  
Pierre M. Larochelle
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Motion Generation ◽  
Generation Task ◽  
Finite Set ◽  
Novel Method ◽  
Task Specification ◽  
Design Case Study ◽  
Spherical Mechanism

Abstract In this paper we present a novel method for motion generation task specification for spherical mechanisms. This is accomplished with a new methodology for determining the optimal design sphere and the orientations on this design sphere for a finite set of desired spatial positions. In addition, we include a modification to the method which enables the designer to require that one of the n desired spatial positions be exactly preserved. The result is that designers can now specify spherical mechanism motion generation tasks without having to introduce into the design space an artificial design sphere. They are now free to work in unconstrained three-dimensional space. The application of this new task specification technique is discussed in a design case study.

Computer Simulation of Path and Motion Generation With Six-Bar Linkage

2003 ◽  
Author(s):  
Lu Yi ◽  
Tatu Leinonen
Keyword(s):  
Computer Simulation ◽  
Analytical Calculation ◽  
Geometric Constraint ◽  
Simulation Approach ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Basic Tool ◽  
Kinematic Synthesis ◽  
Four Bar Linkage ◽  
Accuracy And Repeatability

The basic tool of path or motion generation synthesis for more than four prescribed positions is analytical calculation, but its process is quite complicated and far from straightforward. A novel computer simulation mechanism of six-bar linkage for path or motion generation synthesis is presented in this paper. In the case of five-precision points, using the geometric constraint and dimension-driving techniques, a primary simulation mechanism of four-bar linkage is created. Based on the different tasks of path and motion generation for kinematic dimensional synthesis, the simulation mechanisms of path and motion generation with Stephenson I, II and Watt six-bar linkages are developed from the primary simulation mechanism. The results of kinematic synthesis for five prescribed positions prove that the mechanism simulation approach is not only fairly quick and straightforward, but is also advantageous from the viewpoint of accuracy and repeatability.

scholarly journals Hybrid Seven-bar Press Mechanism

2018 ◽  
Vol 12 (3) ◽  
pp. 181-187
Author(s):  
M. Erkan Kütük ◽  
L. Canan Dülger
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Design Optimization ◽  
Hybrid System ◽  
Degrees Of Freedom ◽  
Dimensional Synthesis ◽  
Design Variables ◽  
Optimization Study ◽  
Metal Stamping

An optimization study with kinetostatic analysis is performed on hybrid seven-bar press mechanism. This study is based on previous studies performed on planar hybrid seven-bar linkage. Dimensional synthesis is performed, and optimum link lengths for the mechanism are found. Optimization study is performed by using genetic algorithm (GA). Genetic Algorithm Toolbox is used with Optimization Toolbox in MATLAB®. The design variables and the constraints are used during design optimization. The objective function is determined and eight precision points are used. A seven-bar linkage system with two degrees of freedom is chosen as an example. Metal stamping operation with a dwell is taken as the case study. Having completed optimization, the kinetostatic analysis is performed. All forces on the links and the crank torques are calculated on the hybrid system with the optimized link lengths

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation

1999 ◽  
Vol 123 (4) ◽  
pp. 535-541 ◽  
Author(s):  
L. Saggere ◽  
S. Kota
Keyword(s):  
Compliant Mechanisms ◽  
Shape Change ◽  
Synthesis Method ◽  
Elastic Equilibrium ◽  
Body Motion ◽  
Motion Generation ◽  
Generation Task ◽  
Potential Applications ◽  
Flexible Segment ◽  
Definition Of

Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

Geometric Design of Symmetric 3-RRS Constrained Parallel Platforms

2004 ◽  
Author(s):  
Eric Wolbrecht ◽  
Hai-Jun Su ◽  
Alba Perez ◽  
J. Michael McCarthy
Keyword(s):  
Geometric Design ◽  
Homotopy Continuation ◽  
Total Degree ◽  
Polynomial Equations ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
Real Solutions ◽  
Parallel Platform ◽  
Three Degree Of Freedom ◽  
Serial Chains

The paper presents the kinematic synthesis of a symmetric parallel platform supported by three RRS serial chains. The dimensional synthesis of this three degree-of-freedom system is obtained using design equations for each of three RRS chains obtained by requiring that they reach a specified set of task positions. The result is 10 polynomial equations in 10 unknowns, which is solved using polynomial homotopy continuation. An example is provided in which the direction of the first revolute joint (2 parameters) and the z component of the base and platform are specified as well as the two task positions. The system of polynomials has a total degree of 4096 which means that in theory it can have as many solutions. Our example has 70 real solutions that define 70 different symmetric platforms that can reach the specified positions.

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