Link Length Bounds on the Four-Bar Chain

1971 ◽  
Vol 93 (1) ◽  
pp. 287-293 ◽  
Author(s):  
P. W. Eschenbach ◽  
D. Tesar
Keyword(s):  
Algebraic Curve ◽  
Inequality Constraints ◽  
Kinematic Chain ◽  
Bounded Region ◽  
Practical Application ◽  
Link Length ◽  
Chain Link ◽  
Transmission Angle

The four-link kinematic chain is studied in an effort to establish a bounded region to limit the chain link lengths based upon transmission angle inequality constraints. The resulting constraint limitations are displayed graphically with the chain and their algebraic curve properties are delineated. Simple approximations of these complex loci are developed to facilitate practical application.

Optimization of Dynamic Forces in the Design of Mechanical Hands

1989 ◽  
Author(s):  
M. A. Nahon ◽  
J. Angeles
Keyword(s):  
Equations Of Motion ◽  
Inequality Constraints ◽  
Kinematic Chain ◽  
Programming Approach ◽  
Quadratic Optimization Problem ◽  
System A ◽  
Redundantly Actuated ◽  
Internal Forces ◽  
Constrained Quadratic Optimization ◽  
Mechanical Hands

Abstract Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated design analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize ‘internal forces’ A technique is proposed for smoothing the discontinuities in the force solution which occur when the toplogy changes.

Optimization of Dynamic Forces in Mechanical Hands

1991 ◽  
Vol 113 (2) ◽  
pp. 167-173 ◽  
Author(s):  
M. A. Nahon ◽  
J. Angeles
Keyword(s):  
Equations Of Motion ◽  
Inequality Constraints ◽  
Kinematic Chain ◽  
Programming Approach ◽  
Quadratic Optimization Problem ◽  
System A ◽  
Redundantly Actuated ◽  
Internal Forces ◽  
Constrained Quadratic Optimization ◽  
Mechanical Hands

Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints, and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize “internal forces.” A technique is proposed for smoothing the discontinuities in the force solution which occur when the topology changes.

Innovation Synthesis of Basic Configurationof Epicyclic Gear Trains with Three-Degrees of Freedom

2011 ◽  
Vol 199-200 ◽  
pp. 358-364
Author(s):  
Heng Bin Ren ◽  
Mao Lin Huang
Keyword(s):  
Degrees Of Freedom ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Practical Application ◽  
New Approach ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Train System ◽  
Three Degrees Of Freedom ◽  
Basic Configuration

Epicyclical gear trains with three-degrees of freedom have found its wide application as the development of new technique. Currently, nearly all domestic researches on epicyclical gear trains with three or more degrees of freedom are aimed at the practical application, and scare works systematically investigate basic configuration and synthesis of the train system. An innovation synthesis method is proposed based on the compound joint kinematic chain and the substitution of low pair with high pair for epicyclical gear trains with three-degrees of freedom, and the possible independent basic configurations of epicyclical gear trains with three-degrees of freedom are obtained by applying the proposed method and the utilization of the method is also discussed. The method provides not only a new approach for innovation synthesis of epicyclical gear trains but also a few basic configurations of epicyclical gear trains with three-degrees of freedom for practice design.

Evolutionary Design of Planar Kinematic Chains

1998 ◽  
Author(s):  
David R. Nielsen ◽  
Kazem Kazerounian
Keyword(s):  
Genetic Algorithm ◽  
Kinematic Chain ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Design Flexibility ◽  
Novel Approach ◽  
Chain Link ◽  
Synthesis Of Mechanisms ◽  
New Ideas ◽  
Crossover And Mutation

Abstract A procedure is developed to optimize planar mechanism type. A Genetic Algorithm is used to cycle populations of kinematic chain link adjacency matrices, through selection, crossover, and mutation. During this optimization, fit kinematic chains survive while unfit kinematic chains do not. Upon convergence, synthesized kinematic chains of high fitness remain. This technique was lead to be called the Genetic Algorithm for Type Synthesis (GATS). GATS introduces four new ideas for the type synthesis of mechanisms. First, it does not permute all possible kinematic chains. It searches for the best kinematic chains depending on a designer’s specifications. Second, larger size mechanisms can be generated because of the genetic algorithm’s evolutionary naturalness. Third, a novel approach was applied to genetic algorithms to allow the encodings to mutate in size. This allowed for addition or elimination of links in kinematic chains during evolution. Forth, a new property was deduced from mechanism topography that describes the mechanism design flexibility.

Design of Centric Drag-Link Mechanisms for Delay Generation With Focus on Space Occupation

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Abdullah F. Al-Dwairi
Keyword(s):  
Length Ratio ◽  
Link Length ◽  
Link Mechanism ◽  
Maximum Delay ◽  
Transmission Angle ◽  
Quality Of Motion ◽  
Nonuniform Rotation ◽  
Drag Link ◽  
Space Occupation

Planar drag-link mechanism is a Grashofian four-bar chain with the shortest link fixed. In practice, the mechanism is used as a coupling between two shafts to convert uniform rotation of the driving shaft into a nonuniform rotation of the driven shaft. The nonuniformity in rotation is characterized by a cyclically increasing and decreasing delay (or advance) in the displacement of the driven shaft relative to that of the driving shaft. Drag-link synthesis problems include synthesizing the mechanism to generate a specified maximum delay. In a drag-link mechanism, the longer links make a full rotation about fixed pivots, which results in a relatively large installation space. This calls for designing drag-link mechanisms with a focus on space occupation, along with the traditional criteria of quality of motion transmission. Using position analysis, we investigate the relationships among mechanism space occupation, extreme transmission angle, and the generated maximum delay. Space occupation is represented by the link-length ratio of input link to fixed link. Given a desired maximum delay, the proposed approach suggests finding a unique extreme transmission angle value for which this link-length ratio is at a minimum. A closed-form solution to drag-link synthesis to generate a specified maximum delay is developed based on a compromise between quality of motion transmission and space occupation. For any drag-link designed by this compromise, the coupler link and the output crank are of the same length. Based on the obtained design equations, a graphical design solution and a method for evaluating space occupation are provided.

Optimum Design of the Crank Rocker Four Bar Mechanism for Specified Output Oscillation Angle and Timing Ratio

1987 ◽  
Author(s):  
D. H. Suchora ◽  
G. Wrightson
Keyword(s):  
Optimum Design ◽  
Cycle Time ◽  
Geometric Construction ◽  
Length Ratio ◽  
Total Output ◽  
Link Length ◽  
Analytic Construction ◽  
Transmission Angle ◽  
Work First ◽  
Parameters Of Interest

Abstract In designing a crank rocker four bar mechanism with a uniform input rotation typical input parameters are the required total output oscillation angle and the timing ratio of the advance to return cycle time. In determining an optimum design the parameters of interest are usually the extreme transmission angles and the ratio of the longest to shortest link length occuring in the mechanism. This work first develops an analytic construction of the link lengths and worst transmission angles based on the necessary geometry for a given output angle of oscillation and required timing ratio. The resulting equations are programmed and graphs developed which give the variation of extreme transmission angle and maximum link length ratio as a function of the specified output angle of oscillation, timing ratio, and geometric construction variables. Using these graphs a designer will be able to easily select optimum designs based on worst transmission angles and link length ratios. Examples are included.

Three-Position Function Generation of Planar Four-Bar Mechanisms With Equal Deviation Transmission Angle Control

1988 ◽  
Vol 110 (4) ◽  
pp. 435-439 ◽  
Author(s):  
C. R. Barker ◽  
Gwo-Huey Shu
Keyword(s):  
Range Of Motion ◽  
Entire Range ◽  
Link Length ◽  
Third Order ◽  
Function Generation ◽  
Transmission Angle ◽  
Order Polynomial ◽  
Cartesian Plane ◽  
Position Synthesis ◽  
The Ideal

This paper is an extension of earlier work on mapping of three-position function generation of planar four-bar mechanisms. Previously, it has been shown that all of the potential solutions to a given problem may be represented in an αβ-plane which can be subdivided into mechanism types. Further, the regions in the αβ-plane may represent two possible forms of assembly plus a change of form class which are not valid solutions. In this paper, we provide a third-order polynomial which defines the locus in the αβ-plane of solutions which have equal deviation of their transmission angle from the ideal of 90° throughout the entire range of motion. When these solutions are mapped into a Cartesian plane, the ground pivot locations produce curves similar to the familiar Burmester curves for four-position synthesis problems. Additional advantages of the approach are that the input link is automatically a crank, the desired link length ratio can be controlled, and the solutions are free of defects.

Design of Quick-Returning R-S-S-R Mechanisms

1988 ◽  
Vol 110 (4) ◽  
pp. 423-428 ◽  
Author(s):  
F. O. Suareo ◽  
K. C. Gupta
Keyword(s):  
Solution Space ◽  
Algebraic Method ◽  
Axial Distance ◽  
Link Length ◽  
Planar Case ◽  
Transmission Angle ◽  
Crank Angle ◽  
Shaft Angle ◽  
The Given ◽  
Crank Length

An algebraic method is presented to synthesize quick-returning R-S-S-R mechanisms which satisfy the given time-ratio and follower oscillation angle requirements. In these designs, the three parameters, which define the follower spheric joint, satisfy a quadratic condition. When the shaft angle between the input and output shafts is zero, this quadratic condition reduces to the equation of a circle which is a familiar classical result for the planar case. The solution space for the quick-returning R-S-S-R linkage is such that, for each set of choices for crank length a2, follower axial distance S4, and initial follower angle φ0, there are four sets of follower length a4, initial crank angle θ0, crank axial distance S2, and coupler length a3. These designs are screened so that they do not have branch defect, have transmission angle values in a given range, and have reasonable link length proportions.

scholarly journals AN INDEFINITE QUADRATIC PROGRAMMING PROBLEMS

2020 ◽  
pp. 223-229
Keyword(s):  
Quadratic Programming ◽  
Local Minimum ◽  
Quadratic Function ◽  
Inequality Constraints ◽  
Practical Application ◽  
Indefinite Quadratic Programming ◽  
Detailed Method ◽  
Quadratic Programming Problems ◽  
Indefinite Quadratic ◽  
Computation Work

In this paper, we give in section (1) compact description of the algorithm for solving general quadratic programming problems (that is, obtaining a local minimum of a quadratic function subject to inequality constraints) is presented. In section (2), we give practical application of the algorithm, we also discuss the computation work and performing by the algorithm and try to achieve efficiency and stability as possible as we can. In section (3), we show how to update the QR-factors of A1 (K), when the tableau is complementary ,we give updating to the LDLT-Factors of (K ) A G . In section (4) we are not going to describe a fully detailed method of obtaini

Design of Drag-Link Mechanisms With Optimum Transmission Angle

1983 ◽  
Vol 105 (2) ◽  
pp. 254-258 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Extreme Values ◽  
Angular Displacement ◽  
Output Link ◽  
Link Length ◽  
Design Charts ◽  
Link Mechanism ◽  
Transmission Angle ◽  
New Criterion ◽  
Four Bar Linkage ◽  
Drag Link

In this paper, a new criterion for the design of a drag-link mechanism with optimum transmission angle is established. The transmission angle, the angle between the coupler link and output link of a four-bar linkage, is considered to be optimized when its extreme values deviate equally from 90 deg. Based on this criterion, design equations and design charts are developed. It is shown that the optimum drag-link mechanism is a turning-block linkage. It is also shown that to displace the drag-link mechanism with optimum transmission angle from its minimum lag to its maximum lag position, the input link must always rotate 180 deg and the corresponding angular displacement of the output link depends only on the link-length ratio of the output link to the fixed-link.

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