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.

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.

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.

scholarly journals Dynamic analysis of two-link flexible manipulator considering the link length ratio and the payload

2017 ◽  
Vol 39 (4) ◽  
pp. 303-313
Author(s):  
Duong Xuan Bien ◽  
Chu Anh My ◽  
Phan Bui Khoi
Keyword(s):  
Mechanical Design ◽  
Flexible Manipulator ◽  
Length Ratio ◽  
Elastic Displacement ◽  
Design Parameters ◽  
Nonlinear Dynamic Model ◽  
Link Length ◽  
Modeling And Analysis ◽  
Robot Systems ◽  
And Control

Dynamic modeling and analysis of flexible manipulators play an essential role in optimizing mechanical design parameters and control law of real robot systems. In this paper, a nonlinear dynamic model of a manipulator is formulated based on the Finite Element Method. To analyze the dynamic behavior effectively, a numerical simulation scheme is proposed by taking full advantages of MATLAB and SIMULINK toolboxes. In this manner, the effect of varying payload and link length ratio of the manipulator to its elastic displacement is dynamically taken into account. The simulation results show that the payload and length link ratio have significant influences on the elastic displacements of the system. In particular, a proper spectrum of the link length ratio, in which the flexural displacement of the end point of the manipulator is smallest, is demonstrated. To this end, the proposed methodology could be used further to select optimal geometric parameters for the links of new robot designs.

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.

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.

Design of a Simple Underactuated Mechanical Gripper

2014 ◽  
Vol 619 ◽  
pp. 44-48
Author(s):  
Mahasak Surakijboworn ◽  
Wittaya Wannasuphoprasit
Keyword(s):  
Distal Phalanx ◽  
Radius Ratio ◽  
Length Ratio ◽  
Stable Configuration ◽  
Link Length ◽  
Simple Geometry ◽  
Primitive Shape

The objective of this paper is to design and develop a simple geometry of an underactuated mechanical gripper which can provide most common hand grasps, fingertip grasp and enveloping grasp. The gripper consists of 2 2-DOF fingers underactuated by a pulley-tendon system, and a movable pulley for underactuation between fingers. Each finger has 2 links and 2 pulleys. A parallel linkage is used to translate distal phalanx toward an object such that fingertip grasp is improved. This work implements stability and force isotropy criteria to optimize the design. The prototype has 0.43 of pulley-radius ratio and 1.72 of link-length ratio. From primitive-shape grasping test, the gripper is able to achieve the stable configuration.

Performance Analysis and Improved Design on the Compliant Micro-Displacement Amplification Mechanism

2013 ◽  
Vol 346 ◽  
pp. 83-88
Author(s):  
Qing Ling Liu
Keyword(s):  
Performance Analysis ◽  
Design Method ◽  
Structural Characteristics ◽  
Thickness Ratio ◽  
Length Ratio ◽  
Link Length ◽  
Compliant Structure ◽  
Flexure Hinges ◽  
Amplification Mechanism ◽  
Improved Design

By analysing the structural characteristics of the compliant micro-displacement amplification mechanism and the examples of the compliant micro-displacement amplification mechanisms with different link length and link angel, the combined compliant structure formed with flexure hinges and link is important component, the length and the angel of the link affect the thickness ratio and length ratio of the combined compliant structure, which plays a key role in amplification of the mechanism. The design method is proposed aiming at improving the amplification, which is used in the improved design of the compliant micro-displacement amplification mechanism. The amplification analysis of the improved mechanism is done, which proves the validity and rationality of the improved design .

Design of Drag-Link Mechanisms With Minimax Transmission Angle Deviation

1983 ◽  
Vol 105 (4) ◽  
pp. 686-690 ◽  
Author(s):  
L.-W. Tsai
Keyword(s):  
Optimum Design ◽  
Design Criterion ◽  
Parameter Design ◽  
Cubic Equation ◽  
Design Charts ◽  
Link Mechanism ◽  
Transmission Angle ◽  
Angle Deviation ◽  
Drag Link ◽  
Maximum Transmission

In this paper, the design equations are derived for the synthesis of a drag-link mechanism, with given output-link rotation and the corresponding input-link rotation. The design criterion used is based on the maximum capability of a drag-link mechanism to provide a given delay or advance in the output motion. The solutions are given as a single-valued parametric set of equations for the link lengths. The transmission-angle optimization is accomplished by the minimization of the maximum transmission-angle deviation from 90 deg. It is shown that the optimum design can be obtained by solving a cubic equation in a single parameter. Design charts for the optimum design of a drag-link mechanism were developed. It is also shown that there is a one-to-one correspondence between the design of a crank-and-rocker mechanism and the drag-link mechanism.

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