Five Position Synthesis of a Slider-Crank Function Generator

2011 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Full Range ◽  
Linear Actuator ◽  
Tolerance Zone ◽  
Function Generator ◽  
Front End ◽  
Input And Output ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Branching Solutions

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

Extension of Freudenstein’s Equation to Geared Linkages

1971 ◽  
Vol 93 (1) ◽  
pp. 201-210 ◽  
Author(s):  
A. V. Mohan Rao ◽  
G. N. Sandor
Keyword(s):  
Matrix Theory ◽  
Generalized Equations ◽  
Algebraic Equations ◽  
Principle Of Superposition ◽  
Function Generator ◽  
Closed Form Solutions ◽  
Input And Output ◽  
The Matrix ◽  
Function Generators ◽  
Scalar Expression

Freudenstein’s equation for planar four-bar function generators correlates input and output crank positions implicitly in a scalar expression, with coefficients that are functions of link proportions. Applying this approach to planar geared function generator linkages leads to nonlinear systems of algebraic equations. By the principle of superposition taken from the matrix theory of linear systems and by Sylvester’s dyalitic elimination, closed form solutions are obtained. When the geared linkages are changed into the planar four-bar by setting certain link lengths equal to zero, the generalized equations derived here specialize to Freudenstein’s well-known equation. Results of computer programs for synthesis and analysis based on this theory are tabulated.

scholarly journals Controlling the Movement of a TRR Spatial Chain With Coupled Six-Bar Function Generators for Biomimetic Motion

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Constant Velocity ◽  
Joint Angle ◽  
Synthesis Process ◽  
Function Generator ◽  
Single Degree Of Freedom ◽  
Wing Motion ◽  
Serial Chain ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Velocity Input

This paper describes a synthesis technique that constrains a spatial serial chain into a single degree-of-freedom mechanism using planar six-bar function generators. The synthesis process begins by specifying the target motion of a serial chain that is parameterized by time. The goal is to create a mechanism with a constant velocity rotary input that will achieve that motion. To do this, we solve the inverse kinematics equations to find functions of each serial joint angle with respect to time. Since a constant velocity input is desired, time is proportional to the angle of the input link, and each serial joint angle can be expressed as functions of the input angle. This poses a separate function generator problem to control each joint of the serial chain. Function generators are linkages that coordinate their input and output angles. Each function is synthesized using a technique that finds 11 position Stephenson II linkages, which are then packaged onto the serial chain. Using pulleys and the scaling capabilities of function generating linkages, the final device can be packaged compactly. We describe this synthesis procedure through the design of a biomimetic device for reproducing a flapping wing motion.

scholarly journals Controlling the Movement of a TRR Spatial Chain With Coupled Six-Bar Function Generators for Biomimetic Motion

2015 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Constant Velocity ◽  
Joint Angle ◽  
Synthesis Process ◽  
Function Generator ◽  
Single Degree Of Freedom ◽  
Wing Motion ◽  
Serial Chain ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Velocity Input

This paper describes a synthesis technique that constrains a spatial serial chain into a single degree-of-freedom mechanism using planar six-bar function generators. The synthesis process begins by specifying the target motion of a serial chain that is parameterized by time. The goal is to create a mechanism with a constant velocity rotary input that will achieve that motion. To do this we solve the inverse kinematics equations to find functions of each serial joint angle with respect to time. Since a constant velocity input is desired, time is proportional to the angle of the input link, and each serial joint angle can be expressed as functions of the input angle. This poses a separate function generator problem to control each joint of the serial chain. Function generators are linkages that coordinate their input and output angles. Each function is synthesized using a technique that finds 11 position Stephenson II linkages, which are then packaged onto the serial chain. Using pulleys and the scaling capabilities of function generating linkages, the final device can be packaged compactly. We describe this synthesis procedure through the design of a biomimetic device for reproducing a flapping wing motion.

Synthesis of Compliant Mechanisms With Specified Equilibrium Positions

2005 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Compliant Mechanisms ◽  
Equilibrium Constraints ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Form Design ◽  
Design Requirements ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Sine And Cosine Functions

This paper presents a synthesis procedure for a compliant four-bar linkage with three specified equilibrium configurations. The finite position synthesis equations are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Solutions to these design equations were computed using a polynomial homotopy solver. In order to provide a design specification, we first compute the six equilibrium configurations of a known compliant four-bar mechanism. We use these results as design requirements to synthesize a compliant four-bar. The solver obtained eight real solutions which we refined using a Newton-Raphson technique. A numerical example is provided to verify the design methodology.

Kinematic Efficiency of Non-Circular Geared Transmissions

1981 ◽  
Vol 103 (1) ◽  
pp. 170-176 ◽  
Author(s):  
R. J. Ferguson ◽  
J. H. Kerr
Keyword(s):  
Power Flow ◽  
High Efficiency ◽  
Function Generator ◽  
Function Generators ◽  
Kinematic Efficiency

Infinitely-variable transmissions of high efficiency can be made using non-circular gears combined in function generators. The efficiency of a function generator depends on the gear parameters, the ratio of the differential, and the direction of power flow. The paper shows how the factors influence the total gear meshing losses and explain how efficiency is calculated. No-load losses are not included.

Direct Analytic Synthesis of Four-Bar Function Generators With Optimal Structural Error

1973 ◽  
Vol 95 (2) ◽  
pp. 563-571 ◽  
Author(s):  
Richard S. Rose ◽  
George N. Sandor
Keyword(s):  
Conventional Method ◽  
Function Generator ◽  
Arbitrary Choice ◽  
Usual Procedure ◽  
Structural Error ◽  
Function Generators ◽  
Conventional Optimization ◽  
Four Bar Linkage ◽  
Additional Constraints

This paper is a departure from the usual procedure for obtaining the optimal dimensions of a four bar function generator by iteration. In the usual procedure, the accuracy points are first chosen by means of Chebishev spacing or some other means. Using these accuracy points, a four bar linkage is synthesized and the error calculated. Freudenstein’s respacing formula may then be used to respace the accuracy points so as to minimize the errors. After the respacing of the accuracy points is calculated, a new mechanism is synthesized. The process is repeated until the magnitudes of the extreme errors occurring between accuracy points are equalized. The procedure adopted in this paper is to immediately force the extreme errors between accuracy points to be equal in magnitude by imposing additional constraints upon the problem. These constraints eliminate the arbitrary choice of the first set of accuracy points. This procedure results in a more extensive set of equations to be solved than the conventional method. However, once the equations are solved, they lead directly to equalized (and thus minimized) extrema of the magnitude of structural errors between the precision points. Thus there is no need to perform the iterative steps of conventional optimization. The proposed method is illustrated with an example.

Design of Four-Bar Function Generators With Mini-Max Transmission Angle

1977 ◽  
Vol 99 (2) ◽  
pp. 360-365 ◽  
Author(s):  
K. C. Gupta
Keyword(s):  
Extreme Values ◽  
New Method ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Function Generators ◽  
Synthesis Procedure

A new method of designing four-bar function generators with optimum transmission angle is presented. Transmission angles are considered optimum, in a mini-max sense, when their extreme values deviate equally from 90 deg. Numerical examples are given to illustrate the synthesis procedure.

Three-Position Synthesis of Spherically Constrained Planar 3R Chains

2015 ◽  
Author(s):  
Kassim Abdul-Sater ◽  
Franz Irlinger ◽  
Tim C. Lueth
Keyword(s):  
Synthesis Procedure ◽  
Position Synthesis ◽  
Triangle Equation

This paper presents a dimensional finite position synthesis procedure for a 8-bar linkage, that we call the spherically constrained planar 3R chain. The procedure aims at using the well-developed constraint-based synthesis equations of spherical RR chains in order to constrain a planar serial 3R guiding chain, synthesized before for a maximum number of three task poses. This maximum number of task positions results from the specific linkage topology, which requires to select specific axes of spherical RR chains. However, three-position synthesis allows it to apply a specific version of the dyad triangle equation of planar RR chains to the problem. A particular assumption forces that this version of the dyad triangle equation becomes nothing but the synthesis equation of a planar 3R chain, which is easily solved for the three prescribed task poses. An example is provided showing a synthesized spherically constrained planar 3R chain reaching three prescribed planar poses.

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