An Intriguing Exponential Inequality

Function Generation is a long standing linkage design problem. It is possible to design a planar four bar linkage whose input and output links will pass through seven coordinated positions. This paper discloses the first graphical solution to this problem. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. This approach enables the designer to explore the range of possible solutions when fewer than seven positions are specified by dragging a fixed or moving pivot in the plane. The selection of free choices is made at the end of the process and the complete mechanism is visible when the choices are made. The constraints only need to be made once which eliminates the repetitive construction required by previous methods to consider multiple pivot locations. Since it is so easy to consider multiple pivot locations and the solution mechanism is visible, the required design time is greatly reduced. A corresponding analytical solution is also developed and solved based on the same constraints. This is a new analytical solution and is defined by a system of 20 nonlinear equations with 20 unknowns.

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Planar Linkage Synthesis for Coupler Point Path Guidance Using Poles and Rotation Angles

Volume 5B: 38th Mechanisms and Robotics Conference ◽

10.1115/detc2014-34058 ◽

2014 ◽

Cited By ~ 1

Author(s):

Ronald A. Zimmerman

Keyword(s):

Analytical Solution ◽

Nonlinear Equations ◽

Design Problem ◽

Graphical Solution ◽

Design Time ◽

Linkage Design ◽

Pass Through ◽

Solution Mechanism ◽

Four Bar Linkage ◽

Selection Of

Coupler point path guidance is a long standing linkage design problem. It is possible to design a four bar linkage with a coupler point that will pass through up to nine specified points. This paper discloses a new graphical solution to this problem. The approach is to consider the constraints imposed by the target points on the linkage through the poles and rotation angles. This approach enables the designer to explore the range of possible solutions when fewer than nine points are specified by dragging a fixed or moving pivot in the plane. The selection of free choices is made at the end of the process and the complete mechanism is visible when the choices are made. The constraints only need to be made once which eliminates the repetitive construction required by previous methods to consider multiple pivot locations. Since it is so easy to consider multiple pivot locations and the solution mechanism is always visible, the required design time is greatly reduced. A corresponding analytical solution is also developed and solved based on the same constraints. The analytical solution is defined by a system of 28 nonlinear equations with 28 unknowns.

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The Specification of Unknown Force within Dynamic Analysis of Slider Crank Mechanism by Three Various Access

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1016.239 ◽

2014 ◽

Vol 1016 ◽

pp. 239-243 ◽

Cited By ~ 2

Author(s):

Katarina Monkova ◽

Andrea Cizikova ◽

Peter Monka

Keyword(s):

Analytical Solution ◽

Dynamic Analysis ◽

Virtual Work ◽

Final Decision ◽

Graphical Solution ◽

Principle Of Superposition ◽

Basic Principles ◽

Computer Aid ◽

Advantages And Disadvantages ◽

Crank Mechanism

The article deals with the specification of unknown force within dynamic analysis of slider crank mechanism by three various access. The method of virtual work was used at the analytical solution; the principle of superposition was used at the graphical solution and the software PTC Creo was used at the solution with computer aid. All three types of the solution have their self-advantages and disadvantages. The final decision, which of methods should be selected for the solution, depends on required result precision and on the abilities of investigator. In all cases, however, it is necessary to know the basic principles of mechanics.

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