02-05-2011, 04:07 PM
abstract
This paper investigates the kinematics of an adjustable six-bar linkage where the rotation
of the input crank is converted into the oscillation of the output link. This single-degree-of
freedom planar linkage will be used as a variable-speed transmission mechanism where
the input crank rotates at a constant speed and the output link consists of an overrunning
clutch mounted on the output shaft. The analysis uses a novel technique in which kinematic
coefficients are obtained with respect to an independent variable. Then kinematic
inversion is used to express the kinematic coefficients with respect to the input variable
of the linkage. This technique decouples the position equations and provides additional
insight into the geometry of the adjustable linkage. The angle through which the output
link oscillates, for each revolution of the input crank, can be adjusted by a control arm. This
arm allows a fixed pivot to be temporarily released and moved along a circular arc about a
permanent ground pivot. The paper shows how to determine the angle of oscillation of the
output link for a specified position of the fixed pivot and investigates the extreme positions
of the output link corresponding to the extreme positions of a point on the coupler link. For
this reason, the paper includes a study of the geometry of the path traced by a coupler
point and determines the location of the ground pivot of the control arm which will cause
the output link to remain stationary during a complete rotation of the input crank. Finally,
the paper shows how the kinematic analysis results can be used, in a straightforward manner,
to redesign the control arm.
1. Introduction
This paper focuses on the kinematics and design of an adjustable six-bar linkage which is proposed here as a variablespeed
transmission mechanism. Such mechanisms are used to change the ratio of the input motor speed to the output shaft
speed. Many variable-speed transmission mechanisms incorporate cams, planetary gear arrangements, multiple drive belt
and pulley systems to power a lawn mower or tractor [1], to improve the wheel drive of garden equipment [2], to connect
an air-conditioning compressor to the prime mover of the automobile [3], to improve an exercise driving mechanism [4], and
to control the movement of valves in an engine [5]. The disadvantages of such mechanisms include high manufacturing
costs, high maintenance costs, large housing requirements, shaking vibrations, and slip. Variable-speed transmission mechanisms
based on only linkages can be used to reduce design complexity and can also be superior to alternative designs especially
at high speeds. Horton [6], for example, designed a linkage-type variable-speed transmission mechanism to replace the
cone-and-belt type of drive that was used in some textile machines. Gasoline-driven railroad section cars have employed
adjustable linkages where the continuous rotation of the input crank is converted into an intermittent rotation of the output
shaft. Several of these mechanisms can be used in combination to approximate a continuous rotation to the output shaft
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