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KINEMATIC ANALYSIS OF MECHANISMS

In this chapter the motion characteristics of the known mechanisms will be determined. General methods for the determination of motion, velocity and acceleration of mechanisms will be given. We shall be concerned with planar mechanisms only. Spatial mechanisms will be beyond the topic.

Before discussing motion analysis, let us define the following terms:
Position:

Location of a rigid body (link) or a particle (point) in a rigid body with respect to a given reference frame.
Path:

Locus of successive positions of a particle (point) on a rigid body (link).
Displacement:

Change in position of a rigid body (link) or a particle (point) with respect to a reference frame. It is a vector quantity whose magnitude is called distance (measured in mm or m).

Velocity:

The rate of change of position of a particle or a rigid body. It is the time rate of change of displacement. It is a vector quantity whose magnitude is called speed (measured in mm/sec = mms-1 or m/sec = ms-1 ).

Acceleration: Time rate of change of velocity. It is a vector quantity whose magnitude is measured in mm/sec2 = mms-2 or m/sec2 = ms-2.

If the displacement of a rigid body is a pure rotation, the displacement magnitude is then measured in radians or revolutions. This is known as the angular displacement. The time rate of change of angular displacement is the angular velocity and its magnitude is measured in rad/sec =s-1, or in rpm (revolutions per minute). The time rate of change of angular velocity is the angular acceleration and its magnitude is measured in rad/sec2 = s-2. Note that radian is dimensionless and all angular the measurements in degrees or in number of revolutions must be converted to radians for the computation.

Motion Analysis of Mechanisms

With motion analysis, we mean the analysis required to determine:

a)
 Relative position of any link or a point on a link with respect to a reference frame which may be attached to a moving link or the fixed link;
b)
 The path traced by a point on a link in plane which is attached to a moving link or the fixed link;
c)
 The angular or linear displacement of a link or a point on a link relative to the fixed link.

From the definition of the degree-freedom of a mechanism, in order to determine the position of each link, the number of independent parameters to be defined must be equal to the degree-of-freedom of the mechanism. The joint parameters will define the relative position of two links connected by a joint. The joint whose parameter is defined will be called the input joint. However, if one of the links connected by the joint is fixed, the word input link may also be used since the joint parameter defines the absolute position of the other link.

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