Introduction(2)

According to type of contact between elements.

(a) Lower pair:

When the two elements of pair have a surface contact when relative motion takes place and surface of one element slides over the surface of other the pair formed is known as the lower pair.

(b) Higher pair:

When the two elements of pair have a line or point contact when relative motion takes place and motion between two elements is partly turning and partly sliding then the pair is known as the higher pair.

According to the type of closure.

(a) Self-closed pair:

When the two elements of a pair are connected together mechanical so that only required kind of relative motion occurs it is known as self-closed pair. Lower pairs are self-closed pair.

(b) Force - closed pair:

When two elements of a pair are not connected mechanical but kept in contact by the action of external forces then the pair is said to be a force-closed pair

Kinematic Chain

When kinematic pairs are coupled in such a way that last link is joined to the first link to transmit definite motion i.e. successfully constrained motion it is called kinematic chain.

If each link is assumed to form the two pairs of two adjacent links then the relation between the number of pairs is ( p ) forming kinematic chain and number of links( l ) can be expressed in the form of an equation,

l = 2p – 4.............................................(i)

Since in a kinematic chain each link forms part of two pairs therefore there will be many links as the number of pairs. Next relation between the number of links (l) and number of joints ( j) which constitute a kinematic chain is given by an expression

j = 3/2l -2.............................(ii)

The equations (i) and (ii) applicable only to kinematic chains where lower pairs are used. These equations can also be applied to kinematic chains in which higher pairs are used. In that case each higher pair is taken as an equivalent to two lower pairs with an additional element.

Inversion

The method of obtaining various mechanisms by fixing different links in a kinematic chain known as inversion of the mechanism. It is noted that the relative motions between the various links are not vary in any manner through the process of inversion but their absolute motions which those measured with respect to the fixed link may be changed drastically.

Transmission of motion

The motion transmission systems allow a transfer of mechanical energy from one object to another without changing the nature of movement rotational to rotational or translation to translation motion. In gears or friction wheels the motor wheel transmitted its rotational movement to following wheel. Both wheels are in the rotation. The transmission of movement can occur by direct contact between two mechanical pieces or with the help of an intermediate device such as a chain or a belt.

Reason

• To recognize the principal mechanisms of motion transmission.
• To outline the advantages and inconveniences of each device.
• To identify motion transmission mechanisms within the machines that surround us.

Mobility, Degree of freedom

In physics the degree of freedom (DOF) of mechanical system is number of independent parameters which define its configuration. In the design or analysis of a mechanism one of the most important point is number of degrees of freedom also called movbility of the mechanism. It is defined as the number of input parameters mostly pair variables which must be independently controlled in order to bring the mechanism into useful engineering purpose. It is possible to determine the number of degrees of freedom of a mechanism directly from the number of links and the number, types of joints which it includes.

Kutzbach Criterion to Plane Mechanisms

We have that Kutzbach criterion for determining the number of degrees of freedom or movability (n) of a plane mechanism is

n = 3(l-1) -2j - h.......................................(iii)

Grubler’s Criterion for Plane Mechanisms

The Grubler’s criterion applies to mechanisms which has only single degree of freedom joints where the overall movability of the mechanism is unity. Placing n = 1 and h = 0 in Kutzbach equation, we have

1 = 3 (l – 1) – 2 j or 3l – 2j – 4 = 0...............................(iv)

This equation is known the Grubler's criterion for plane mechanisms with constrained motion. A consideration will show that a plane mechanism has a movability of 1 and only single degree of freedom joints can not have an odd number of links.

Types of joint

Binary joint

When two links are joined at the same connection, the joint is known as binary joint. In order to determine the nature of chain, i.e. whether the chain is a locked chain (or structure) or kinematic chain or unsucessfully chain. The following relation between the number of links and the number of binary joints as given by A.W. Klein.

j + h/2 =3/2 l −2………………….. (v)

where j = Number of binary joints,

h = Number of higher pairs, and

l = Number of links.

Ternary joint

When three links are joined at the same connection, the joint is known as ternary joint. It is equivalent to the two binary joints as one of the three links joined carry the pin for the other two links.

Quaternary joint

When four links are joined at the same connection the joint is called a quaternary joint. It is equivalent to the three binary joints. In general when l number of links are joined at the same connection the joint is equivalent to (l – 1) of binary joints.

Types of Constrained Motions

Completely constrained motion:

When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion.

Incompletely constrained motion:

When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion. The change in the direction of impressed force may alter the direction of relative motion between the pair.

Successfully constrained motion:

When the motion between the elements, forming a pair,is such that the constrained motion is not completed by itself, but by some other means, then the motion is said to be successfully constrained motion.

References:
1. H.H. Mabie and C. F. Reinholtz, “Mechanism and Dynamics of Machinery”, Wiley.
2. J.S. Rao & R.V. Dukkipati Mechanisms and Machine Theory, New Age International (P) Limited..
3. J.E. Shigley and J.J. Uicker, Jr., “ Theory of Machines and Mechanisms”, McGraw Hill.
4. B. Paul, “Kinematics and Dynamics of Planar Machinery”, Prentice Hall.
5. C. E. Wilson, J.P. Sadler and W.J. Michels, “Kinematics and Dynamics of Machinery”, Harper Row.