Pair 3 Link 3 and link 5 constitute a single turning pair Pair 2 Link 2 and link 3 constitute a single turning pair Pair 1 Link 1 (ground) and link 2 constitute a single turning pair Numbers pairs having one degrees of freedom=10 by counting So, inspection should be done in certain cases to find the degrees of freedom.Įxample: 2.1 Find the degree of freedom of the mechanism given below. It should be noted here that gruebler’s criterion does not take care of geometry of the mechanism so it can give wrong prediction. This equation is known as Gruebler’s criterion for degrees of freedom of plane mechanism. Therefore, for plane mechanism, the following relation can be used for degrees of freedom, This can be shown with the help of figure 2.10 that a link has three degree of freedom in two dimensions.įig.2.9 a line in a plane has three DOF: x, y, θ Most of the mechanism we generally study are two dimensional in nature, such as slider-crank mechanism in which translatory motion is possible along two axes(one restraint) and rotary motion about only one axis(two restraints).Thus there are three general restraints in a two dimensional mechanism. Other pairs having 2, 3, 4 and 5 degrees of freedom reduce the degree of freedom of the mechanism by putting constraints on the mechanism as well.į = 6(N-1) - 5J 1 - 4J 2 - 3J 3 - 2J 4 - 1J 5 (Because each movable link has six degree of freedom) Each pair having one degree of freedom imposes 5 restraints on the mechanism reducing its degrees of freedom by 5J 1 this is because of the fact that the restraint on any of the link is common to the mechanism as well. ![]() ![]() Then, the number of the movable links are = N - 1ĭegrees of freedom of (N- 1) movable links = 6(N-1) When one of the links is fixed in a mechanism J 2 = number of pairs having two degree of freedom and so on. J 1 = number of pairs having one degree of freedom It can be observed from the figure 2.9 c that this chain is locked due to its geometry.ĭegrees of freedom of a mechanism in space can be explained as follows: The reason for this indefinite motion lies in the fact that if we give motion to any of the link in the chain then the other links can take indefinite position.Ĭ) Redundant chain: There is no motion possible in the redundant chain. redundant chainī) Non-kinematic chain: In case the motion of a link results in indefinite motions of others links, it is a non-kinematic chain. (5) As element can revolve around X,Y & Z axis & can move in X & Z axisĪ) Kinematic chain: A kinematic chain is an assembly of links which are interconnected through joints or pairs, in which the relative motions between the links is possible and the motion of each link relative to the other is definite.Ī. ![]() (5) As an element can revolve around X,Y&Z axis & can move in X & Z axis (4) As element can revolve around Z & Y axis & can move in Z & X axis (4) As element can revolve around Z & Y axis & can move in Y axis (3) As element can revolve around Y axis & can move in Z & X axis (3) As element can revolve around X,Y&Z axis ![]() (2) As element inside can revolve around Z axis and also move in Z axis (2) As one element can move in Z axis & also revolve around Z axis (1) As movement is possible only in Z direction. (0) As there is no motion hence DOF is zero
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