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I hope you have learned about degrees of freedom.\). You can use this equation to predict D.O.F following 3 dimensional mechanism Where Pn represents number of pairs which block ‘n’ degrees of freedom. So equation for degrees of freedom would be as follows - D.O.F = 6(N - 1) -5P 5 - 4P 4 - 3P 3 - 2P 2. If the mechanism is 3 dimensional in nature, you could easily derive an equation for mobilityĬoncept. Fig 9 : 5-bar linkage, 5 links, 5 lower pairs A 3-Dimensional mechanism This mechanism is having 5 links and 5 lower pairs. So mobility is again oneįig 8 : Cam and follower, 3 links, 2 lower pairs, 1 higher pair 5-Bar linkage Fig 7 : 4 bar linkage, it is having 4 links and 4 lower pairs The cam and followerĬam and follower is having 3 links, 2 lower pairs, and one higher pair. So you can predict from Kuthbach equation that mobility of the mechanism is 1. 4-Bar linkageīack to same old planar mechanisms.This mechanism is having 4 links, and 4 lower pairs (refer Figħ). ![]() Here N represent total number of links in the mechanism. This equation is also known as Kuthbach equation. The general equation to find out degrees of freedom of a planarīelow. Means, by knowing position of only one cam, weĭetermine this mechanism. So this mechanism has got 1 degrees of freedom. Here we have got 1 higher pair.įig 6 : Lower pairs and higher pairs in a mechanism, a lower pair arrests 2 D.O.F, while This kind of pair is called higher pair(refer Fig 6). So for each such pairs, there will be deduction of 1 mobility If joint between 2 links is having lineīoth the link should have same translational motion along the common normal. Now consider the joint which is having a line contact. Represents number of pairs with surface contacts. So for each such pairs, there will be a deduction of 2 mobility from total mobility. Links is having surface contact as shown below, then both the links will have same translatoryĭirections. When we connect it together through pairs, links will not have the same 3 degrees of freedom. So total degrees of freedom, or mobility is 3(N-1). So degrees of freedom of a rigid body in a plane is 3 (refer Figįig 5 : The links were not connected, except the 3 D.O.F land If the body is in a plane it can have only 3 In total we need 6 inputs to determine itsįreedom of rigid body in space is 6 (refer Fig 2). It could have 3 translatoryĪlso it could have 3 rotary motions as shown. Degrees of freedom of a rigid bodyĬonsider the rigid body shown below, which is situated in space. So in coming sections we will see how we can predict degree of ![]() You have predicted degree of freedom of some simple mechanisms from your intuition. Fig 1 : Examples of degrees of freedom of different mechanisms But to determine position of the slider crank mechanismĪngle or displacement of at least 2 members. Similarly degrees ofĪnd follower mechanism is also one. Position of this 4 bar mechanism can beĬonsider position of any one of the member. In this article, we will understand how to predict degrees of freedom of aĬonsider the mechanism shown in first figure of Fig 1. ![]() Degree of freedom means how many variables are required to determine Degrees of freedom is the one of the most important concept in mechanics.
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