Question

How to calculate the number of degrees of mobility of plane and spatial mechanisms?

Give the explanations for the formulas. Draw the schemes of mechanisms with passive constraints (links) and local (excess) degrees of mobility.

Answer 1

of 6 degree of Solutions het there are total in number of links. connected together to make a kinematic chain with one link fixed- We know that an object have maximum 6 degree freedom in space; and 3 in a plane so, total (n-1) links will have freedom each if separate/ alone. But in a kinematic chain the joint (specifically lower pairs) restrict 5 degree of freedom (except one as totation in one plane), so (n-1) links will have 5* tatal number lower joints restriction in d.o.f. Further if there are higher joints (point / line contact between any links) they will they will further restrict 4 more dof. If there are any passive constraint in the mechanism blocks the doof of that constraints are also doof of the mechanism. Doof of the spatial mechanism is- D.of 6(n-1) - sj- 4h-fr. An of So,

Similarly, in a Planer mechanism- but if het consider a kinematic chain o with total noi of links in and one link is fixed Each link has 3 d.o.of in a plane (2 linear & 1 rotation) one link is fixed. The total degree of freedom of chals links = 3(h-1) links are connected by 'I lower joint each lower joint restrict 2 So, g' hoc ho. of lower pairs will restrict aj d.o.f. (except rotation). Similarly, if mechanism has th' ho of higher joints they will restrict h def. So Doof of the mechanism is- Dof= 32h-1)-2j-h d.o.fi > water If mechanism has 'Fr nou of passive constraints' ID OF 36h-1)-g-h-Fr So,

Planer mechanism with passive links. Total hoi 4 of links link 5 is passive. Its motion or the motion of other links does nt affect the motion of the mechanism Mechanism with local (excess) dom. 2 3 4 TIT 77777 0 links 2, 3 & 4 are parallel. Here link 3 is not needed. It is only increasing the d'of with ho use