Question

4) Determine the mobility of each planar linkage shown below, specify the number of joints and members. 5) Determine the mobility of each of the planar linkages shown below. Specify the number of links and members. 6) Determine the mobility associated with the mechanism below. The round part rolls without slipping on the pieces in contact with it 7) If position information is available for all points in the planar linkage shown below, can all the velocities be determined uniquely if the value of w is given

Answer 1

翳 4(a) 4(b) 14(c) 12 10 5(a) 5(b) 5(c)

Mobility is the number of independent inputs required by a mechanism for a unique configuration.

(For example if Mobility is 2, it means you need to provide two inputs to make the mechanism fully defined in configuration)

Mobility is called Degree of Freedom (DOF)

According to Grubler's criterion

DOF = 3(N-1) - 2L - H

Where N = number of links in the mechanism

L = number of lower pairs (Indicated by red dots)

H = Number of higher pairs (Indicated by yellow dots)

Also remember one ternary pair = two binary pairs and one quaternery pair = three binary pairs.

4.

(a) Links 3,4,5 have a ternary pair. So count that common joint twice.

Links 5,6,7,8 have a quaternary pair so count thrice.

N = 9

L = 11

DOF = 3(9-1) - 2(11)

DOF = 2

(b) Links 4,5,6 have binary pair

N = 7

L = 9

DOF = 3(7-1) - 2(9)

DOF = 0

(c) Links 7,8,9 have ternary pair.

N = 10

L = 12

DOF = 3(10-1) - 2(12)

DOF = 3

5.

(a) Pin at the end of link 3 slides into the slot of link 2 thus creating a line contact. Hence the yellow joint shown is higher pair.

N = 5

L = 5

H = 1

DOF = 3(5-1) - 2(5) - 1

DOF = 1

(b) Links 5,3,7 have ternary joint.

N = 7

L = 9

DOF = 3(7-1) - 2(9)

DOF = 0

(c) Links (4,5,6), (6,7,10),(9,10,11),(1,7,8),(2,5,12) have ternary joints

N = 12

L = 15

DOF = 3(12-1) - 2(15)

DOF = 3

6. Two grey blocks also belong to the fixed link since they do not have relative motion with respect to the fixed walls.

N = 2

H = 1 (Link 2 is connected to link 1 through a higher pair: Imagine a cam follower mechanism in which the follower surrounds the cam- there we take one higher pair. Similar situation exists here)

DOF = 3(2-1) - 1

DOF = 2

7. The velocities can be determined uniquely if for a given input velocity there is a constrained and predictable motion of the other links. This is only possible if the degree of freedom is one.

Here,

N = 7

L = 8

DOF = 3(7-1) - 2(8)

DOF = 2

Thus the velocities determined will not be unique.