Question

1. (40%) For each mechanism shown below, determine the number of links, number of joints, and the degrees of freedom. (a) (b) (c) (d) Rolling Contact Slider (C, E, G-sliders)

Answer 1

Black color shows link no.

Red color shows lower pair

Blue color shows higher pair

2 7110 2 3 A 5 P De 11 (C, E, G - sliders)

a:- No. of links L = 5 no. of binary joints= 5 (1,2,3,4,5) no. of lower pairs j = 5 no. of higher pair h= 1

DOF = 3(L-1) - 2j - h DOF = 3(5-1) - 2x5 - 1 DOF = 1

b:-

No. of links L = 8 no. of binary joints= 8 (1,2,3,4,6,7,8,9) no. of lower pairs j = 10 no. of higher pair h= 0

DOF = 3(L-1) - 2j - h DOF = 3(8-1) - 2x10 DOF=1

c:- NOTE:- in above diagram link HF is not considered plz consider it so no. of link become 10

No. of links L = 10 no. of binary joints= 8 (1,2,3,5,7,9,10,F) no. of lower pairs j = 11 no. of higher pair h= 1

DOF = 3(L-1) - 2j - h DOF= 3(10-1) - 2x11 -1 DOF= 4

d:-

No. of links L = 9 no. of binary joints= 8 (1,2,3,4,5,6,7,8)

at link 9 there is a ternary joint that is equal to two binary joints(9,10)

   no. of lower pairs j = 11 no. of higher pair h= 0

DOF = 3(L-1) - 2j - h DOF = 3(9-1) - 2x11 -0 DOF = 2