Consider the mechanism below in this configuration The locat

Consider the mechanism below in this configuration. The location of some instant centres is given for you. Determine using instant centers: the angular velocity of link 3 (magnitude and direction). the angular velocity of link 5 (magnitude and direction). the linear velocity of point D on link 5 (magnitude and show direction on diagram).

Solution

Note: In Instantaneous Center (IC) method, mechanism needs to be drawn (suitable scale) to find ICs and determine various distances (r).

a) Angular velocity of link 3 (w₃-read as omega) can be calculated using known value of angular velocity of link 2 w₂=400 rpm CCW.

Consider a common Instantaneous center (IC) for link 2 and 3, P_2,3:

If we assume that P_2,3 is on link 2, then linear velocity of point v_2,3= w₂xr_P1,2-P2,3 (Direction - to left)

If we assume P_2,3 is on link 3, then linear velocity of point v_2,3= w₃xr_P1,3P2,3

Equating above two equations we get w₃.(Direction - CW)

b) Find angular velocity of link 5 (w₅): Consider IC P_3,5

Assuming P_3,5 link 3, linear velocity of point P_3,5 : v_3,5 = w₃X r_P1,3-P3,5 (Direction - Up)

Now w₅ can be calculated considering IC P_1,5

Assuming P_3,5 on link 5, v_3,5 = w₅X r_P1,5-P3,5 ---- calculate w₅ (Direction - CCW).

c) Linear velocity of point D: Consider IC P_1,5  --- v_D = w₅ X r_P1,5-D (Direction - Up)