Please show detailed work For the mechanisms shown point C m

For the mechanisms shown, point C moves in a vertical straight line. For the values shown, determine: the velocity of point C (V_c). the acceleration of point C (a_c) the angular acceleration of link 3. (alpha_3)

Solution

Given:
Angular Velocity at A= 20Rad/Sec
Acceleration at A = 140 Rad/sec²
AB=BC=BD=100mm =0.1m

Formula to be used:          Velocity = Ang. Vel X Radius
                                                Acceleration = Vel ² /Radius

Line Diagram of the Problem

Angular Velocity of B w.r.t A = Angular Velocity of Link A
(_b)_a = 20Rad/Sec.

(V_b)_a = 20 X 0.1
         = 2m/sec

(V_b)_a = (V_c)_b

(V_c)_b = 2m/sec.        Answer

Acceleration at Pt. C W.R.T B
a_(cb) = (2)² X 0.1
a_(cb) = 40m/sec²       Answer

Angular Velocity (₃) of Link 3 = Angular Velocity (₂) of Link 2
                                                    _{3 =} 20 Rad/Sec

Acceleration of Link 3 WRT B (_3B) = (₃)² X R
                                                                 = (20)² X 0.2
Acceleration of Link 3 WRT B (_3B) = 80m/sec²

Answers: