Question

The punch as shown in the following figure, is operated by a single harmonic motion of the pivoted sector given by θ θ0 sin 2nt, where θ0--rad. When θ-0 [2 marks] [2 marks] [3 marks] [3 marks] [3 marks] 7 marks] (a) What is the angular velocity of OA? (b) What is the angular velocity of AB? (c) What is the velocity of pin A? (d) What is the velocity of pin B, i.e. the punch? (e) What is the acceleration of pin A? (f) What is the acceleration of the pin B, i.e. the punch? 140

Answer 1

Given:

6, sin 2rt ..(1)

Where

●=12

Horizontal equation-

140 sin θ-100 sin β .. (2)

Vertical equation-

140 co s θ+ 100 co s β--08 ..(3)

Differentiation equation (2), (3) and (1)

140 sin θ * aoa + 100 sin β * OAB-VB .. (5)

d(e sin 2nt) OA dt dt

OA2 12

(a) Angular velocity of OA

As given that , t = 0s

θ=0

Rewriting above equations (6)

OA 12

=62rad ..(7) π- .. (7) =

(b) Angular velocity of AB

Rewriting above equations (2)

140 sin θ 100 sin β

140 sin 0-100 sin β

Rewriting above equations (4)

140 cos θ * ω 100 cos β * ω

140 cos 0 *--100 cos 0 * ω B 6

7 T2 ОАв_ 30

(c) Velocity of pin A can be given as

Tangential velocity = Angular Velocity * Radius of rotation

6 140 7m

VA-230.29- 230.29 77

(d) Velocity of pin B

Rewriting above equations (5)

= 140 sin 0 *-+ 100 sin 0 * 6 30

=0mm

(e) Acceleration of pin A

Equation (6)

OA2 12

On differentiating, angular acceleration of pin A

OA 12

For , t = 0s

θ=0

-2π * 15 * 2π * sin 0 OA

So, tangential acceleration of the pin A will be

Radial acceleration of pin A is given by the relation

(Tangentail velocity)2 ik. Radius of rotation

ar = 140mm

230.292 ik. 140

mm ar 378.81

(f)Acceleration of pin B

Equation (4)

On differentiating

On substituting values

140 cos 0 * 0-140 *-* sin 0 100 cos 0 * αΑΒ-100 *-* sin 0 6

rad an AB 2

Equation (5)

140 sin θ * aoa + 100 sin β * OAB-VB .. (5)

On differentiation

On substituting values

ав = 140 sin 0 * 0 + 140 * cos 0 + 100 sin 0 * 0 + 100 *-* cos 0 6 30

ag - 460.58 2