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 2

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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)

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media%2F99f%2F99ff8c71-b645-4580-a01b-36

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

d(e sin 2nt) OA dt dt

media%2Fe65%2Fe653e79e-c5c5-4f60-9dde-bc

OA2 12

(a) Angular velocity of OA

As given thatθ=0 , t = 0s

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

media%2F521%2F5214219a-17f8-4477-98b6-ff

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

media%2Faf0%2Faf0b810a-49fb-4f38-b1a7-83

6 140 7m

VA-230.29- 230.29 77

(d) Velocity of pin B

Rewriting above equations (5)

media%2F6f2%2F6f2b594b-677c-458c-b22b-a7

= 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

Forθ=0 , t = 0s

-2π * 15 * 2π * sin 0 OA

media%2Fe89%2Fe89c4504-7020-401f-85fa-a6

So, tangential acceleration of the pin A will be media%2Ffae%2Ffaea33cc-592f-4b7a-afee-a7

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)

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On differentiating

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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

media%2Fcab%2Fcabdfe58-835f-45a0-8ab0-6e

On substituting values

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

ag - 460.58 2

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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 mar...
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