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Unformatted text preview: e of motions for the train considered is given below :
Table 13.14. Table of motions.
Revolutions of elements
Step No. Conditons of motion Arm Wheel 1 1. Arm fixed  wheel 1 rotated
through + 1 revolution
(anticlockwise) 0 +1 – 2. Arm fixed  wheel 1 rotated
through + x revolutions 0 +x – x× +y +y +y y x +y y – x× 3.
4. Add + y r evolutions to all
elements
Total motion Wheel 2 T1
T2 Wheel 3 – T1
T2 T1 T2
T
×
=– 1
T2 T3
T3
– x× T1
T3 +y T1
T2 y – x× T1
T3 456 l Theory of Machines Let us assume that wheel 1 makes 1 r.p.s. anticlockwise.
∴ x+y=1 ...(i) Also the wheel 3 is stationary, therefore from the fourth row of the table, y – x×
∴ y– T1
=0
T3 y – x× or 80
=0
120 2
x=0
3 ...(ii) From equations (i) and (ii), x = 0.6, and y = 0.4 ∴ Speed of arm or casing C = y = 0.4 r.p.s. = y – x× and speed of wheel 2 or arm E 80
T1
= 0.4 – 0.6 ×
= – 2 r.p.s.
20
T2 = 2 r.p.s. (clockwise)
Let us now consider the train of annular wheel 4 (on C), wheel 5 (on E), wheel 6 (on F) and
arm E. We know that
T6 + 2 T5 = T 4
∴ or 20 + 2 T 5 = 100 T 5 = 40 The table of motions is given below :
Table 13.15. Table of motions.
Revolutions of elements
Step
No. Conditions of motion Arm E or
wheel 2 Wheel 6 Wheel 5 1. Arm fixed, wheel 6 rotated
through + 1 revolution 0 +1 – 2. Arm fixed, wheel 6 rotated
through + x 1 revolutions 0 x1 – x1 × 3. Add + y 1 revolutions to all
elements + y1 + y1 + y1 4. Total motion + y1 x1 + y1 y1 – x1 × T6
T5 Wheel 4 – T6
T5 T6 T5
T
×
=– 6
T5 T4
T4
– x1 × T6
T4 + y1 T6
T5 y1 – x1 × T6
T4 We know that speed of arm E = Speed of wheel 2 in the first train
∴ y1 = – 2 ...(iii) Also speed of wheel 4 = Speed of arm or casing C in the first train
∴ or y1 – x1 × T6
= 0.4
T4 or x1 = (–2 – 0.4) –2 – x1 ×
100
= – 12
20 20
= 0.4
100 ...(iv) l Chapter 13 : Gear Trains 457 ∴ Speed of wheel 6 (or F)
= x 1 + y 1 = – 12 – 2 = – 14 r.p.s. = 14 r.p.s. (clockwise)
Now consider the train of wheels 6 and 7 (both o...
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This note was uploaded on 02/13/2014 for the course MIE 301 taught by Professor Celghorn during the Fall '08 term at University of Toronto Toronto.
 Fall '08
 CELGHORN

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