Arm fixed wheel 1 rotated through x revolutions 0 x

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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.

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