3 t b t c l chapter 13 gear trains 445 the table

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Unformatted text preview: 5 ...(3 T B = T C) l Chapter 13 : Gear Trains 445 The table of motions is given below : Table 13.6. Table of motions. Revolutions of elements Step No. Conditions of motion Arm Compound gear B-C 0 Arm fixed , g ear A r otates through – 1 revolution (i .e . 1 rev. clockwise) 1. Gear A –1 + TA TB TA TB 2. Arm fixed, gear A r otates through – x revolutions 0 –x + x× 3. Add – y r evolutions to all elements –y –y Total motion –y –x–y + TA TB T × =+ A TB TD TD –y 4. Gear D x× TA –y TB + x× TA TD –y x× TA –y TD 1. Speed of arm when A makes 1 revolution clockwise and D makes half revolution anticlockwise Since the gear A makes 1 revolution clockwise, therefore from the fourth row of the table, – x – y = –1 or x+y=1 ...(i) Also, the gear D makes half revolution anticlockwise, therefore x× ∴ 1 TA –y= 2 TD 40 x – 90 y = 45 x× or x – 2.25 y = 1.125 From equations (i) and (ii), x = 1.04 ∴ 40 1 – y= 90 2 or and ...(ii) y = – 0.04 Speed of arm = – y = – (– 0.04) = + 0.04 = 0.04 revolution anticlockwise Ans. 2. Speed of arm when A makes 1 revolution clockwise and D is stationary Since the gear A makes 1 revolution clockwise, therefore from the fourth row of the table, –x –y =–1 or x+y=1 ...(iii) Also the gear D is stationary, therefore TA – y=0 TD or 40 x – 90 y = 0 or x× ∴ x× 40 – y=0 90 x – 2.25 y = 0 From equations (iii) and (iv), x = 0.692 ∴ and y = 0.308 Speed of arm = – y = – 0.308 = 0.308 revolution clockwise Ans. ...(iv) 446 l Theory of Machines Example 13.8. In an epicyclic gear train, the internal wheels A and B and compound wheels C and D rotate independently about axis O. The wheels E and F rotate on pins fixed to the arm G. E gears with A and C and F gears with B and D. All the wheels have the same module and the number of teeth are : TC = 28; TD = 26; T E = TF = 18. 1. Sketch the arrangement ; 2. Find the number of teeth on A and B ; 3. If the arm G makes 100 r.p.m. clockwise and A is fix...
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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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