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Conditions of motion arm wheel a 1 arm fixed a rotated

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Unformatted text preview: wheel E The table of motions is drawn as follows : Table 13.10. Table of motions. Revolutions of elements Step No. Conditions of motion Arm Wheel A 1. Arm fixed A rotated through – 1 revolution (i.e. 1 revolution clockwise) 0 2. Arm fixed-wheel A rotated through – x revolutions 0 –x + x× 3. Add – y revolutions to all elements –y –y –y 4. Total motion –y –x–y –1 Compound wheel B-C + TA TB Wheel D + TA TC × TB TD Wheel E + TA TB × TB TE =+ x× TA TB TA –y TB + x× TA TC × TB TD + x× –y x× TA TC × –y TB TD TA TE TA TE –y x× TA –y TE Chapter 13 : Gear Trains l 451 Since the wheel A makes 1 r.p.s. clockwise, therefore from the fourth row of the table, – x – y = – 1 or x+y=1 ...(i) Also, the wheel D makes 5 r.p.s. counter clockwise, therefore TA TC 12 14 – y=5 × or x× – y=5 × TB TD 30 56 ∴ 0.1 x – y = 5 From equations (i) and (ii), x = 5.45 and y = – 4.45 ∴ Angular velocity of arm OP = – y = –(– 4.45) = 4.45 r.p.s = 4.45 × 2 π = 27.964 rad/s (counter clockwise) Ans. x× ...(ii) 12 TA – y = 5.45 × – (– 4.45) = 5.36 r.p.s. 72 TE = 5.36 × 2 π = 33.68 rad/s (counter clockwise) Ans. Example 13.12. An internal wheel B with 80 teeth is keyed to a shaft F. A fixed internal wheel C with 82 teeth is concentric with B. A compound wheel D-E gears with the two internal wheels; D has 28 teeth and gears with C while E gears with B. The compound wheels revolve freely on a pin which projects from a disc keyed to a shaft A co-axial with F. If the wheels have the same pitch and the shaft A makes 800 r.p.m., what is the speed of the Helicopter shaft F ? Sketch the arrangement. and angular velocity of wheel E = x × Solution. Given : T B = 80 ; T C = 82 ; T D = 28 ; N A = 500 r.p.m. Note : This picture is given as additional information and is not a direct example of the current chapter. The arrangement is shown in Fig. 13.16. Fig. 13.16 First of all, let us find out the number of teeth on wheel E (T E). Let dB , dC , dD and dE be the pitch circle diameter of wheels B , C, D and E respectively. From the geometry of the figure, dB = dC – (dD – dE ) 452 l Theory of Machines or dE = dB + dD –...
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