Pm clockwise and wheel a makes 10 rpm counter

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Unformatted text preview: ed, find the speed of B ; and 4. If the arm G makes 100 r.p.m. clockwise and wheel A makes 10 r.p.m. counter clockwise ; find the speed of wheel B. Solution. Given : T C = 28 ; T D = 26 ; T E = T F = 18 1. Sketch the arrangement The arrangement is shown in Fig. 13.12. Fig. 13.12 2. Number of teeth on wheels A and B Let TA = Number of teeth on wheel A , and TB = Number of teeth on wheel B . If dA , dB , dC , dD , dE and dF are the pitch circle diameters of wheels A , B , C, D, E and F respectively, then from the geometry of Fig. 13.12, dA = dC + 2 dE and dB = dD + 2 dF Since the number of teeth are proportional to their pitch circle diameters, for the same module, therefore Ans. TA = T C + 2 T E = 28 + 2 × 18 = 64 and TB = T D + 2 T F = 26 + 2 × 18 = 62 Ans. 3. Speed of wheel B when arm G makes 100 r.p.m. clockwise and wheel A is fixed First of all, the table of motions is drawn as given below : Table 13.7. Table of motions. Revolutions of elements Step No. Conditions of motion Arm Wheel G A 1. Arm fixed- wheel A rotates through + 1 revolution (i.e. 1 rev. anticlockwise) 0 2. Arm fixed-wheel A rotates through + x revolutions 0 +x + x× 3. Add + y revolutions to all elements +y +y +y 4. Total motion +y x+y +1 Wheel E + TA TE Compound wheel C-D – TA TE × TE TC =– TA TE y + x× – x× TA TC y–x× + TA TD × TC TF TA TC +y TA TE Wheel F + TA TD TF ×× TC TF TB =+ + x× TA TD × TC TF +y TA TC Wheel B y + x× TA TD × TC TF TA TD × TC TB + x× TA TD × TC TB +y y + x× TA TD × TC TB Chapter 13 : Gear Trains 447 l Since the arm G makes 100 r.p.m. clockwise, therefore from the fourth row of the table, y = – 100 ...(i) Also, the wheel A is fixed, therefore from the fourth row of the table, x+y=0 or x = – y = 100 ∴ Speed of wheel B = y + x × ...(ii) 64 26 TA TD × = – 100 + 100 × × = – 100 + 95.8 r.p.m. 28 62 TC TB = – 4.2 r.p.m. = 4.2 r.p.m. clockwise Ans. 4. Speed of wheel B when arm G makes 100 r.p.m. clockwise and wheel A makes 10 r.p.m. counter clockwise Since the arm G m akes 1...
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