For external ratchet For internal ratchet The ratio of a=d (internal ratchet) The module The bending moment on pawl The bending stress The diameter of pawl pin ¼ 148 to 178 ð24-266Þ ¼ 178 to 308 ð24-267Þ a=d ¼ 0:35 to 0:43 ð24-268Þ m ¼ 2 3 ffiffiffiffiffiffiffiffiffiffiffiffiffi M t z ba s ð24-269Þ M b1 ¼ F n e 2 ð24-270Þ b ¼ 6M b1 bs 2 1 þ F n bs 1 ba ð24-271Þ d 1 ¼ 2:71 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F n 2 ba b 2 þ t h s ð24-272Þ where t h ¼ thickness of hub on pawl Particular Formula p s 2 s 1 r 1 r 2 h 1 d 2 2 h 2 FIGURE 24-53 Definitions and dimensions of ratchet wheel. TABLE 24-23 F à b Material kN/m lbf/in MPa kpsi Cast iron 49–98 280–560 19.5–29.5 2.85–4.27 Steel or cast steel 98–196 560–1120 39–68.5 5.69–10.0 Hardened steel 196–392 1120–2240 58.8–98 8.54–14.23 MISCELLANEOUS MACHINE ELEMENTS 24.81 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS 24.9 GENEVA MECHANISM SYMBOLS 2,3 a ¼ r 1 sin center distance, m (in) F 1 the component of force acting on the crank or the driving shaft due to the torque, M 1t , kN (lbf) (Fig. 24-57) F 2 the component of force acting on the driven Geneva wheel shaft due to the torque M 2t , kN (lbf) (Fig. 24-57) F 2ðmaxÞ maximum force (pressure) at the point of contact between the roller pin and slotted Geneva wheel, kN (lbf) F ðmaxÞ the component of maximum friction force at the point of contact due to the friction torque M 2t , on the driven Geneva wheel shaft, kN (lbf) F iðmaxÞ the component of maximum inertia force at the point of contact due to the inertia torque on the driven Geneva wheel shaft, kN (lbf) i ¼ z À 2 z gear ratio J polar moment of inertia of all the masses of parts attached to Geneva wheel shaft, m 4 (in 4 ) k the working time coefficient of the Geneva wheel M 1t total torque on the driver or crank, N m (lbf in) M 2t total torque on the driven or Geneva wheel, N m (lbf in) M 2ti inertia torque on the Geneva wheel, N m (lbf in) M 2t friction or resistance torque on Geneva wheel, N m (lbf in) n 0 speed, rps n speed, rpm P power, kW (hp) r 1 radius to center of driving pin, m (in) r 2 radius of Geneva wheel, m (in) r 0 2 distance of center of semicircular end of slot from the center of Geneva wheel, m (in) r a2 outside radius of Geneva wheel, which includes correction for finite pin diameter, m (in) r p pin radius, m (in) R r ¼ r 2 r 1 radius ratio t total time required for a full revolution of the driver or crank, s t i time required for indexing Geneva wheel, s t r time during which Geneva wheel is at rest, s v velocity, m/s z number of slots on the Geneva wheel crank angle or angle of driver at any instant, deg (Fig. 24-54) 2a angular acceleration, m/s 2 (ft/s 2 ) angular acceleration of Geneva wheel, m/s 2 (ft/s 2 ) m angular position of the crank or driver radius at which the product ! 2a is maximum, deg angle of the driven wheel or Geneva wheel at any instant, deg (Fig. 24-54) ¼ r 1 a the ratio of the driver radius to center distance efficiency of Geneva mechanism 24.82 CHAPTER TWENTY-FOUR Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS locking angle of driver or crank, rad or deg ratio of time of motion of Geneva wheel to time for one revolution of driver or crank ¼ 360 2z semi-indexing or Geneva wheel angle, or half the angle subtended by an adjacent slot, deg (Fig. 24-54) crank or driver angle, deg (Fig. 24-54) ! ¼ 2n 60 angular velocity of driver or crank (assumed constant), rad/s ! 1 , ! 2 angular velocities of driver or crank and Geneva wheel, respectively, rad/s a 1 β α φ ψ a 2 a 3 ω 2 r 2 r 1 ω 1 a FIGURE 24-54 Design of Geneva mechanism. The angular velocity (constant) of driver or crank Gear ratio The semi-indexing angle or Geneva wheel angle or half the angle subtended by two adjacent slots The angle through which the Geneva wheel rotates EXTERNAL GENEVA WHEEL The angle of rotation of driver through which the Geneva wheel is at rest or angle of locking action (Fig. 24-55) The crank or driver angle ! 1 ¼ 2n 60 ð24-273Þ i ¼ angle moved by crank or driver during rotation angle moved by Geneva wheel during rotation i ¼ z À 2 z ð24-274Þ ¼ 360 2z or z ð24-275Þ 2 ¼ 360 z or 2 z ð24-276Þ ¼ 2ð À Þ¼ þ 2 ¼ z ðz þ 2Þð24-277Þ ¼ 2 À ¼ ðz À 2Þ 2z ð24-278Þ Particular Formula MISCELLANEOUS MACHINE ELEMENTS 24.83 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS DISPLACEMENT The center distance (Fig. 24-55) The radius ratio The ratio of crank radius to center distance The relation between crank angle and Geneva wheel angle VELOCITY The angular velocity of the Geneva wheel The maximum angular velocity of Geneva wheel at angle ¼ 0 a ¼ r 1 sin ð24-279Þ R r ¼ r 2 r 1 ¼ cot ð24-280Þ ¼ r 1 a ¼ sin ¼ sin z ð24-281Þ ¼ tan À1 sin 1 À cos ð24-282Þ ! 2 ¼ d dt ¼ ðcos À Þ 1 À 2 cos þ 2 ! 1 ð24-283aÞ ! 2 ¼ sinð=zÞðcos À sin =zÞ 1 À 2 sinð=zÞcos þ sin 2 =z ! 1 ð24-283bÞ ! 2ðmaxÞ ¼ d dt max ¼ 1 À ! 1 ¼ sin z 1 À sin z ! 1 ð24-283cÞ Particular Formula r o2 r 1 90” r’ 2 a ω 1 ω 2 ψ φ FIGURE 24-55 External Geneva mechanism. 24.84 CHAPTER TWENTY-FOUR Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS ACCELERATION The angular acceleration, a 2a , of Geneva wheel For angular velocity and angular acceleration curves for three-slot external Geneva wheel with driver velocity, ! 1 ¼ 1 rad/s The maximum angular acceleration of Geneva wheel which occurs at ¼ ðmaxÞ The angular acceleration of Geneva wheel at start and finish of indexing Total time required for a full revolution of the crank or driver a 2a ¼ d 2 dt 2 ¼ ð 3 À Þsin ð1 þ 2 À 2 cos Þ 2 ! 2 1 ð24-284aÞ a 2a ¼Æ sinð=zÞcos 2 ð=zÞsin 1 À 2 sinð=zÞcos þ sin 2 ð=zÞ ! 2 1 ð24-284bÞ Refer to Fig. 24-56. cos ðmaxÞ ¼À þ ffiffiffiffiffiffiffiffiffiffiffiffiffi 2 þ 2 p ð24-284cÞ where ¼ 1 4 þ 1 ð 2a Þ i; f ¼Æ sinð=zÞcos 3 ð=zÞ ½1 À 2 sin 2 ð=zÞþsin 2 ð=zÞ ! 2 1 ¼Æ! 2 1 tan ¼Æ! 2 1 tan =z ¼Æ! 2 1 r 1 r 2 ð24-285Þ t ¼ 60 n ð24-286Þ Particular Formula 30 20 10 00 10 20 30 2 4 6 ω 2 ω 1 ω 2 ω 1 α 2a ω 1 2 α 2a ω 1 2 α 2a ω 1 2 α FIGURE 24-56 Angular velocity and angular acceleration curves for three-slot external Geneva wheel. a 2a is the symbol used for angular acceleration of Geneva wheel; is the crank or driver angle at any given instant. MISCELLANEOUS MACHINE ELEMENTS 24.85 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS The ratio of t i to t The ratio of t r to t The sum of angles of ( þ ) The time required for indexing Geneva wheel, in seconds The time during which Geneva wheel is at rest, in seconds The working time coefficient of Geneva wheel Ratio of time of motion of Geneva wheel to time for one revolution of crank or driver The required speed of the driver shaft or crankshaft SHOCK OR JERK The jerk or shock, J 2 , on Geneva wheel The jerk or shock at ¼ 0 The jerk or shock at start, i.e., ¼ The length of the slot (Fig. 24-54) The condition to be satisfied by diameter on which the driver or crank is mounted The condition to be satisfied by the diameter on which Geneva wheel is mounted t i t ¼ 2 2 ¼ ¼ z À 2 2z ð24-287Þ t r t ¼ 2ð À Þ 2 ¼ 1 À ¼ z þ 2 2z ð24-288Þ þ ¼ 908 ð24-289Þ t i ¼ z À 2 2z t ¼ z À 2 z 60 2n ð24-290Þ t r ¼ z þ 2 z 60 2n ð24-291Þ k ¼ t i t r ¼ z À 2 z þ 2 ð24-292Þ v ¼ z À 2 2z < 1 2 ð24-293Þ n ¼ z þ 2 z 60 2t r ð24-294Þ where n in rpm J 2 ¼ ð À1Þ½2 cos 2 þð1 þ 2 Þcos À 4 ð1 þ 2 À 2 cos Þ 3 þ ! 3 1 ð24-295Þ ðJ 2 Þ ¼0 ¼ d 3 dt 3 ¼0 ¼ ð þ1Þ ð À1Þ 3 ! 3 1 ð24-296Þ ðJ 2 Þ ¼ ¼ d 3 dt 3 ¼ ¼ 3 2 1 À 2 ! 3 1 ð24-297Þ a 2 ¼ r 1 þ r 2 À a ¼ a sin z þ cos z À 1 ð24-298Þ d 1 < 2a 3 ¼ 2ða Àr 2 Þ¼2a 1 À cos z ð24-299Þ or d 1 a < 2 1 À cos z ¼ 4 sin 2 2z ð24-300Þ d 2 a < 2 1 À sin z ¼ 4 sin 2 4 À 2z ð24-301Þ Particular Formula 24.86 CHAPTER TWENTY-FOUR Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS TORQUE ACTING ON SHAFTS OF GENEVA WHEEL AND DRIVER The total torque acting on Geneva wheel shaft The torque on the shaft of crank or driver The efficiency of Geneva mechanism INSTANTANEOUS POWER The instantaneous power on the crank or driving shaft Calculation of average power The average torque M tiðavÞ for complete cycle The average torque for first half-cycle M 2t ¼ M 2t þ M 2ti ¼ M 2t þ J 2a ð24-302Þ It is assumed that M 2t is constant. M 1t ¼ M 2t ! 2 ! 1 1 ¼ðM 2t þ J 2a Þ ! 2 ! 1 1 ð24-303Þ ¼ 0.80 to 0.90 when Geneva wheel shaft is mounted on journal bearings (24-304a) ¼ 0.95 when drive shaft is mounted on rolling contact bearings (24-304b) ¼ 0.75 when the diameter of bearing surface is larger than the outside diameter of Geneva wheel (24-304c) P ¼ M t ! 1000 SI ð24-305aÞ where P in kW, M t in N m, and ! in rad/s P ¼ M t ! 102  10 3 Customary Metric ð24-305bÞ where P in kW, M t in kgf mm, and ! in rad/s P ¼ M t ! 75  10 3 Customary Metric ð24-305cÞ where P in hp m , M t in kgf mm, and ! in rad/s P ¼ M t n 63,000 USCS ð24-305dÞ where P in hp, M t in lbf in, and n in rpm M tiðavÞ ¼ 0 ð24-306Þ M tðavÞ ¼ M ðavÞ ¼ 2 z À 2 M 2t þ zJ 2 1 À 2 ! 2 1 "# 1 ð24-307Þ where J ¼ polar moment of inertia, m 4 ,cm 4 (in 4 ) Particular Formula MISCELLANEOUS MACHINE ELEMENTS 24.87 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS The average power required on the crank or driving shaft Calculation of maximum power The maximum torque on the driven shaft of Geneva wheel The maximum torque on the driving shaft of the crank r 2 r 1 a ω 1 ω 2 F 1 F 2 β β+α α β+α FIGURE 24-57 Forces acting on Geneva wheel. The maximum power required on the shaft of the crank or driver P av ¼ M tðavÞ 1000 ! SI ð24-308aÞ where P av in kW, M tðavÞ in N m, and ! in rad/s P av ¼ M tðavÞ ! 75  10 3 Customary Metric ð24-308bÞ where P av in hp m , M tðavÞ in kgf mm, and ! in rad/s P av ¼ M tðavÞ n 63,000 USCS ð24-308cÞ where P av in hp, M tðavÞ in lbf in, and n in rpm M 2tðmaxÞ ¼ M 2t þ M 2tiðmaxÞ ð24-309Þ where M 2t is constant M 2tiðmaxÞ ¼ J 2aðmaxÞ ¼ J 2aðmaxÞ ! 2 1 2n 60 2 M 1tðmaxÞ ¼ M 2t 1 ! 2ðmaxÞ ! 1 þ J ! 1 1 ð 2a ! 2 Þ max ð24-310aÞ M 1tðmaxÞ ’ M 2t 1 À 1 þ 2 ð1 À 2 Þðcos m À Þsin m ð1 À 2 cos m þ 2 Þ 3  J! 2 1 1 ð24-310bÞ where ¼ m at which M t1 is maximum P 1ðmaxÞ ¼ M 1tðmaxÞ ! 1000 SI ð24-311aÞ where P 1ðmaxÞ in kW, M 1tðmaxÞ in N m, and ! in rad/s P 1ðmaxÞ ¼ M 1tðmaxÞ ! 102  10 3 Customary Metric ð24-311bÞ where P 1ðmaxÞ in kW, M 1tðmaxÞ in kgf mm, and ! in rad/s Particular Formula 24.88 CHAPTER TWENTY-FOUR Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS FORCES AT THE POINT OF CONTACT (Fig. 24-57) The maximum force at the point of contact between the roller pin and slotted Geneva wheel The component of maximum friction force at the point of contact due to the friction torque M 2t on the driven Geneva wheel shaft For maximum values of F 2i For design data for external Geneva mechanism INTERNAL GENEVA WHEEL The time required for indexing Geneva wheel, s The time during which Geneva wheel is at rest, s The t i =t ratio The t r =t ratio The working time coefficient of Geneva wheel The relationship between crank or driver angle and Geneva wheel angle P 1ðmaxÞ ¼ M 1tðmaxÞ n 63,000 USCS ð24-311cÞ where P 1ðmaxÞ in hp, M 1tðmaxÞ in lbf in, and n in rpm F 2ðmaxÞ ¼ M 2t r 2 ð24-312aÞ F 2ðmaxÞ ¼ F ðmaxÞ þ F iðmaxÞ ð24-312bÞ where r 2 ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 2 À 2ar 1 cos þ r 2 1 q ¼ r 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 À 2 cos þ 2 q F 2ðmaxÞ ¼ M 2t r 2ðminÞ ¼ M 2t r 1 1 À ð24-313Þ where r 2ðminÞ ¼ a Àr 1 ¼ 1 À 1 r 1 Refer to Table 24-24. Refer to Table 24-25A. t i ¼ z þ 2 z 60 2n ð24-314Þ t r ¼ z À 2 z 60 2n ð24-315Þ t i t ¼ z þ 2 2z ð24-316Þ t r t ¼ z À 2 2z ð24-317Þ k ¼ z þ 2 z À 2 > 1 ð24-318Þ ¼ tan À1 sin 1 þ cos ð24-319Þ Particular Formula MISCELLANEOUS MACHINE ELEMENTS 24.89 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS The angular velocity of Geneva wheel The maximum angular velocity of Geneva wheel The angular acceleration, 2a , of Geneva wheel For values of 2a at start and finish of indexing For curves of angular velocity and angular accelera- tion of internal Geneva wheel The contact forces between the slotted wheel and the pin on the driving crank of the internal Geneva wheel are calculated in a manner similar to that for the external Geneva wheel Materials Chromium steel 15 Cr 65 case-hardened to R c 58 to 65 is used for the roller pin on the driver or crank. Chromium steel 40 Cr 1 hardened and tempered to R c 45 to 55 is used for the sides of slotted Geneva wheel. ! 2 ¼ d dt ¼ ðcos þ Þ 1 þ 2 cos þ 2 ! 1 ð24-320Þ ! 2ðmaxÞ ¼ 1 þ ! 1 ð24-321Þ 2a ¼ d 2 dt 2 ¼Æ ð1 À 2 Þsin ð1 þ 2 cos þ 2 Þ 2 ! 2 1 ð24-322Þ Use Eq. (24-285) of external Geneva wheel. Refer to Fig. 24-58. 0 αα α 2a ω 1 2 α 2a ω 1 2 α 2a ω 1 2 ω 2 ω 1 ω 2 ω 1 0 0.25 0.50 0.75 1.00 0 0.2 0.4 0.6 0.8 FIGURE 24-58 Angular velocity and angular acceleration for four-slot internal Geneva wheel. Particular Formula TABLE 24-24 Maximum F 2i values z 345 6 8 F 2iðmaxÞ Jn 2 r 1 ! 1.966 0.126 0.0318 0.0131 0.00424 TABLE 24-25A Design data for external Geneva mechanism 2aðinitialÞ z ir 1 =ar 2 =aR r r 0 2 =a ! 2ðmaxÞ ¼À ðmaxÞ J max J ¼0 3608 308 0.5 0.886 0.500 0.577 0.134 3008 0.167 6.46 1.732 4846 0 31.44 À672 4458 458 1 0.707 0.707 1.000 0.293 2708 0.250 2.41 1.000 11824 0 5.41 À48 6308 608 2 0.500 0.866 1.732 0.500 2408 0.333 1.00 0.577 22854 0 1.35 À6 822830 0 67830 0 3 0.383 0.924 2.414 0.617 2258 0.375 0.620 0.414 31838 0 0.699 À2.25 10 188 728 4 0.309 0.951 3.078 0.690 2168 0.400 0.447 0.325 38830 0 0.465 À1.24 24.90 CHAPTER TWENTY-FOUR Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MISCELLANEOUS MACHINE ELEMENTS [...]... (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð24-300Þ ð24-301Þ MISCELLANEOUS MACHINE ELEMENTS 24.87 MISCELLANEOUS MACHINE ELEMENTS Particular Formula TORQUE ACTING ON SHAFTS OF GENEVA WHEEL AND DRIVER The total torque acting on Geneva wheel shaft M2t ¼ M2t þ M2ti ¼ M2t þ J 2a ð24-302Þ It is assumed that... (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MISCELLANEOUS MACHINE ELEMENTS MISCELLANEOUS MACHINE ELEMENTS Particular 24.89 Formula P1ðmaxÞ ¼ M1tðmaxÞ n 63,000 USCS ð24-311cÞ where P1ðmaxÞ in hp, M1tðmaxÞ in lbf in, and n in rpm FORCES AT THE POINT OF CONTACT (Fig 24-57) The maximum... 1.732 1.000 0.577 0. 414 0.325 48460 118240 228540 318380 388300 31.44 5.41 1.35 0.699 0.465 À672 À48 À6 À2.25 À1.24 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MISCELLANEOUS MACHINE ELEMENTS MISCELLANEOUS MACHINE ELEMENTS 24.91... m (lbf in) design torque, N m (lbf in) speed, rpm speed, rps power to be transmitted by universal joint, kW (hp) design power, kW (hp) angle between two intersecting shafts 1 and 2, deg angle of rotation of the driver shaft 1, deg angle of rotation of the driven shaft 2, deg angular velocities of driver and driven shafts respectively, rad/s d Ks Kct Kct l L Mt Mtd n n0 P Pd !1 , !2 Particular Formula... r2ðminÞ ¼ a À r1 ¼ ð24-313Þ 1 1À r 1 For maximum values of F2i Refer to Table 24-24 For design data for external Geneva mechanism Refer to Table 24-25A INTERNAL GENEVA WHEEL The time required for indexing Geneva wheel, s The time during which Geneva wheel is at rest, s zþ2 ti ¼ z tr ¼ zÀ2 z 60 2n 60 2n ð24- 314 ð24-315Þ The ti =t ratio ti z þ 2 ¼ t 2z ð24-316Þ The tr =t ratio tr z À 2 ¼ t 2z... (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð24-318Þ ð24-319Þ MISCELLANEOUS MACHINE ELEMENTS 24.90 CHAPTER TWENTY-FOUR Particular Formula The angular velocity of Geneva wheel !2 ¼ The maximum angular velocity of Geneva wheel d ¼ dt !2ðmaxÞ ¼ The angular acceleration, 2a , of Geneva wheel 2a ¼ ... angular acceleration for four-slot internal Geneva wheel TABLE 24-25A Design data for external Geneva mechanism z 3 4 6 8 10 608 458 308 228300 188 i 308 458 608 678300 728 r1 =a r2 =a Rr r02 =a !2ðmaxÞ 2aðinitialÞ ¼ À ðmaxÞ Jmax J ¼ 0 0.5 1 2 3 4 0.886 0.707 0.500 0.383 0.309 0.500 0.707 0.866 0.924 0.951 0.577 1.000 1.732 2. 414 3.078 0.134 0.293 0.500 0.617 0.690 3008 2708 2408 2258 2168 0.167... McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MISCELLANEOUS MACHINE ELEMENTS 24.88 CHAPTER TWENTY-FOUR Particular The average power required on the crank or driving shaft Formula MtðavÞ ! SI ð24-308aÞ 1000 where Pav in kW, MtðavÞ in N m, and ! in rad/s Pav ¼ MtðavÞ ! Customary Metric...MISCELLANEOUS MACHINE ELEMENTS 24.86 CHAPTER TWENTY-FOUR Particular Formula The ratio of ti to t ti 2 zÀ2 ¼ ¼ ¼ t 2 2z ð24-287Þ The ratio of tr to t tr 2ð À Þ zþ2 ¼ ¼1À ¼ t 2 2z ð24-288Þ The sum of angles of ( þ ) þ ð24-289Þ The... McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MISCELLANEOUS MACHINE ELEMENTS 24.92 CHAPTER TWENTY-FOUR Particular The maximum value of !2 =!1 The minimum value of !2 =!1 Formula !2 !1 ¼ max cos 1 ¼ 1 À sin2 cos ð24-325Þ when sin ¼ þ1, i.e., ¼ 908, 2708, or =2 or 3=2, etc . joint The design torque of universal joint The design power of universal joint For calculation of torque and power transmitted by universal joint for various angles of inclination For design data. rpm 5000 0 . 98 1 . 96 2 . 94 3 . 92 4 . 90 5 . 88 7 . 85 9 . 81 19 . 61 29 . 42 39 . 23 49 . 03 58 . 84 78 . 45 98 . 10 196 . 1 294 . 2 392 . 3 490 . 3 588 . 4 784 . 5 981 . 0 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 8 Design torque, (M td ), kgf m Design torque, (M td ), N m 2 3 4 5 6 8 10 15 18 kgf m 176 . 5 Nm 20 30 40 50 60 80 100 1 FIGURE 24-64 Design curves for single universal. 2 ! 2 1 "# 1 ð24-307Þ where J ¼ polar moment of inertia, m 4 ,cm 4 (in 4 ) Particular Formula MISCELLANEOUS MACHINE ELEMENTS 24.87 Downloaded from Digital Engineering Library @ McGraw-Hill