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Name Class Student No. Date Ex.2-1 Draw the kinematic diagrams of the mechanisms shown below. 4 1 3 2 1 4 2 3 1 Name Class Student No. Date Ex.2-2 Draw the kinematic diagrams of the mechanisms shown below. 1 4 2 3 5 4 6 2 Name Class Student No. Date Ex.2-3 Draw the kinematic diagram of the mechanism shown below. 3 Name Class Student No. Date Ex.2-4 Calculate the degree of freedom of the mechanisms shown below. Indicate all points for attention before the calculation of the DOF. A B C I F H D E J G Fig.2-4(a) I H D B J C A G K F E Fig.2-4(b) 4 Name Class Student No. Date Ex.2-5 Calculate the degree of freedom of the mechanisms shown below. Indicate all points for attention before the calculation of the DOF. M N L C O B D A F E G Fig.2-5(a) A D B Fig.2-5(b) 5 Name Class Student No. Date Ex.2-6 Calculate the degree of freedom of the mechanisms shown below. Indicate all points for attention before the calculation of the DOF. B C A D E Fig.2-6(a) AB=CD BC=AD C B A D Fig.2-6(b) 6 Name Class Student No. Date Ex.2-7 Shown below is the kinematic diagram of an engine mechanism. (1) Calculate the degree of freedom of the mechanism. Indicate all points for attention before the calculation of the DOF. (2) Carry out the structural analysis for the mechanism. (3) Carry out the structural analysis for the mechanism if link EFG is a driver. Note: During structural analysis, list the assembly order of Assur groups, the type of group, the grade of group, the grade of the mechanism, the link serial numbers, the inner pair and the outer pairs of each group in each mechanism. B D 2 C 1 4 A E 3 5 8 F 7 G H 6 7 Name Class Student No. Date Ex.2-8 Carry out the structural analysis for the mechanism (a) if link 1 is a driver. (b) if link 5 is a driver. Note: During structural analysis, list the assembly order of Assur groups, the type of group, the grade of group, the grade of the mechanism, the link serial numbers, the inner pair and the outer pairs of each group in each mechanism. D 5 4 E B 2 1 A 3 C 6 8 Name Class Student No. Date Ex.2-9 Someone tries to design a punch machine which will transform a continuous rotation of gear 1 into a translation of the punch 4. Shown below is the schematic diagram of the mechanism he designs. Can the mechanism realize the task? How do you rectify it? 3 2 4 5 1 Ex.2-10 Someone tries to design a mechanism which would transform a continuous rotation into an oscillation. Shown below is the schematic diagram of the mechanism he designs. Can the mechanism realize the task? How do you rectify it? E C 2 3 B 4 1 A D 9 Name Class Student No. Date Ex.3-1 Locate all instant centres of mechanisms for the position shown. 2 2 3 1 3 1 4 4 Fig3-1(a) Fig3-1(b) 3 n C 3 4 2 F D A 1 n E 2 5 B 1 Fig3-1(c) Fig3-1(d) 3 2 2 4 3 1 4 1 Fig3-1(e) Fig3-1(f) 10 Name Class Student No. Date Ex.3-2 For the position shown of a geared linkage, determine graphically the ratio 3/1 of the angular velocity of gear 3 to that of gear 1, using the method of instant centres. 2 C E 4 B F 5 1 A D 6 3 Ex.3-3 For the position shown of cam mechanism, determine graphically the ratio 2/1 of the angular velocity of follower 2 to that of cam 1, using the method of instant centres. 3 2 1 O ω1 11 Name Class Student No. Date Ex.3-4 In the pivot four-bar linkage shown below, 1= -10rad/sec. Using the method of instant centers graphically, (a) find the velocity of point C for the position shown. (b) for the position shown, locate point E on the line BC (or its extension) which has the minimum velocity among all the points on line BC and its extension, and then calculate its velocity. (c) draw two positions of crank AB corresponding to VC=0. C 2 3 B 1 ω1 4 D A 12 Name Class Student No. Date Ex.3-5 In the six-bar mechanism shown below, XA=0, YA=0, XD=450mm, YD=0, LAB=150mm, LBC=400mm, LDC=350mm, CDE=30, LDE=150mm, LEF=400mm. Crank AB rotates at a constant speed 10rad/sec. A main program is required to analyze the output motions of the point F. The mechanism will be analyzed for the whole cycle when the driver AB rotates from 0 to 360 with a step size of 1 =5. C 2 B E 3 ω θ 1 5 1 F A D 4 6 13 Name Class Student No. Date Ex.3-6 The mechanism shown below has the following dimensions: X A=0, YA=0, XD=200mm, YD=0, LAB=80mm, LCD=60mm and LBE=380mm. Crank AB rotates at a constant speed of 10rad/sec. A main program is required to analyze the output motions of the point E. The mechanism will be analyzed for the whole cycle when the driver BA rotates from 0 to 360 with a step size of 1 =5. E C θ1 3 A D ω1 2 4 14 Name Class Student No. Date Ex3-7 . In the mechanism shown below, XG=YG=0, XB= - 42, YB=39, XD=10, YD=75, LBA=23mm, LGF=12mm, LFE=95mm, LEC=69mm, LDC=48mm, EFG=90. Crank BA rotates at a constant speed of 10 rad/sec. A main program is required to analyze the output motions of the point C. The mechanism will be analyzed for the whole cycle when the driver BA rotates from 0 to 360 with a step size of 1 =5. E 6 D 2 4 A B 5 1 6 3 C G F 6 15 Name Class Student No. Date Ex.3-8 In the six-bar mechanism shown below, XB=0, YB=0, XF=37.2, YF=17.5, YC=28.8, LFE=16.8mm, LEC=39.2mm, LCD=20.633mm, LDE=36.4mm, BGA=90, LBG=9mm, LGA=58mm. Crank FE rotates clockwise at a constant speed of -10 rad/sec. A main program is required to analyze the output motions of point A. The mechanism will be analyzed for the whole cycle when driver FE rotates from 360 to 0 with a step size of 1 =-5. A D 6 5 C 3 F 4 2 ω1 B E 16 Name Class Student No. Date Ex.4-1 According to link dimensions, determine the type of the pivot four-bar linkages shown below. 90 100 110 70 70 45 40 120 50 100 100 90 70 60 70 17 Name Class Student No. Date Ex.4-2 In the revolute four-bar mechanism shown below, the crank AB is a driver. (a) Find the pressure angle and the transmission angle of the mechanism at the position shown. (b) Find the angular stroke max of the link DC. (c) Find the crank acute angle between the two limiting positions. (d) Find the maximum pressure angle max and the minimum transmission angle min. (e) Are there any dead-points in the whole cycle of the motion if link DC is the driver? If so, when or where? Draw the dead-point positions of the mechanism. C 3 2 A D 1 4 B 18 Name Class Student No. Date Ex.4-3 In an offset slider-crank mechanism ABC, crank AB is the driver. The maximum pressure angle MAX=30. Find the stroke H of the slider and the crank acute angle between the two limiting positions. B A e Ex.4-4 Determine graphically the angular strokes of rockers AB and CD, respectively. C A D 19 Name Class Student No. Date Ex.4-5 Shown are the two positions, B1C1 and B2C2, of coupler BC of a revolute four-bar linkage ABCD. Link AB is the driver. The pressure angle at the first position is 0o. The second position of the mechanism is a toggle position. Design the linkage. Describe briefly the drawing steps. B1 C1 B2 C2 20 Name Class Student No. Date Ex.4-6 In a crank-slider mechanism, two sets of corresponding positions between the slider and a line segment AE on the crank ABE are known, as shown below. The position C1 of the slider is its left limiting position. Find the first position B1 of the revolute B. Describe briefly the drawing steps. E1 E2 A C1 C2 21 Name Class Student No. Date Ex.4-7 In a revolute four-bar linkage ABCD, side link AB is the driver. The positions of side link CD and line segment CE on the coupler CBE corresponding to two positions of the linkage are known. The first position of the linkage is also a dead point. Find the second position B2 of the revolute B. Describe briefly the drawing steps. 2 E1 C2 C1 D A 22 Name Class Student No. Date Ex.4-8 In a crank-rocker linkage ABCD, side link AB is the driver. The positions of the rocker CD corresponding to two positions of the linkage are shown below. At the first position of the linkage, the pressure angle of the linkage is zero. Position DC2 is one of the limit positions of the rocker. Find the first position B1 of the revolute B. Describe briefly the drawing steps. C1 C2 A D 23 Name Class Student No. Date Ex.4-9 In an offset slider-crank mechanism ABC, two sets of corresponding positions between crank AB and point F on slider are known. When the crank AB is located at position AB1, the slider reaches its left limit position. Find the first position C1 of the revolute C on the slider. Describe briefly the drawing steps. B2 F1 F2 A B1 24 Name Class Student No. Date Ex.4-10 Design a crank-rocker mechanism ABCD that will give a k value of 1.25 with an angular stroke =60o for rocker DC, as crank AB rotates in a constant speed. The length of the rocker DC is 60mm. The length of frame AD is 75mm. Describe briefly the drawing steps. ψ D 25 Name Class Student No. Date Ex.4-11 In an offset slider-crank mechanism, the offset e is 20mm. The coefficient k of travel speed variation is to be 1.3. The working stroke H of the slider is to be 50mm. Design the offset slider-crank mechanism Ex.4-12 Design an offset slider-crank mechanism. The ratio of the length of the coupler BC to the length of the crank AB is to be 4. The coefficient k of travel speed variation is to be 1.2. The working stroke H of the slider is to be 200mm. 26 Name Class Student No. Date Ex.5-1 A plate cam with positive-offset translating roller follower is to have the following motion: a rise through lift h=40mm with a sine acceleration motion curve during 0=150, S=30, a return with a 3-4-5 polynomial motion curve during 0'=120, and S'=60. The cam rotates clockwise. The given dimensions are: rP=40mm. rR=12mm, e=12mm and rC=25mm. Construct the pitch curve and the cam contour graphically with a scale of 1:1. Label in red ink the centreline of the follower, S, the roller and the pressure angle corresponding to = 60 and = 0. 0 30 60 90 120 150 180 210 240 270 300 330 360 S 27 Name Class Student No. Date Ex.5-2 A plate cam with translating offset roller follower has the same motion curve and dimensions as those in Ex.5-1. Write a program to calculate the co-ordinates of the pitch curve, the cam contour and the locus of the centre of the milling cutter, the pressure angle , and the radius B of curvature of the pitch curve. 28 Name Class Student No. Date Ex.5-3 For the plate cam with translating offset roller follower as shown below, arcs GH and IJ are two arcs with centre at O. Indicate the radius rP of prime circle, offset e, cam angle 0 for rise, cam angle S for outer dwell, cam angle 0' for return, cam angle S' for inner dwell and lift h. For the position shown, indicate pressure angle , displacement S and the corresponding cam angle . B I H O ω G J 29 Name Class Student No. Date Ex.5-4 For the plate cam with translating offset roller follower as shown below, arcs EA, AB and BCD are three arcs with centre at O, N and P, respectively. Indicate the radius rP of prime circle, offset e, cam angle 0 for rise, cam angle S for outer dwell, cam angle 0' for return, cam angle S' for inner dwell and lift h. For the position shown, indicate pressure angle , displacement S and the corresponding cam angle . A B O P C ω N E 30 Name Class Student No. Date Ex.5-5 A plate cam with an oscillating roller follower similar to that in Fig.5-36 of textbook is to have the following motion: an angular lift MAX =20 with a sine acceleration motion curve during 0=150, S=30, a return with a 3-4-5 polynomial motion curve during 0'=120 and S'=60. The given dimensions are: rP=40mm, LOA=80mm, LAB=76mm, rR=12mm and rC=16mm. Construct the pitch curve and the cam contour graphically with a scale of 1:1. Label in red ink the frame OA, , centreline AB of the follower, the roller and corresponding to =60 and =0. 0 30 60 90 120 150 180 210 240 270 300 330 360 31 Name Class Student No. Date Ex.5-6 A plate cam with an oscillating roller follower has the same motion curve and dimensions as those in Ex.5-5. Write a program to calculate the co-ordinates of the pitch curve, the cam contour and the locus of the centre of the milling cutter, the pressure angle and the radius B of curvature of the pitch curve. 32 Name Class Student No. Date Ex.5-7 For the plate cam with oscillating roller follower as shown below, arcs GH and IJ are two arcs with centre at O. Indicate radius of prime circle rP, cam angle for rise 0, cam angle for outer dwell S, cam angle for return 0', cam angle for inner dwell S' and angular lift MAX. For the position shown, indicate pressure angle , angular displacement of follower and the corresponding cam angle . A H B ω G O I J 33 Name Class Student No. Date Ex.5-8 A plate cam with a translating flat-faced follower is to have the following motion: a rise through lift h=50mm with a sine acceleration motion curve during 0=150, S=30, a return with a 3-4-5 polynomial motion curve during 0'=120 and S'=60. The cam rotates clockwise. The given dimensions are: rP=50mm. rC=20mm. Construct the pitch curve and the cam contour graphically with a scale of 1:1. Label in red ink the follower centreline, S, the flat face, the tangent point T between the cam contour and the flat face and corresponding to =60 and =0. 0 30 60 90 120 150 180 210 240 270 300 330 360 S 34 Name Class Student No. Date Ex.5-9 A plate cam with a translating flat-faced follower has the same motion curve and dimensions as those in Ex.5-8. Write a program to calculate the co-ordinates of the pitch curve, the cam contour and the locus of the centre of the milling cutter and the radius T of curvature of the cam contour. 35 Name Class Student No. Date Ex.6-1 A pair of standard spur involute gears has a module of 5mm, pressure angle =20 , centre distance a=350mm, transmission ratio i12 =9/5. Calculate the numbers of teeth(Z1 and Z2), reference diameters(d1 and d2), addendum diameters(da1 and da2), base diameters(db1 and db2), tooth thickness s, spacewidth e, pressure angles on the addendum circles(a1 and a2), the radii of curvatures of tooth profile on the reference circles(1 and 2), and the radii of curvatures of tooth profile on the addendum circles(a1 and a2). Ex.6-2 How many teeth would an external standard spur involute gear have when its dedendum circle and its base circle coincide? Which one is bigger as the number of teeth increases ? 36 Name Class Student No. Date Ex.6-3 Shown are a pair of involute profiles C1 and C2 with the common normal n-n passing through the contact point K. (1) Draw the two base circles and two pitch circles. (3) Label the theoretical line of action N1N2 and actual line of action B1B2. (3) Label the working pressure angle ’ and pressure angle K at the point K. (4) Label the actual working section DG of the profile C2. (5) Find out point M2 on the profile C2 which will engage with point M1 on the profile C1. O1 n M1 C2 K C1 n O2 37 Name Class Student No. Date Ex.6-4 Shown are a pair of involute pinion and rack with their pitch circle and pitch line. Determine graphically the actual line of action B1B2, the actual working section EF on the tooth profile of the pinion 1 and the actual working section GH on the tooth profile of the rack. O1 P 38 Name Class Student No. Date Ex.6-5 A pair of external spur gears have the parameters as: Z1=10, Z2=27, m=10mm, =20, ha*=1, c*=0.25, working center distance a’=185mm. Neither gear has cutter interference. (1) What type of corrected gear pair does it belong to? Why? (2) What are the ranges of modification coefficients x1 and x2, respectively? (3) If x1=0.5, calculate ra2, rb2, S2, a2, and a2 for gear 2. 39 Name Class Student No. Date Ex.6-6 A pair of external spur gears have the parameters as: Z1=20, Z2=40, m=2mm, =20, ha*=1, c*=0.25, df1=37.0mm, S2=2.413652185mm. (1) What are the modification coefficients x1 and x2? (2) What type of corrected gear pair does it belong to? Why? (3) Calculate rb1, ra1, a1, a1, S1, and 1 for gear 1. 40 Name Class Student No. Date Ex.6-7 There is a pair of external standard spur gears in a shaping machine with Z1=17, Z2=118, m=5mm, =20, ha*=1, c*=0.25. The pinion is worn out and the gear is worn to such an extent that the tooth thickness is decreased by 0.75mm. The gear is to be repaired by addendum modification and a new pinion is to be manufactured to mesh with the repaired gear. What is the minimum modification coefficient of the new pinion if the original frame is still used? If x 1=0.3, calculate ra1, rf1, S1, a1, a1, and . 41 Name Class Student No. Date Ex.6-8 In the gear train shown below, both gear pairs must have the same working center distance. Z1=27, Z2=60, Z2’=63, Z3=25, ha*=1, c*=0.25, m=5mm. The gear pair 2’ and 3 is a corrected gear pair with reference center distance. The modification coefficient x2 of the gear 2 is zero. What type of corrected gear pair should the gear pair 1 and 2 adopt? Give the brief reason. (2) Is the gear 2 a standard gear? Why? (3) Calculate x1, S1, rb1, rf1, a1, and a1. 1 3 2 2' 42 Name Class Student No. Date Ex.6-9 The following dimensions of a pair of external spur gears are known: m, Z1, i12, , ha*, c*, S1, and rf2. Write all formulae to calculate according to calculation steps. 43 Name Class Student No. Date Ex.6-10 A pair of standard external helical gears have the following parameters: Z1 =20, Z2 =40, mn =8mm, n =20, han*=1, B=30mm, a=250mm. Find the helix angle , total contact ratio and the virtual numbers of teeth Zv1, Zv2. 44 Name Class Student No. Date Ex.6-11 A pair of standard external helical gears with transmission ratio i3.5 is to be designed. According the strength calculation, mn=2.5mm, amin=111.5mm. Find a integral center distance a, Z1, Z2, and the helix angle . 45 Name Class Student No. Date Ex.6-12 A standard worm wheel has the number of teeth Z2 = 40, reference diameter d2=320mm. It meshes with a single-threaded worm. (1) Determine module of the worm gear set on the mid-plane mt2 and mx1; (2) Determine axial pitch px1 and lead l of the worm; (3) Choose reference diameter of worm; (4) Calculate lead angle 1 of the worm; (5) Calculate centre distance a without modification. 46 Name Class Student No. Date Ex.6-13 A pair of straight bevel gears have parameters Z1 =15, Z2 =30, m=5mm, ha*=1, c* =0.2, =90 . Determine other dimensions d1, d2, da1, da2, df1, df2, 1, 2, a1, a2, f1, f2 , R, Zv1 and Zv2 with constant bottom clearance. 47 Name Class Student No. Date Ex.7-1 Shown below is a hoist. The teeth numbers of all the gears are: Z1=20, Z2=50, Z2’=15, Z3=30, Z3’=1, Z4=40, Z4’=18, Z5=52. Find the train ratio i15 and point out the rotating direction of the handle to raise the weight. 4 5 4' 3' 2 3 1 2' 48 Name Class Student No. Date Ex.7-2 Shown below is the gear train in a clock. S, M and H denote the pointers of second, minute and hour, respectively. The given numbers of teeth are Z1=Z2’=8, Z2=64, Z3’=12, Z4’=15. If the modules of gear 4 and gear 5 are equal, find the numbers of teeth Z3, Z4, and Z5. 4 4' 3 M 3' H 5 2' 2 S 1 49 Name Class Student No. Date Ex.7-3 Shown below is a gear train in which gear 3 engages with gears 2 and 4 simultaneously. What kind of gear train is it? If Z1=34, Z2=Z3=20, and Z4=74, find the train ratio i1H. 2 H 1 4 50 Name Class Student No. Date Ex.7-4 Shown below is a differential gear train with Z1=15, Z2=25, Z2’=20, Z3=60, n1=200 r/min, n3=50 r/min. Find both the magnitude and the direction of nH when (1) n1 and n3 are in the same direction; (2) n1 and n3 are in the opposite directions. 2 2' H 1 3 51 Name Class Student No. Date Ex.7-5 In the combined gear train shown below, Z1=36, Z2=60, Z2’=23, Z3=49, Z3’=69, Z4=31, Z5=131, Z6=94, Z7=36, Z8=167, n1=3549 r/min. Find both the magnitude and the direction of nH. H 7 4 3 6 3' 2' 8 5 n1 1 2 52 Name Class Student No. Date Ex.7-6 In the combined gear train shown below, Z1=20, Z2=25, Z3=15, Z1’=30, Z4=70, Z4’=60, nH=110 r/min. Find both the magnitude and the direction of n1. 2 3 1 1' H nH 4 4' 53 Name Class Student No. Date Ex.7-7 In the combined gear train shown below, Z1= Z5= Z6=17, Z2=18, Z2’=27, Z3=34, Z4=51. n1=110 r/min. Find both the magnitude and the direction of n6. 2' n1 2 6 5 1 3 4 54 Name Class Student No. Date Ex.7-8 Shown below is a gear train with Z1=16, Z2= Z2’ =25, Z3=57, Z4=56. Find the train ratio i14. 2 2' H 1 3 4 55 Name Class Student No. Date Ex.7-9 In the gear train shown below, Z2=15, rotation speed of the shaft M of electric motor relative to the rotating frame H is n M =12rpm, nH= － 2rpm. H Calculate Z1. M H 2 1 56 Name Class Student No. Date Ex.7-10 In the gear train shown below, Z1=20 and i1H=4.5. All the gears are * standard spur gears with h a =1. Determine the numbers of teeth Z2 and Z3 and the number of planet gears k. If the mechanical efficiency of every pair of gears is =0.9, find the mechanical efficiency of the gear train 1H. 2 H 1 3 57 Name Class Student No. Date Ex.9-1 In the cam-linkage shown below, the driving rotary block 1 rotates continuously. By designing the contour of the fixed cam correctly, the sliding block 4 can get a predetermined motion. Analyze the motion transmission route and draw its structural block diagram. What is the combination pattern of this combined mechanism? B 2 3 A C 1 4 5 5 Ex.9-2 In the combined gear train shown below, gear 1 is the driver, link 6 is the output. Analyze the motion transmission route and draw its structural block diagram. What is the combination pattern of this combined mechanism? 2' n1 2 6 5 1 3 4 58 Name Class Student No. Date Ex.9-3 In the gear-linkage shown below, crank AB is the driver. The output pinion 4 is located on shaft A. Analyze the motion transmission route and draw its structural block diagram. What is the combination pattern of the combined mechanism? 5 D A 3 4 1 B 2 C Ex.9-4 The kinematic chain shown below is similar to that in Fig.9-16a of textbook. However, in the kinematic chain shown below, the driver is link 3 instead of gear 1, while gear 5 is still an output gear. Analyze the motion transmission route and draw its structural block diagram. What is the combination pattern of this combined mechanism? 6 C 2 B 3 1 5 A D 4 59 Name Class Student No. Date Ex.10-1 There are four imbalances in a disk-like rotor. The masses, rotating radii and angular orientations are: m1=8kg, m2=10kg, m3=8kg and m4=7kg, r1=10mm, r2=10mm, r3=15mm and r4=20mm. The rotor is to be balanced by removing a mass mC at a rotating radius of 25mm. Find the magnitude mC and its location angle C. m1 m2 r2 r r 1 4 r3 m4 m3 Ex.10-2 Among the following rotors, rotors are statically balanced only, rotors are dynamically balanced. m r r r r r r r r m m m m L L L L L L (a) (b) 2m m 3m r r r r r 3m 2r m L L L m 1.5L 1.5L 60 Name Class Student No. Date Ex.10-3 On a circular rotating disk, there are two circular holes. d 1=40mm, d2=50mm. The rotating radii of the hole centers is r1=100mm and r2=140mm, respectively. The location of the two holes are shown below. The disk is to be balanced by drilling third hole. The rotating radius of the third hole center is to be r3=150mm. Find the diameter d3 and its location angle 3. d2 r2 30° r1 d1 61 Name Class Student No. Date Ex.10-4 Four unbalanced masses m1, m2, m3 and m4 exist on four transverse planes spaced equally. Their mass-radius products are: m1r1=3kgmm, m2r2=2kgmm, m3r3=5kgmm, and m4r4=4kgmm, respectively. Their locations are as shown. Suppose the system is to be balanced fully by two balancing mass-radius products, Pb1 and Pb3, on the planes I and III, respectively. Determine the amounts and angular locations of the two balancing mass-radius products. III I y m2 m3 r2 r3 r1 r4 m1 m4 x L L L 62 Name Class Student No. Date Ex.10-5 On the non-disk rigid rotor shown below, there exist four unbalanced masses. Their masses, rotating radii and angular locations are: m1=10kg, m2=15kg, m3=20kg and m4=10kg, r1=40mm, r2=30mm, r3=20mm and r4=30mm and 1=120, 2=240, 3=300 and 4=30. L12 =L23 =L34. The system is to be balanced dynamically by adding a mass mA on the balancing plane A at a rotating radius rA of 50mm and removing a mass mB on the balancing plane B at a rotating radius rB of 60mm. Determine the magnitudes (mA and mB) and angular locations (A and B) of the required masses. A B m1 m1 Y r 1 m4 m4 1 r4 4 r3 X m3 2 3 m3 m2 r2 m2 L 12 L 23 L 34 63 Name Class Student No. Date Ex.11-1 Shown below is a slider-crank mechanism driven by a pair of gears. Z1 =20, Z2=60. The moment of inertia of pinion 1 about its centre of mass A is J1=0.15kgm2. The moment of inertia of gear 2 about its centre of mass B is J2=1.8kgm2. The length of crank BC is 100mm. The mass of coupler CD is m3=10kg. Its centre of mass is located at the middle of CD. Its moment of inertia is J4=1kgm2. The mass of slider 4 is m4=5kg. The resistant force F4 acts on slider 4. F4=25kN. Take the pinion 1 as the equivalent link. Find the equivalent resistant moment of force Mr of F4 and the equivalent moment of inertia J of the whole mechanism for the position shown. 2 4 B F4 A 1 D 5 3 C 64 Name Class Student No. Date Ex.11-2 A planetary gear train with two planets is shown below. The module of all the gears is m. The numbers of teeth are Z1, Z2, and Z3, respectively. The moments of inertia of the links are J1, J2, and JH. The mass of a planet is m2. The resistant moment of force MH acts on the planet carrier H. Take gear 1 as the equivalent link. Find the equivalent resistant moment of force Mr of MH and the equivalent moment of inertia J of the whole gear train. 2 MH H OH O1 1 65 Name Class Student No. Date Ex.11-3 Shown below is a hoister driven by a pair of gears. Z1 =20, Z2=60. The moment of inertia of the pinion 1 about its centre of mass is J1=0.25kgm2. The moment of inertia of the gear 2 about its centre of mass is J 2=1.8kgm2. The diameter of the tub wheel is D=300mm. The mass lifted is Q=100kg. Take the the pinion 1 as the equivalent link. Find the equivalent moment of inertia Je of the whole mechanism and the equivalent resistant moment Mr of weight Q. 2 D 1 Q 66 Name Class Student No. Date Ex.11-4 The driven moment Mr of a machine on the equivalent link is a given function of the rotating angle as shown in the figure. The angular period of moment is T=2. The input moment Md is constant. (1) Calculate the input moment Md. (2) Calculate the maximum increment of work Wmax. (3) The average speed is nm =620 r/min. The allowable coefficient of speed fluctuation is []=0.01. Masses and moments of inertia of all the links are neglected. Find the minimum moment of inertia JF of the flywheel on the equivalent link. Mr 100Nm T 0 3 6 7 2 4 4 4 67 Name Class Student No. Date Ex.11-5 In a mechanical system running at a periodic and stable speed, a rotating link is selected as the equivalent link. The equivalent input moment Md and the equivalent driven moment Mr on the equivalent link are given functions of the rotating angle as shown in the figure. The works of the some phases are: f2=1000Nm, f3=800Nm, f4=700Nm, f5=1000Nm, f6=900Nm, f7=400Nm, respectively. Therefore, f1= Nm. The maximum increment of work Wmax= Nm. If the equivalent moment of inertia Je is constant, then the maximum speed of the equivalent link will take place at , the minimum speed of the equivalent link will take place at . Mr f2 f4 Md f6 f1 f3 f5 f7 a b c d e g h i 0 T 68 Name Class Student No. Date Ex.12-1 List and draw the schematic diagrams of four mechanisms which have at most 4 links and can transform a continuous rotation into an oscillation. Give the name of each mechanism. 69 Name Class Student No. Date Ex.12-2 List and draw the schematic diagrams of four mechanisms which have at most 4 links and can transform a continuous rotation into a translation back and forth. Give the name of each mechanism. 70