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2-1Please draw the kinematic diagrams of the mechanisms shown below。
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Exercise of mechanisms and machine theory
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2-2 Please calculate the DOF of mechanisms as follows, can you point out these mechanisms have a determined motion or not ? (The link with arrow is driving link)
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（c） （d）
Exercise of mechanisms and machine theory
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Exercise of mechanisms and machine theory
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3-1 Please confirm the location of the instant centres of mechanisms as follows（Using the sign Pij）。
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Exercise of mechanisms and machine theory
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4-1 According to the link dimension ,determine the type
of four-bar linkage holding different link as frame？
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Exercise of mechanisms and machine theory
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4-2 In a revolute four-bar linkage ABCD shown as below b=100mm c=80mm d=110mm
(1)Find the range of the values for the length LAB of link AB if the linkage is either (a) crank-rocker mechanism with crank AB ,or(b) a double-rocker mechanism.
(2) Can the linkage be a double-crank mechanism by choosing LAB suitably?Why?
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Exercise of mechanisms and machine theory
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4-3 In the double-crank linkage ABCD shown as below LAB =80mm LBC =180mm LCD =230mm LAD=200 The driver BC rotates at a constant speed. Find the minimum transmission angle γminof the linkage
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Exercise of mechanisms and machine theory
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4-4 In the revolute four-bar linkage ABCD Let link AD is the frame LAB =60mm LBC =130mm LCD =140mm LAD=200mm and ∠BAD=1350
(1)Determine the type of the revolute four-bar mechanism
(2) If the side link AB is a driver and rotates at a constant speed (a)find the pressure angle α and transmission angle γ of the mechanism at that position
(b) Find the angular ϕmax stroke of the link CD
(c) Find the crank acute angleθ between the two limiting positions
(d) Calculate the time ratio K
(e) Will any dead-point occur during the whole cycle of the motion?
(f) Find the maximum pressure angle αmax and the minimum
transmission angle γmin
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Exercise of mechanisms and machine theory
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4-5 Design the revolute four-bar linkage ABCD according to the figure as below:
Let the length of rocker LCD =75mm , LAD=100mm and Link AD is the frame , the time ratio K=1.5 , The angle between one limiting position of rocker and the frame ∠CDA=450,Calculate the length of LAB 、 LBC （has two results）
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Exercise of mechanisms and machine theory
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4-6 Design the offset slider-crank mechanism ABC according to the figure as below: The crank AB is the driver, Let the length of crank LAB =25mm, The offset e=10mm, The maximum pressure angle αmax=300 Find the stroke H of the slider and the crank acute angle
θ between the two limiting positions.
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Exercise of mechanisms and machine theory
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4-7 图所示为一牛头刨床的主传动机构，已知lAB=75mm，
lDE=100mm ，行程速比系数K=2，刨头5的行程H=300mm，要求在整个行程中，推动刨头5有较小的压力角，试设计此机构。
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Exercise of mechanisms and machine theory
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5-1 For the plate cam with translating offset knife-edge follower Let the lifth=2.4mm，cam angle for rise
δ0=1200，cam angle for outer dwell δs=600，cam
′=1200，cam angle for inner dwell angle for return δ0
δs′=600.The follower rise as constant acceleration and
deceleration motion curve；and return as cosine acceleration motion curve.
Please draw the displacement curve of the follower.
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Exercise of mechanisms and machine theory
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5-2 For the plate cam with translating offset knife-edge follower shown as below
Please draw the displacement curve of the follower by graphical method
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Exercise of mechanisms and machine theory
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5-3 图示为一偏置滚子从动件盘形凸轮机构。已知凸轮轮廓由三段圆弧和
一直线组成，它们的圆心分别O、O/及O//，半径分别为
r=18mm,r′=36mm及r′′=5mm，偏距e=8mm。滚子半径rT=5mm。现要求：
1）、画出凸轮的理论轮廓曲线及基圆；
2）、求出从动件的行程h、推程运动角δa及回程运动角δc； 3）、标出图示位置从动件的位移s及凸轮机构的压力角α； 4）、标出凸轮由图示位置转过600时，从动件的位移S/及凸轮机构的
压力角α′。
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Exercise of mechanisms and machine theory
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6-1 For the figure shown as below，Let the radius of base circle rb=30mm The radius of the involute at the point K rk=35mm,KK′=15mm，Find：
1) The radius of the involute at the point K/ rk′and the pressure angleαk′。 2) ifrk′′
=rk′。Calculate the length of arcK′K′′.
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Exercise of mechanisms and machine theory
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6-2 An involute standard spur gear has parameters Z=26, m=3mm, h*a=1,α=200. Find the radii of curvature of tooth profile on the reference circle and the tip circle and the pressure angle on the tip circle
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Exercise of mechanisms and machine theory
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6-3 A pair of standard external spur involute gears has a
0
α=20module of 5mm, pressure angle ,center distance
a=350mm, transmission ratio i12=9/5.
Calculate the numbers of teeth Z1,Z2,reference diameters d1,d2,addendum diameters da1,da2,base diameters db1,db2,tooth thickness s and spacewidth e.
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Exercise of mechanisms and machine theory
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6-4 For a pair of external standard spur gears pressure angle α=200, module m=20mm, Z1=30, Z2=40.
(1)Calculate the working pressure angle α′ when the working center distance is a/=725mm.
(2)If the working pressure angle center distance is a/.
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′=22030′,find the αExercise of mechanisms and machine theory
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6-5 For a pair of external standard spur gears
α′=α=200, m=5mm, Z1=19, Z2=42.
Calculate the contact ratio
εα
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Exercise of mechanisms and machine theory
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6-6 已知一对外啮合变位齿轮传动，Z1=Z2=12，m=10mm，
*
α＝200，ha=1,a′=130mm，试设计这对齿轮传动(列表给出两轮
的y,ha,hf,d,da,df,db,s)，并验算重合度及齿顶圆齿厚（Sa应大
于0.25m，取x1=x2）。
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Exercise of mechanisms and machine theory
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6-7 A pair of standard external helical gears have the following parameters:, m=5mm, Z1=20, Z2=118 B=30mm
*
a=350mm,αn=200han=1.Find the helix angle β,total
contact ratio εγand the virtual numbers of teeth Zv1,Zv2.
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Exercise of mechanisms and machine theory
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7-1 Shown in figure below . The teeth numbers of some gears are given Z1=Z1′=15, Z2=35, Z4′=1 (righthanded), Z5=40, Z6=1(lefthanded), Z7=28 Z5′=64, Find the teeth number ofZ2′, Z3, Z4 .
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Exercise of mechanisms and machine theory
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7-2 shown in figure below. It is a differential gear train with
Z1=15,
Z2=25,
Z2′=20,
Z3=60. n1=200r/min.
n3=50r/min. Find nH when
(1) n1 and n3 are in the same direction (2) n1 and n3 are in the opposite direction
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Exercise of mechanisms and machine theory
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7-3 shown as figure below. Every gear is standard gear and they have the same module, The teeth numbers are given Z1=14Z2=38,Z3=70. Find the ratio i1H.
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Exercise of mechanisms and machine theory
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7-4 In the combined gear train shown in figure below
Z1=36,Z2=60,Z3=23,Z4=49,Z4/=69,Z5=31,Z6=131,
Z7=94,Z8=36,Z9=166,n1=3549r/min. Find both the
magnitude and the direction of nH.
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Exercise of mechanisms and machine theory
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7-5 In the combined gear train shown in figure below
Z1=Z5=Z6=17,Z2=27,Z2′=18,Z3=34,Z4=51,Find the
train ratio i16.
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Exercise of mechanisms and machine theory
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7-6如图所示为一减速器，已知：Z1=26,Z2=32,Z1/=18,Z5=14,
Z4/=24,Z4=Z3=Z2/=12。试求 i1H=?
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Exercise of mechanisms and machine theory
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7-7 现需设计一如图所示的2K—H型行星减速器，要求的减速比
为5.33，设行星轮数k=4，并采用标准齿轮传动，试确定各轮的齿数。
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Exercise of mechanisms and machine theory
Name： class ： Order number： Grade： 8-1 某自动机床的工作台要求有六个工位，转台停歇时进行工艺动作，其中最长的一个工序为30秒钟。现拟采用一槽轮机构来完成间歇转位工作。设已知槽轮机构的中心距L=300mm，圆销半径r=25mm，槽轮齿顶厚b=12.5mm，试绘出其机构简图，并计算槽轮机构主动轮的转速。
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Exercise of mechanisms and machine theory
Name： class ： Order number： Grade： 8-2 下图所示为某牛头刨床工作台送进机构中的螺旋传动，丝杠2的导程为6mm，要求设计一棘轮机构来驱动丝杠，实现工作台的间歇进给运动，而且使每次送进量可在0.2~1.2mm之间作有级调整（共6级），又设棘轮机构由一曲柄摇杆机构驱动（棘爪装在摇杆上），试绘出机构简图，并作必要的计算和说明。
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Exercise of mechanisms and machine theory
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8-3 在利用图示镗刀头镗一φ55mm的孔时，发现被镗孔的实际直
径为φ54.88mm，问镗刀头应如何调整方能获得所需的尺寸？
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Exercise of mechanisms and machine theory
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10-1 The disk-like rotor in fig below has unbalanced masses m1=10kg,m2=21.4kg,m3=36kgat rotating radii
r1=100mm,r2=112mm,r3=110mm, angular orientations
θ1=300,θ2=1300,θ3=2700.Determine the magnitude mC and
the location angle θC of the counterweight if it is to be placed at a rotating radii rC of 115 mm
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Exercise of mechanisms and machine theory
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10-2 On the non-disk rigid rotor shown in fig below ,there exist four unbalanced masses. Their masses rooting radii, and angular locations are:m1=10kg，
m2=15kg
，m3=20kg，m4=10kg，r1=40cm，
，
r3=20cm
r2=r4=30cm
，and
θ1=1200,θ2=2400,θ3=3000,θ4=300, l12=l23=l34=30cm.The
system is to be balanced dynamically by adding a mass mA in the balancing plane A at a rotating radius rA of 50 mm 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(θAandθB) of the required massed
A B
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Exercise of mechanisms and machine theory
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11-1The train gear shown in fig below, the teeth number are given Z1=Z2′=20，Z2=Z3=40，and moment of inertia of gears are given too, J1=J2′=0.01kg.m2
，
J2=J3=0.04kg.m2，The resistant moment on shaft O3 is M3=40N.m. Take gear 1 as the equivalent link, Find the
equivalent moment of inertia Je and the equivalent moment of force Me
2/ 21O3 3 34
Exercise of mechanisms and machine theory
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11-2 The output moment of force Md of an internal combustion engine on the crankshaft is a given function of the rotating angle as shown in fig below . The angular period of moment is ϕT=π.The average speed is
nm=620r/min.The engine is used to drive a machine with
constant resistant moment .The allowable coefficient of speed fluctuation is [δ]＝0.01.Masses and moment of inertia of all the links are neglected .Fine the moment of inertia JF of the flywheel on the crankshaft
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Exercise of mechanisms and machine theory
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11-3 下图所示为某机械系统的等效驱动力矩Med及等效阻抗力矩Mer对转
角ϕ的变化曲线，ϕT为其变化的周期转角。设已知各块面积为
Aab=200mm2，Abc=260mm2，Acd=100mm2，Ade=190mm2，
Aef=320mm2，Afg=220mm2，Aga/=50mm2，而单位面积所代表的
功为μA=10N.m/mm，试求系统的最大盈亏功ΔWmax。又如设已知其等效构件的平均转速为nm=1000r/min。等效转动惯量为Je=5kg.m，试求该系统的最大转速nmax及最小转速nmin，并指出最大转速与最小转速出现的位置。
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2
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