MT Chap5 Synthesis of Planar Linkages

2020-02-27 170浏览

  • 1.
  • 2.5.1 Characteristics and Types of Planar Linkages 1.The Characteristics of Planar Linkages 1) A linkage has a simple structure and it is easy to manufacture, so it has a low cost. 2) The pressure in a lower pair with surface contact is lower, so the linkage has a large load capacity. 3) A linkage can achieve various motions by designing its dimensio ns of the links. 4) A linkage can transmit motion within a long distance. 5) It is difficult to perform precision motion; this is a disadvantage of linkages.
  • 3.2.Types of Planar Linkages Fig.5-1 Types of four-bar linkages(铰链四杆机构的类型) Fig.5-2 Types of four-bar linkages with a sliding pair(含有一个移动副的四杆机构类型)
  • 4.(1) Crank rocker linkage If a four bar linkage shown in Fig 5-1a is designed s o that link 1 can rotate continuously while link 3 only oscillates through an ang le, it is called a crank rocker linkage. (2) Double crank linkage Both link 2 and link 4 in Fig 5-1b can rotate continu ously relative to the frame 1; this linkage is called a double crank linkage. (3) Double rocker linkage Both link 2 and link 4 in Fig 5-1c can not rotate com pletely relative to the frame 3; this linkage is called a double rocker linkage. (4) Parallel crank four bar linkage If in a four bar linkage, two opposite links a re parallel and equal in length, as shown in Fig 5-1d, cranks 2 and 4 always h ave the same angular velocity. This mechanism is called a parallel crank four bar linkage. It is widely used, such as in the coupling of locomotive wheels, in pantograph, etc. (5) Isosceles trapezium linkage If two rockers of a double rocker linkage are equal in length, see the Fig 5-1e, this linkage is called an isosceles trapezium linkage; it can be used in the steering mechanism in automobiles.
  • 5.(6) Slider crank linkage This linkage is shown in Fig 5-2a, in which side link 1 is a crank, and the other side link 3 is a slider. Turning pairs A and B are full turning pairs, and C is oscillating turning pair. (7) Rotating guide bar linkage If both the side link 2 and side link 4 can rota te completely, this linkage is called a rotating guide bar linkage shown in Fig 5-2b, in which the coupler becomes a slider in shape. (8) Rocking block linkage The crank rotates completely while the block only oscillates about its pivot center C, this linkage is called rock block linkage sho wn in Fig 5-2c. It is widely used in hydraulic cylinder mechanism. (9) Sliding guide bar linkage If the guide link 4 reciprocates along the axis o f the fixed block, and the other side link 2 oscillates about the pivot C, the link age is called a sliding guide bar linkage shown in Fig 5-2d. It can be used in some water pumps. (10) Rocking guide bar linkage If the link 2 can rotates about pivot B compl etely, and the link 4 oscillates about the pivot A shown in Fig 5-2e, this linkag e is called a rocking guide bar linkage. It is used in machine tools such as sh apers.
  • 6.(11) Double slider crank linkage In a four bar linkage, if two side links 1 and 3 become sliders which are reciprocating along each axis of cross frame, an d the two pairs of the same kind are adjacent, it is known as a double slider c rank linkage shown in Fig 5-3a. This linkage can draw ellipses. (12) Double rotating block linkage If two sliders are rotating completely abo ut their pivots A and B relative to the frame 2, this linkage is called a double r otating block mechanism shown in Fig 5-3b. It can also be called Oldham lin kage, and it is used to connect two shafts having parallel misalignment. (13)Sine linkage This linkage can also be called a Scotch yoke linkage, in which the crank 2 rotates about its pivot. Acompletely, and link 4 reciprocate s in the fixed link 1 to produce a simple harmonic motion. It is shown in Fig 53c. (14)Tangent linkage In a tangent mechanism, the side link 2 oscillates abo ut its pivot A, the other link 4 reciprocates along its axis, and the link 3 is a sli der in shape. It is also called the Rapsons slide linkage. The displacement of link 4 has a tangent motion.
  • 7.Fig.5-3 Types of four-bar linkages with two sliding pairs (含有两个移动副的四杆机构类型)
  • 8.3.Evolution and Mutation of Planar Linkages (1)Inversion of a four bar linkage Different mechanisms can be obtained by fix ing different links of a mechanism. This is known as inversion. The principle is that the relative motion between links of a four bar linkage does not change in d ifferent inversion. (2) Converting a turning pair into a sliding pair If the radius of the pin D is increased to a length of lDC, and the rocker 3 is made a slider with a curve which radius is lDC, then this mechanism becomes a curve slider crank mechanism shown in Fig 5-4b. If the lDC were made infinite in length, then point C would have rectilinear motion and link 3 could be replaced by a slider, Fig.5-4 Evolution from turning pair to sliding pair(转动副向 as shown in Fig 5-4c. 移动副的演化)
  • 9.(3) Expansion of pin size in a turning pair If we increase the size of the crank pin B shown in Fig 5-5a until it is larger than the length of the crank, this enlarged crank pin is called an eccentric disk and can be used to replace the crank shown in Fig 5-5a. The crank consists of a circular disk with center B, which is pivoted off center at A to the frame. The disk rotates inside the ring end of coupler 2. Fig.5-5 Eccentric disk mechanism(偏心盘机构)
  • 10.4.Applications of Planar Linkages (1) Applications of linkages consisted of turning pairs Fig 5-6a is a jaw crush er. It consists of a crank rocker linkage. The connecting rod is the moving jaw used to crush the rocks. Its kinematic diagram is shown in Fig 5-6b. Fig 5-6c s hows a dough mixing machine; it consists of a crank rocker linkage also. Fig.5-6 Applications of crank-rocker linkage(曲柄摇杆机构的应用) 1—eccentric disk(偏心盘)2—belt wheel(带轮)3—moving jaw(动鄂) 4—moving ja w board(动鄂板) 5—fixed jaw board(静鄂板)6—rocker(摆杆)7—spring(弹簧)
  • 11.Fig 5-7a shows a crane which is used in ports. It consists of a double rocker linkage . The point E on coupler can move along a straight line. or nearly along a straight line, therefore the lifted body may move steadily along this path. Fig.5-7 Applications of double-rocker linkage(双摇杆机构的应用)
  • 12.Fig 5-8a shows a inertia vibrating screen. It is a double crank linkage, and is also called a drag link linkage. If the driver AC rotates counterclockwise with constant angular velocity, the slider makes a slow stroke and returns with a quick stroke. The inertia forces can cause vibration of the screen to perform separation of the materials. Fig 5-8b shows a parallel double crank linkage used in the coupler of locomotive wheels, and Fig 5-8c shows a hydraulic lift with two sets of parallel double crank linkages. Fig.5-8 Applications of double-crank linkage(双曲柄机构的应用)
  • 13.(2) Applications of slider crank linkage Slider crank linkages ar e used widely in various multi cylinder engines. Fig 5-9a is a V engine with eight cylinders. This engine consists of eight slider c rank linkages. Fig 5-9b shows a shearing machine. It consists of one slider crank linkage. Fig.5-9 Applications of slider-crank linkage(曲柄滑块机构的应用)
  • 14.(3) Application of crank slider quick return linkage Fig 5-10a is a shaper; it consists of gear mechanism and sliding guide bar lin kage. Fig 5-10b is a shaper too; it consists of rotating guide bar l inkage. Fig.5-10 Applications rocking guide-bar linkage and rotating guide-bar linkage (摆动导杆机构和转动导杆机构)
  • 15.Fig 5-11a shows a hand pump, in which link 4 is made in the form of a cylinder and a plunger fixed to the link 3 reciprocates in it； it consists of sliding guide bar linkage. Fig 5-11b shows a self loading truck, in which a rocking block linkage is used to perform self loading work. Fig.5-11 Applications of sliding guide-bar linkage and rocking-block linkage (移动导杆机构和曲柄摇块机构的应用) 1—handle(手柄) 2—link(连杆) 3—cylinder(简体) 4—plunger(活塞)
  • 16.(4) Application of four bar linkages with two sliding pairs Fig 5 -12a shows an elliptical trammel in which the fixed link 1 is in t he form of guides for sliders 2 and 4. Fig 5-12b shows an Old ha ms coupling, and it consists of a double rotating block linkage s hown in Fig 5-3b. Fig 5-12c shows a mechanism which is used t o drive the needle of a sewing machine; it is a sine linkage. Fig.5-12 Applications of four-bar linkages with two sliding pairs(含有两个移动副机 构的应用)
  • 17.5.2 Fundamental Features of Four bar Linkages 1.Grash of Criteria Fig 5-13 shows a four bar linkage ABCD, and if the link AB can rotate through a full revolution with an angular velocity ω clockwise, it must pass through the positions AB1 and AB2. Fig.5-13 Grashoflaw(曲柄存在条件)
  • 18.The link 1 which can rotate through a full revolution must be the sho rtest link; the sum of the length of shortest link and the longest link (t here must be a longest link among b, c, d) can not be greater than the sum of the remaining two links. The Grash of criteria can be stated asfollowing:1) A linkage, in which the sum of the length of the shortest and lon gest links is less than the sum of the length of the other two links, mu st have a crank. 2) The crank must be the shortest link.
  • 19.2. Quick return Motion When the crank rotates through a full revolution with an angular velocity ω clockwise, and the rocker only oscillates through an angle ψ, the crank and coupler will form a straight line at each extreme position. Fig -14 shows a crank rocker linkage in the two extreme positions of the driven link. Fig.5-14 Quick-return characteristics(急回特性)
  • 20.3.Pressure Angle and Transmission Angle The pressure angle α is the acute angle between the direction of the static force transferred through the coupler and the absolute velocity of the output link at the connected point, such as at C. Since the coupler is a two force link, the direction of the static force of the coupler is along the line of its pin joints. The acute angle γ between the coupler and output link is known as transmission angle shown in Fig5-15. Notice that in this case, α+γ=90. Fig.5-15 Transmission angle and pressure angle (传动角和压力角)
  • 21.The transmission angle in a slider crank linkage is shown in Fig 5-16. Fig.5-16 Transmission angle in a slider-crank linkage (曲柄滑块机构的传动角)
  • 22.4.Dead Point Fig 5-17 shows a crank rocker linkage. When the crank rotates completely, ther e is no danger of the linkage locking, because the transmission angle can not be zero at any positions. However, if the rocker becomes a driving link, the crank i s a driven link, and then the rocker moves to the extreme position DC1 and DC 2, the transmission angles become zero, the linkage locking will occur. We call t hese positions as dead points or toggle positions. The rocker will then have to b e driven to get the linkage out of the toggle position. Fig.5-17 Dead points(死点)
  • 23.Fig 5-18 shows a single cylinder engine with four stroke cycle. The flywheel can carry the piston through the engines exhaust stroke, intake stroke and compression stroke. Fig.5-18 Overcome dead point by using flywheel (利用飞轮克服死点) 1—flywheel(飞轮)2—crank shaft(曲轴) 3—cam shaft(凸轮轴)4—valve(气门) 5—piston(活塞)6—connect link(连杆)
  • 24.Fig 5-19 is a driving mechanism of the locomotive wheels; the phase angle of the cranks is 90°. If one of them is at the dead position, the other can be driven easily. Fig.5-19 Overcome dead points by using different phase(错位排列克服死点)
  • 25.Fig 5-20 shows a clamping device, in which after a small force Fapplied on the coupler has been removed, the reaction force of the clamped work piece to the link AB can not drive the linkage to move at all. We can also design many devices using the dead point position. Fig.5-20 Self-locking clamp(自锁夹具)
  • 26.5.3 Synthesis of Four bar Linkages 1.Introduction （1）Motion generation Fig 5-21a shows a overturning device used in a castin g workshop. This device is designed to guide the sandbox which is fixed to the coupler in two positions B1C1 and B2C2. Fig5-21b shows a speed change devic e which is controlled by hand. It is designed to actualize the input and output lin ks through the three positions. （2）Path generation A coupler is the most interesting link in a mechanism. Fig.5-21 Problems of synthesis of a four-bar linkage 1(四杆机构设计基本问题1)
  • 27.Fig 5-22a shows a four bar linkage which is on the extreme positions , and from this figure wehave:a=（AC1－AC2）/2 This formula for calculating the length of the crank is very useful to design a four bar linkage. Fig.5-22 Problems of synthesis of four-bar linkages 2(四杆机构设计基本问题2)
  • 28.2.Graphical Synthesis of Four bar Linkage (1) Design of a four bar mechanism for specified coupler positions Guiding a body through two or three link positions are often used to design a four bar linkage. 1) Two prescribed link positions. Fig 5-23a shows two positions of a coupler BC. It is desired to design a mechanism which will carry the link through these two positions. Fig.5-23 Guiding a body through two coupler positions (按连杆的两个位置设计四杆机构)
  • 29.2) Three prescribed link positions. The procedure is similar to the above processes(Fig5-24). Fig.5-24 Guiding a body through three coupler positions(按连杆的三个位置设计四 杆机构)
  • 30.3) Two or three prescribed positions of the coupler plane. Three prescribed positions of a coupler plane are shown in Fig 5-25. Fig.5-25 Guiding a body through a number of link plane positions (按连杆平面位置设计四杆机构)
  • 31.（2）Design of a four bar linkage for correlated angular positions of input and output links 1) Inversion method. Fig 5-26 shows a four bar linkage; the motion of the input link AB from the φ1 to φ2 causes a motion of the output link DC from ψ1 to ψ2. Fig.5-26 Principle of inversion(反转法的原理)
  • 32.2) Three prescribed angular positions of the input and output links. Fig 5-27 illustrates a problem in which it is desired to determine the dimensions of a linkage in which the output link is to occupy three angular positions ψ1, ψ2 and ψ3 corresponding to the three given positions φ1, φ2 and φ3 of the input link. Fig.5-27 Coordination of the positions of the input an d output links (按两连架杆的三组对应位置设计四杆机构)
  • 33.（3）Design of a four bar linkage for quick return motion Some e xternal work is being done by the linkage on the forward stroke, an d the return stroke needs to be accomplished as rapidly as possible so that a maximum time will be available for working stroke. 1) Crank rocker linkage. Synthe sizing a crank rocker linkage for specified value of K, the length of rocker DC and the angle ψ b etween the two extreme positio ns of the rocker are known.The procedures are in Fig5-28. Fig.5-28 Synthesis of a crank-rocker linkage for a given K(已知K设计 曲柄摇杆机构)
  • 34.2) Slider crank linkage. Fig.5-29 Synthesis of a slider-crank linkage for a given K(已知K值设计 曲柄滑块机构)
  • 35.3) Guide bar mechanism. Fig.5-30 Synthesis of a guide-bar linkage for a given K (已知K值设计导杆机构)
  • 36.（4）Design of a four bar linkage for specified tracing path Coupler curves can be capable of approximating straight lines and large circle arcs with remote centers, so they are quite useful path motions for machine design. Fig 5-31 shows a four bar linkage, in which the point F on the coupler can generate a close path. Fig.5-31 Coupler curve(连杆曲线)
  • 37.3.Analytical Synthesis of Four bar Linkage (1) Design of a four bar linkage for specified coupler positions Fig 5-32 shows three positions of a coupler BC in which the coordinates of the point B and C ar e shown in Fig 5-32. It is desired to design a mechanism which will carry the lin k through these positions by using analytical method. Fig.5-32 Guiding a body through a number of link positions(按连杆的对应位置设计 四杆机构)
  • 38.(2) Design of a four bar linkage for correlated positions of input and output links Usually the lengths of the link AB and the frame AD are given by a designer. Fig.5-33 Coordination of the positions of the input and output links(按连架杆的对应 位置设计四杆机构)
  • 39.（3）Design of a four bar linkage for quick return motion Fig 5-34 shows a four bar linkage in the extreme positions. Fig.5-34 Synthesis of a four-bar linkage for a given K(已知K设计四杆机构)
  • 40.（4）Design of a four bar linkage for coupler curve A four bar linkage ABCD with a coupler point P is shown in Fig5-35. The position of point P on the coupler may be located by length of e, f and angle γ shown in Fig 535. Fig.5-35 Design of a four-bar linkage for coupler curve(按连杆曲线设计四杆机构)