Chapter 5 Synthesis 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 dimensions 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.,5.1 Characteristics and Types of Planar Linkages,Fig.5-1 Types of four-bar linkages(铰链四杆机构的类型),2.Types of Planar Linkages,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),(1) Crank rocker linkage If a four bar linkage shown in Fig 5-1a is designed so that link 1 can rotate continuously while link 3 only oscillates through an angle, it is called a crank rocker linkage. (2) Double crank linkage Both link 2 and link 4 in Fig 5-1b can rotate continuously 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 completely 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 are parallel and equal in length, as shown in Fig 5-1d, cranks 2 and 4 always have 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.,(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 rotate 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 shown 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 of the fixed block, and the other side link 2 oscillates about the pivot C, the linkage 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 completely, and the link 4 oscillates about the pivot A shown in Fig 5-2e, this linkage is called a rocking guide bar linkage. It is used in machine tools such as shapers.,(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, and the two pairs of the same kind are adjacent, it is known as a double slider crank linkage shown in Fig 5-3a. This linkage can draw ellipses. (12) Double rotating block linkage If two sliders are rotating completely about their pivots A and B relative to the frame 2, this linkage is called a double rotating block mechanism shown in Fig 5-3b. It can also be called Oldham linkage, 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 reciprocates in the fixed link 1 to produce a simple harmonic motion. It is shown in Fig 5-3c. (14)Tangent linkage In a tangent mechanism, the side link 2 oscillates about its pivot A, the other link 4 reciprocates along its axis, and the link 3 is a slider in shape. It is also called the Rapsons slide linkage. The displacement of link 4 has a tangent motion.,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),3.Evolution and Mutation of Planar Linkages,(1)Inversion of a four bar linkage Different mechanisms can be obtained by fixing 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 different inversion.,Fig.5-4 Evolution from turning pair to sliding pair(转动副向移动副的演化),(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, as shown in Fig 5-4c.,Fig.5-5 Eccentric disk mechanism(偏心盘机构),(3) Expansion of pin size in a turning pair If we increase the