4-11 Design a crank-rocker mechanism ABCD to move a line EF on the coupler BC from position E1F1 to position E2F2 and then to position E3F3. xA=0. yA=0. xD=100mm. yD=0. xE1=2.18mm. yE1= -15.1mm. xE2= -3.19mm. yE2=-56.8mm. xE3=67.5mm. yE3= -32.8mm. E1F1=61.7. E2F2=73.4. E3F3=108.5. LEF=125mm. Find the required moving revolute centres B1 and C1 on the coupler.4-12 Design a revolute four-bar linkage ABCD so that a point E on the coupler BEC will pass through the three points, E1, E2 and E3. B1、A and D have been specified. xA=0. yA=0. xD=100mm. yD=0. xB1=44.2mm. yB1=22.2mm. xE1=50.4mm. yE1=128.5mm. xE2= -44.65mm. yE2=115.4mm. xE3= -63.4mm. yE3=29.35mm. Find C1.作E2B2=E1B1, E3B3=E1B1, 得B2和B3点。故BE是运动已知构件。C为待定活动铰链点。BE运动已知，故BEC是待定活动铰链点C所联结的运动已知构件，选为参考系。D是待定活动铰链点C所联结的运动未知构件上的运动已知点，选为圆周点。DE1B1 、DE2B2和DE3B3分别代表D点相对于BE的第一、第二和第三个位置。作B1E1D2B2E2D，B1E1D3B3E3D，使B2E2、B3E3 与E1B1重合，得D2点和D3点。作DD3和D3D2的中垂线，交点就是待定活动铰链点C的第一个位置点C1。作B2E2C2B1E1C1， B3E3C3B1E1C1 ，得C2和C3点。检验运动未知构件DC杆长：DC1=DC2=DC3。4-14. In a revolute four-bar linkage ABCD, as the driver side link AB rotates from position 1 to position 2, the other side link DC rotates 24.6o counter-clockwise. As the link AB goes from position 2 to position 3, the link DC rotates 39.3o counter-clockwise. LAB= 50mm and LAD=100mm. Synthesize the linkage graphically. 在第一位置，摇杆DC上必有一直线为竖直状态，如DE1。作E1DE2=24.6， E2DE3=39.3，得E2和E3点。 DCE是运动已知构件。 C为待定活动铰链点。DC是待定活动铰链点C所联结的运动已知构件，选为参考系。B是待定活动铰链点C所联结的运动未知构件上的运动已知点，选为圆周点。DE1B1 、DE2B2和DE3B3分别代表B点相对于DE的第一、第二和第三个位置。作DE1B2DE2B2，DE1B3DE3B3，得B2点和B3点。作B1B2和B2B3的中垂线，交点就是待定活动铰链点C的第一个位置点C1。作C1DC2=24.6， C2DC3=39.3，得C2和C3点。检验运动未知构件BC的杆长：B1C1=B2C2=B3C3。4-15 Design an offset slider-crank mechanism similar to the one in Fig.4-5. As the crank AB rotates 100o counter-clockwise from position 1 to position 2, the revolute centre C on the slider will translate from point C1 to point C2 . As the crank AB rotates 100o counter-clockwise from position 2 to position 3, the revolute centre C translates from point C2 to point C3. Offset e=10mm. xA=0. yA=0. xC1=28.76mm. xC2=40.88mm. xC3=69.08mm. 在第一位置，构件AB上必有一直线为竖直状态，如AE1。作E1AE2=100， E2AE3=100，得E2和E3点。故ABE为运动已知构件。 B为待定活动铰链点。AB是待定活动铰链点B所联结的运动已知构件，选为参考系。C是待定活动铰链点B所联结的运动未知构件BC上的运动已知点，选为圆周点。AE1C1 、AE2C2和AE3C3分别代表C点相对于AE的第一、第二和第三个位置。作AE3C1AE1C1， AE3C2AE2C2，得C1 点和C2点。作C3C2和C2C1的中垂线，交点就是待定活动铰链点B的第三个位置点B3。作B2AB3=100， B1AB2=100， 得B2和B1点。检验运动未知构件BC的杆长：B1C1=B2C2=B3C3。4-16 In an offset slider-crank mechanism, a point F on the slider will displace 23.25mm from point F1 to point F2 when the crank AB rotates from position AB1 to position AB2. As the crank AB rotates from position AB2 to position AB3, the point F displaces 52.13mm from point F2 to point F3. LAB=50mm. Designthe offset slider-crank mechanism. C为待定活动铰链点。滑块是待定活动铰链点C所联结的运动已知构件，选为参考系。B是待定活动铰链点C所联结的运动未知构件BC上的运动已知点，选为圆周点。 在第一位置，运动已知构件滑块上必有一直线为竖直状态，如E1F1。作E2F2=E3F3= E1F1 ，得E2和E3点。E2B2F2和E3B3F3分别代表B点相对于EF的第二和第三个位置。作E1F1B2E2F2B2，E1F1B3E3F3B3，得B2点和B3点。作B1B2和B2B3的中垂线，交点就是待定活动铰链点C的第一个位置点C1。作C1C2=F1F2， C1C3=F1F3，得C2和C3点。检验运动未知构件BC的杆长：B1C1=B2C2=B3C3。4-17 In an offset slider-rocker mechanism ABC, the position of the fixed pivot A and the two positions, C1P1 and C2P2, of a line CP on the coupler BC are known, as shown in Fig.4-53. xA=0. yA=0. xC1=26.05mm. yC1=45mm. xC2=66.5mm. yC2=45mm. 1=7. 2=11. Themoving revolute centre B is on the line CP. Locate the first position B1 of the point B.The revolute centre B is an UMRC. It connects the determined link CBP and the undetermined link AB. The link CP is selected as the reference link. The point A is selected as circumference point. Triangles AC1P1 and AC2P2 represent the two position relationships between the circumference point A and the reference link CP at the two instants. Constructing A1C2P2AC1P1, we get points A1. The points A and A1 are two positions of the point A relative to link CP when the link CP is stationary at C2P2. The intersection between the mid-normal and the C2P2 is the second position B2 of the UMRC B.Constructing C1B1=C2B2, we get points B1. Last, the length of the undetermined link AB must be checked to see whether the length is kept unchanged during motion, i.e., AB1=AB2.4-18 In a revolute four-bar linkage ABCD, side link AB is a driver. The positions of the side link CD and a 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. LAD=100mm. LCD=64.5508mm. ADC1=42.39. ADC2=133.8. C1E1=104.7. C2E2=93.7. Find the second position B2 of the revolute B. B为待定活动铰链点。CE是运动已知构件，CEB是待定活动铰链点B所联结的运动已知构件，选为参考系。A是待定活动铰链点B所联结的运动未知构件AB上的运动已知点，选为圆周点。AC1E1和AC2E2分别代表A点相对于CE的第一和第二个位置。作A2C1E1AC2E2，得A2点。因AB为原动件且机构第一位置为死点，所以B1点在DC1的延长线上。作AA2的中垂线与DC1的延长线交于待定活动铰链点B的第一个位置点B1。作B2C2E2B1C1E1 ，得B2点。检验运动未知构件AB的杆长：AB1=AB2。4-19 In a crank-slider mechanism, two sets of corresponding positions between the slider and a line segment AE on the crank ABE are known. The position C1 of the slider is also one of its limit positions. xA=0. yA=0. xC1= -100mm. yC1= -28.15mm. xC2= -65.56mm. Find the first position B1 of the revolute B. B为待定活动铰链点。AE是运动已知构件，所以ABE是待定活动铰链点B所联结的运动已知构件，选为参考系。C是待定活动铰链点B所联结的运动未知构件BC上的运动已知点，选为圆周点。AC1E1和AC2E2分别代表A点相对于CE的第一和第二个位置。作AC2E1AC2E2，得C2点。因C1为滑块的极限位置之一，所以B1点在AC1连线上。作C1C2的中垂线与AC1交于待定活动铰链点B的第一个位置点B1。作AB2E2AB1E1 ，得B2点。检验运动未知构件BC的杆长：B1C1=B2C2。4-20 In a crank-rocker linkage ABCD, side link AB is a driver. The positions of the rocker CD corresponding to two positions of the linkage are known. LAD=100mm. LCD=75mm. ADC1=64.3. ADC2=134.2. At the first position of the linkage, the pressure angle of the linkage is zero. Position DC2 is one of the limitpositions of the rocker. Find the second position B2 of the revolute B.因为AB为原动件,且在机构第一位置, 机构压力角=0, 所以B1C1C1D. 又因为C2D为摇杆CD的一个极限位置, 所以AB2C2三点共线。因此BC为运动已知构件。B为待定活动铰链点。BC是待定活动铰链点B所联结的运动已知构件，选为参考系。A是待定活动铰链点B所联结的运动未知构件AB上的运动已知点，选为圆周点。AB1C1和AB2C2分别代表A点相对于BC的第一和第二个位置。因A点在C2B2延长线上, 故在C1B1延长线上截取C1A2=C2A，得A2点。作AA2的中垂线与C1B1交于待定活动铰链点B的第一个位置点B1。截取B2C2=B1C1 ，得B2点。检验运动未知构件AB的杆长：AB1=AB2。4-21 In an offset slider-crank mechanism ABC, two sets of corresponding positions between the crank AB and a point F on the slider are known. When the crank AB is located at position AB1, the slider reaches its left limit position. LAB=30mm. B2AB1=112.8. LF1F2=32.96mm. Find the first position C1 of the revolute C on the slider. C为待定活动铰链点。滑块是待定活动铰链点C所联结的运动已知构件，选为参考系。B是待定活动铰链点C所联结的运动未知构件BC上的运动已知点，选为圆周点。 在第一位置，运动已知构件滑块上必有一直线为竖直状态，如E1F1。作E2F2= E1F1 ，得E2点。E1B1F1、E2B2F2分别代表B点相对于EF的第一和第二个位置。作E1F1B2E2F2B2，得B2点。因为第一位置是滑块的左极限位置,故C1在B1A的延长线上. 作B1B2的中垂线，交B1A的延长线于待定活动铰链点C的第一个位置点C1。作C1C2=F1F2，得C2点。检验运动未知构件BC的杆长：B1C1=B2C2。4-22 When the wheel of the landing mechanism in an airplane is at its lowest position, links BC and CD are collinear. Suppose the position of revolute C is unknown. Find the position of the revolute C on line DCB so that the link AB will rotate 90 counter-clockwise when the link DC rotates 60 clockwise. The known dimensions are: xA=0, yA=0, xD=103mm, yD=23.55mm, and LAB=100mm.B1AB2=90, C1DC2=60。由题意知, 两连架杆AB 和DC均为运动已知构件。C为待定活动铰链点。BC为运动未知构件。DC是待定活动铰链点C所联结的运动已知构件，选为参考系。B是待定活动铰链点C所联结的运动未知构件BC上的运动已知点，选为圆周点。因B1点在DC1延长线上, 故在DC2延长线上截取DB1=DB1，得B1点。作B2B1的中垂线与DC2交于待定活动铰链点C的第二个位置点C2。截取DC1=DC2 ，得C1点。检验运动未知构件BC的杆长：B1C1=B2C2。