上游充通大学 SHANGHAI JIAO TONG UNIVERSITY LECTURE 6-II Planar Linkage Mechanisms 强 a 6 SHANG 1日gG ERSITY
LECTURE 6-II Planar Linkage Mechanisms Planar Linkage Mechanisms
上游充通大学 OUTLINE SHANGHAI JIAO TONG UNIVERSITY Planar Linkages and 4-bar mechanism Transformations of Planar Kinematic Chains Important kinematic characteristics Grashof Condition ME357 Design Manufacturing ll
OUTLINE Planar Linkages and 4-bar mechanism T f ti f Pl Ki ti Ch i Trans formations o f Planar Kinematic Ch ains Important kinematic characteristics Grashof Condition ME357 Design & Manufacturing II
上海充通大 Planar Linkages and 4-bar mechanism SHANGHAI JIAO TONG UNIVERSITY 4-Bar Nomenclature ·Ground link(连架杆) Links pivoted to gound -Crank(曲柄) -Rocker(摇杆) ·Coupler(连杆) length Link 3,length b B Link Coupler P Rocker length Crank Link -length-d Ground Link Pivot 0 Pivot 0 ME357 Design Manufacturing ll
Planar Linkages and 4-bar mechanism 4-Bar Nomenclature • G d li k( Groun d li nk(连架杆 ) • Links pivoted to gound – Crank(曲柄 ) – Rocker(摇杆 ) • Coupler(连杆 ) B Coupler A Crank Rocker Ground Link Link 1, length d Pi t 0 Pi t 0 Crank ME357 Design & Manufacturing II Pivo t 02 Pivo t 0 4
上海充通大 Planar Linkages and 4-bar mechanism SHANGHAI JIAO TONG UNIVERSITY Some definitions: Path Tracer Point Crank(曲柄)-a link 0- which makes a complete Coupler Coupler Curve Link revolution and is pivoted to ground @Rocker(摇杆)-a link 3 which has oscillatory (back and forth)rotation and is pivoted to ground. Input Follower Link Link Coupler (or connecting A rod连杆)-a link which Fixed Link has complex motion and is not pivoted to ground
Planar Linkages and 4-bar mechanism Some definitions: Cran k（曲柄） – a li kn k which makes a complete revolution and is pivoted revolution and is pivoted to ground Rocker （摇杆 ） – a link which has oscillatory (back and forth) rotation (back and forth) rotation and is pivoted to ground. Coupler (or connecting (or connecting rod连杆 ) – a link which has com plex motion and 4 is not pivoted to ground
上海充通大 Planar Linkages and 4-bar mechanism SHANGHAI JIAO TONG UNIVERSITY Types of 4-Bar linkages B Crank Rocker Rocker Crank D A 77777 D A O777 D Crank-rocker Double-rocker Double-crank 曲柄-摇杆机构 双摇杆 Or Drag link 双曲柄 Depend on range of motion of links connected to ground
Planar Linkages and 4-bar mechanism Types of 4-Bar linkages C C B C Crank B B Rocker Rocker Crank Crank A D A D A D Double-rocker 双摇杆 Double-crank Or Drag link 双曲柄 Crank-rocker 曲柄 -摇杆机构 Depend on range of motion of links connected t d o groun d
上游充通大学 SHANGHAI JIAO TONG UNIVERSITY 11 1 名 9 签 D A 2 8 B 10 6 6 OE 5 77777 777777777777 2 4
12 11 P 8 9 10 12 8 7 D A E 12 10 C B 6 3 C 2 6 E 5 3 2 3 A B 1 D 2 3 4 2 1 1 4
上游充通大￥ Planar Linkages and 4-bar mechanism SHANGHAI JIAO TONG UNIVERSITY L1=1.000 L2=2.170 L3=2.067 Vc/o L4=2.310 Normalized L5=5.400 Vc/ Velocity of Slider 2 1 0 -1 -2 -3 V/2 versus s 0 90180270360 FIGURE 3-33 02 (deg) Approximate constant velocity,draglink driven slider-crank sixbar mechanism(22)
Planar Linkages and 4-bar mechanism
Basic 4-Bar linkage Classification Applications 上游充通大学 SHANGHAI JIAO TONG UNIVERSITY B Application categories >Function generation 77777 (函数机构) =Relative motion between links is of Function generator interest =Does not require path tracer point on coupler A 77777 >Path generation (轨迹机构) =Point on coupler traces desired output =Only path of trace 77777 B point of interest Path generator =Not rotation of coupler link C2 C3 >Motion generation 位置2 (刚体导引机构) B bC' =Entire motion of B 位置 coupler link of interest Motion generator
Application categories ¾Function generation （函数机构 ） =Relative motion between links is of interest =Does not require path tracer point on coupler ¾Path generation （轨迹机构） =Point on coupler traces desired output =Only path of trace Only path of trace point of interest =Not rotation of coupler link ¾Motion generation （刚体导引机构） =Entire motion of coupl li k f ler li n k o f it t n erest
上游充通大学 Transformations of PKC SHANGHAI JIAO TONG UNIVERSITY MECHANISM TRANSFORMATION RULES: 1 Revolute joints in any loop can be replaced by prismatic joint with no change in DOF of the mechanism,provided that at least two revolute joint remain in the loop. 2 Any full joint can be replaced by a half joint,but this will increase DOF by one. 3 Removal of a link will reduce the DOF by one. 4 The combination of rules 2 and 3 will keep the original DOF unchanged. 5 Any ternary or higher order link can be partially shrunk to a lower- order link by coalescing nodes without any change in the DOF. 6 Complete shrinkage of a higher-order link is equivalent to its removal and DOF will be reduced. ME357 Design Manufacturing ll
Transformations of PKC MECHANISM TRANSFORMATION RULES: 1 Revolute joints in any loop can be replaced by prismatic joint with no change in DOF of the mechanism, provided that at least two revolute j i o nt remaii hl nn t he loop. 2 Any full joint can be replaced by a half joint, but this will increase DOF by one. 3 Removal of a link will reduce the DOF by one. 4 The combination of rules 2 and 3 will kee p g the ori ginal DOF unchanged. 5 Any ternary or higher order link can be partially shrunk to a lowerorder link by coalescing nodes without any change in the DOF. 6 Complete shrinkage of a higher-order link is equivalent to its removal and DOF will be reduced ME357 Design & Manufacturing II and DOF will be reduced
上游充通大学 Transformations of PKC SHANGHAI JIAO TONG UNIVERSITY Grashof crank nocker Grashof slider-crank Slider block 1 Revolute joints in any loop can be replaced by prismatic joint with no change in DOF of the Effective link 4 Effective rocker Rocker pivot pivot is at infinity mechanism,provided that at least two revolute joint remain (c)Trarsforming a fourbar crank-rocker to a sider-crank in the loop. Crank 2 Effective link 3 Crank2 Effective link 3 2 Any full joint can be replaced SIxler4 by a half joint,but this will increase DOF by one. 3 Removal of a link will reduce ()Tronstorming the der-crank to the Scotch yoke the DOF by one. Roll-stide Effective link 3 4 The combination of rules 2 and Chalf)joint Effective link 2 Effective link 4 3 will keep the original DOF Follower Cam unchanged. (c The cam-follower mechanism has an effective fourbar equivalent FIGURE 2-12 Linkage transformation
Transformations of PKC 1 Revolute joints in any loop can be replaced by prismatic joint with no change in DOF of the mechanism, provided that at least two revolute joint two revolute revolute joint remain in the loop. 2 Any full joint can be replaced by a half joint, but this will increase DOF by one. 3 R l f li k ill d 3 Removal o f a li n k will re duce the DOF by one. 4 The combination of rules 2 and 4 The combination of rules 2 and 3 will keep the original DOF unchanged