圆上清支大学 西+口 LECTURE 3 ME371/ME337 DESIGN AND MANUFACTURING Planar Linkage Mechanisms Covered:Ch2-in Design of Machinery SHAN 圈上泽夫道大学 OUTLINE Planar Linkages and 4-bar mechanism Transformations of Planar Kinematic Chains Important kinematic characteristics ▣Grashof Condition 1
1 Planar Linkage Mechanisms LECTURE 3 ME371/ME337 DESIGN AND MANUFACTURING Covered：Ch2- in Design of Machinery OUTLINE Planar Linkages and 4-bar mechanism Transformations of Planar Kinematic Chains Important kinematic characteristics Grashof Condition
上海文通大学 NUMBER SYNTHESIS NUMBER SYNTHESIS:the determination of the number and order of links and joints necessary to produce motion of a particular DOF; ④ Order refers to the number of nodes perlink,i.e.,binary, ternary,quaternary etc; ©Conclusions: >For one DOF,the simplest linkage is four Binary links-the 4-bar linkage. >The addition or subtraction of Ternary links in pairs will not affect the DOF of the mechanism. How to prove? )上海充通大￥ NUMBER SYNTHESIS 1-2-0-生 3 (rewriting Gruebler's equation) Try:M=2m L=2n-1 (even-odd,vice versa) J=3n-m-3 CL=B+T+0+P+H nodes 2B+3T +40+5P+6H 2 2 M=B-Q-2P-3H-3 (1) L-3-M=T+2Q+3P+4H (2) 2
2 NUMBER SYNTHESIS: the determination of the number and order of links and joints necessary to produce motion of a particular DOF; Order refers to the number of nodes perlink, i.e., binary, ternary, quaternary etc; Conclusions: For one DOF, the simplest linkage is four Binary links- the 4-bar linkage. The addition or subtraction of Ternary links in pairs will not affect the DOF of the mechanism. NUMBER SYNTHESIS How to prove? (rewriting Gruebler's equation) (even-odd, vice versa) (1) (2) NUMBER SYNTHESIS
圈上泽支大峰 NUMBER SYNTHESIS when M=1,L=4,then B=4 When M=1,L=6,then B=4,T=2,or B=5,Q=1 James Watt (1736.1月一1819.8) Using in car suspension system 圈上涤夫道大学 Planar Linkages and 4-bar mechanism Some definitions: ©Crank(曲柄)-a link which Path Tracer Point makes a complete revolution Coupier and is pivoted to ground Curve ©Rocker(摇杆)-a link which has oscillatory (back and forth)rotation and is pivoted to ground. Coupler (or connecting rod 杆)-a link which has Follower Lin complex motion and is not pivoted to ground Fixed Link 3
3 when M=1, L=4, then B =4 When M=1, L=6, then B=4, T=2, or B =5, Q=1 NUMBER SYNTHESIS Using in car suspension system James Watt (1736.1月 — 1819.8) Some definitions: Crank（曲柄） – a link which makes a complete revolution and is pivoted to ground Rocker （摇杆）– a link which has oscillatory (back and forth) rotation and is pivoted to ground. Coupler (or connecting rod连 杆) – a link which has complex motion and is not pivoted to ground Planar Linkages and 4-bar mechanism
圆上泽文大学 se十g1Hnk Classification Applications Application categories: ,Function generation(函数机构) =Relative motion between links is of interest =Does not require path tracer point on coupler >Path generation(轨迹机构) =Point on coupler traces desired output =Only path of trace point of interest =Not rotation of coupler link >Motion generation(刚体导引机构) =Entire motion of coupler 位置2 link of interest 圈上泽夫通大学 Planar Linkages and 4-bar mechanism Types of 4-Bar linkages B Crank Crank Rocker B Rocker 77777 D 77777 D A 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 4
4 Application categories: Function generation =Relative motion between links is of interest =Does not require path tracer point on coupler Path generation（轨迹机构） =Point on coupler traces desired output =Only path of trace point of interest =Not rotation of coupler link Motion generation =Entire motion of coupler link of interest (函数机构） （刚体导引机构) Types of 4-Bar linkages C A D B C A D B Rocker Rocker C A D B Crank Crank Double-rocker 双摇杆 Double-crank Or Drag link 双曲柄 Planar Linkages and 4-bar mechanism Crank-rocker 曲柄-摇杆机构 Depend on range of motion of links connected to ground
圈上海文通大华 Crank-rocker .Crank-rocker >Input crank:Rotates continuously through 360 >output link:Oscillates or rocks 3 AD Radar Blender Sewing （Input::Crank) Input:Rocker) 圆上泽夫道大学 Double-crank -Double-crank (Drag-link) >Input crank:Rotates continuously through 360 >Output link:Rotates continuously through 360 777777777777 unbalanced-throw sceen(惯性筛) 5
5 Radar Sewing （ Input: Crank） （ Input: Rocker） Blender Crank-rocker •Crank-rocker Input crank: Rotates continuously through 360o output link: Oscillates or rocks unbalanced –throw sceen (惯性筛) Double-crank A B D C 1 2 3 4 6 E •Double-crank (Drag-link) Input crank: Rotates continuously through 360o Output link: Rotates continuously through 360o
图上涤支大峰 Double-rocker .Double-rocker >Input rocker:Limited rotation >Output link:Limited rotation e Q Steering mechanism Crane 周 上海充通大学 Two links:length is equal position is parallel 77777777 Coupler: horizontal motion ABCD BC ZAD Lift car Train wheel 6
6 Steering mechanism Double-rocker Crane A B D C E •Double-rocker Input rocker: Limited rotation Output link: Limited rotation Train wheel AB = CD BC = AD Lift car Two links: length is equal position is parallel Coupler: horizontal motion
国上清文大华 Mechanism inversion Inversion:grounding a different link in the kinematic chain Crank-slider Guidear Slider is rocking Slider is stationary 曲柄-滑块机构 导杆机构 摇块机构 定块机构 © 上海充廷大学 Application 回程 小型创床 (转动导杆机构) 牛头创床 (摆动导杆机构) 插步刀占 7
7 Crank-slider 曲柄-滑块机构 Guide-bar 导杆机构 Slider is rocking 摇块机构 Slider is stationary 定块机构 Mechanism inversion Inversion: grounding a different link in the kinematic chain 牛头刨床 （摆动导杆机构） 小型刨床 （转动导杆机构） Application
圈上海文大华 Mechanism inversion Tangent Mechanism Sine Mechanism Elliptical Trammel Mechanism 正切机构 正弦机构 双转块机构 椭圆机构 圈上游充大些 Mechanism inversion(机构倒置) Inversion:grounding a different link in the kinematic chain d Double-crank Double-rock Crank-rocker 8
8 Tangent Mechanism 正切机构 Sine Mechanism 正弦机构 双转块机构 Elliptical Trammel Mechanism 椭圆机构 Mechanism inversion Crank-rocker Double-crank Double-rock Inversion: grounding a different link in the kinematic chain Mechanism inversion(机构倒置)
国 上海文通大学 Exercise in Class For the engine mechanism; a)Scale the diagrams for dimensions; b)Find the DOF of the mechanism; c)List the basic mechanism 火花寒 圆上泽夫通大学 Exercise in Class 8 6,7 772 9
9 Exercise in Class For the engine mechanism; a) Scale the diagrams for dimensions; b) Find the DOF of the mechanism; c) List the basic mechanism Exercise in Class
圈上泽文大峰 OUTLINE Planar Linkages and 4-bar mechanism Transformations of Planar Kinematic Chains Important kinematic characteristics ☐Grashof Condition 圆上泽夫通大学 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 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. 10
10 OUTLINE Planar Linkages and 4-bar mechanism Transformations of Planar Kinematic Chains Important kinematic characteristics Grashof Condition 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 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 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