⊕ 上泽充通大学 eb人口 LECTURE 4 Planar Linkage Mechanisms 漏 1日▣ 国 上泽充通大警 OUTLINE Planar Linkages and 4-bar mechanism Transformations of Planar Kinematic Chains Important kinematic characteristics ©Grashof Condition ME357 Design Manufacturing ll 1
1 Planar Linkage Mechanisms LECTURE 4 ME357 Design & Manufacturing II OUTLINE Planar Linkages and 4-bar mechanism Transformations of Planar Kinematic Chains Important kinematic characteristics Grashof Condition
国 上游克夏大￥ Planar Linkages and 4-bar mechanism ©4-Bar Nomenclature ·Ground link(机架) Links pivoted to gound -Crank(曲柄) Rocker(摇杆) ·Coupler(连杆) Link 3,length b Coupler Rocker ,length Crank Link 1.length d Ground Link Pivot 02 Pivot 0 ME357 Design Manufacturing ll 圈上清庆大坐 Planar Linkages and 4-bar mechanism Some definitions: Path Tracer Point ©Crank(曲柄)-a link 0- which makes a complete Coupler Link revolution and is pivoted to ground © Rocker(摇杆)-a link which has oscillatory (back and forth)rotation and is pivoted to ground Follower Lin Coupler (or connecting rod连杆)-a link which xed Link has complex motion and is not pivoted to ground 2
2 ME357 Design & Manufacturing II Ground Link Coupler Link 1, length d Pivot 02 Pivot 04 A B Crank Rocker Planar Linkages and 4-bar mechanism 4-Bar Nomenclature • Ground link(机架) • Links pivoted to gound – Crank(曲柄) – Rocker(摇杆) • Coupler(连杆) 4 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
® 上游克夏大￥ Planar Linkages and 4-bar mechanism Types of 4-Bar linkages B C C Crank Crank B Rocker Rocker 77777 77777 OD 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 圈上洋文大学 11 12 10 9 6 777777777 3
3 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 A B D C 1 2 3 4 6 E 8 5 6 7 8 9 10 12 11 12 10 P 1 4 2 3 1 2 3 A B D C E
周 上游克夏大￥ Planar Linkages and 4-bar mechanism L1=1.000 L2=2.170 L3=2.067 5 4/2 L4=2.310 L5=5.400 Vekciry of Slider 2 102° 2 Ve/0 versus s 90180270360 FIGURE 3-33 O (deg) Approximate constant velocity,draglink driven slider-crank sibar mechanism(22) Ba1e4书u1 inksg台 Clarsification Applicationg 圈 上游文通大学 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 Path generator =Not rotation of coupler link C:C >Motion generation 位置2 (刚体导引机构) =Entire motion of coupler link of interest Nation 4
4 Planar Linkages and 4-bar mechanism 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 point of interest =Not rotation of coupler link ¾Motion generation （刚体导引机构） =Entire motion of coupler link of interest
园 上活大学 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. Any full joint can be replaced by a half joint,but this will increase DOF 2 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 国 上游文通大学 Transformations of PKC Giof在kokw Gratot der-cnnk 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 o 3 will keep the original DOF unchanged. FIGURE 2-12 5
5 ME357 Design & Manufacturing II 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. 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 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
周 上泽文通大￥ Transformations of PKC 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. Shrunk link Shrunk link_ DOF=1 D0F=1 DOF=1 DOF=0 FIGURE 2-13 Link shrinkage 国 上帝充通大学 Transformations of PKC 比山 Crank-slider Guide -bar Slider is rocking Slider is stationa 曲柄-滑块机构 导杆机构 摇块机构 定块机构 6
6 ME357 Design & Manufacturing II Transformations of PKC 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. Transformations of PKC Crank-slider 曲柄-滑块机构 Guide-bar 导杆机构 Slider is rocking 摇块机构 Slider is stationar 定块机构
国 上浒充大￥ Transformations of PKC sin 0 Tangent Mechanism Sine Mechanism Elliptical Trammel Mechanism 正切机构 正弦机构 双转块机构 椭圆机构 国 上净文通大学 Important kinematic characteristics ©Limit position 极限位置 Time ratio 急回特性 © Transmission angle传动角 ©Toggle position死点 ME357 Design Manufacturing ll 7
7 Transformations of PKC Tangent Mechanism 正切机构 Sine Mechanism 正弦机构 双转块机构 Elliptical Trammel Mechanism 椭圆机构 ME357 Design & Manufacturing II Important kinematic characteristics Limit position 极限位置 Time ratio 急回特性 Transmission angle 传动角 Toggle position 死点
国上泽通大￥ Important kinematic characteristics ©Limit positions C. 圆上活夫大峰 Important kinematic characteristics ©Time ratio t=(180°-0)/o C y=CC,h,=C,o1(180°-0) 42=(180°+0)1o B. V2=CC2/,=CC301(180°+0) TR= V2= CC,/= 80°-0 C1C2/%,12180°+0 B 8
8 Important kinematic characteristics Limit positions Important kinematic characteristics Time ratio 1 t = °− (180 ) / θ ω 1 1 2 1 V = C C t 1 2 = C C ω / (1 8 0 ) ° − θ 2t = °+ (180 ) / θ ω 2 1 2 2 V = C C t 1 2 = °+ C C ω / (1 8 0 ) θ 2 1 R V T V = 180 180 θ α θ β ° − = = 2 ° + 1 t t = 1 2 1 1 2 2 C C t C C t =
国上活我大等 Important kinematic characteristics Transmission angle(传动角) Definition 1:acute angle between coupler and output link. Definition 2:Transmission angle is defined as the acute angle between the direction of the velocity-difference vector of the floating link and the direction of the absolute velocity of the output link. Definition 3:complementary angle to deviation angle(some time called pressure angle压力角 & 2 国 上游文廷大￥ Important kinematic characteristics Transmission angle Y=arccos 2+c2-(d-a2 2bc Y2=180°-arccos 2+c2-(d+a)2 2bc C 。 C 9
9 α F23 γ F23 ′ F23 ″ A B D C 4 1 2 3 Vc Important kinematic characteristics Transmission angle(传动角) Definition 1: acute angle between coupler and output link. Definition 2: Transmission angle is defined as the acute angle between the direction of the velocity-difference vector of the floating link and the direction of the absolute velocity of the output link. Definition 3: complementary angle to deviation angle(some time called pressure angle压力角) C1 B1 a b c d A D γ1 γ2 B2 C2 22 2 1 ( ) arccos 2 b c da bc γ +−− = 22 2 2 ( ) 180 arccos 2 b c da bc γ +−+ = −o Important kinematic characteristics Transmission angle
⊕ 上泽文通大￥ Important kinematic characteristics ©Toggle Position 国 上游文大￥ Important kinematic characteristics Toggle Position y=0 C B C y=0 nnnnnnn Work piece 777777777777777777 777777 10
10 F γ = 0 Vc F γ = 0 Vc Important kinematic characteristics Toggle Position A B C D 1 2 3 4 Work piece P γ =0 F A B C D F F0 γ =0 Important kinematic characteristics Toggle Position