圆上清支大学 e+口 LECTURE 2 ME371/ME337 DESIGN AND MANUFACTURING Kinematic Fundamentals Fun with MECHANISMS Covered:Ch2-in Design of Machinery 圆上泽夫道大学 OUTLINE Basic concepts and definitions How does a MECHANISM work? The kinematic diagram A simple equation-Gruebler Criterion Exceptions to Gruebler's Equation 1
1 Kinematic Fundamentals ——Fun with MECHANISMS LECTURE 2 Covered：Ch2- in Design of Machinery ME371/ME337 DESIGN AND MANUFACTURING OUTLINE Basic concepts and definitions How does a MECHANISM work? The kinematic diagram A simple equation-Gruebler Criterion Exceptions to Gruebler’s Equation
圈上海文通大华 Degree of Freedom Y移动 X移动 Z转 地中中 z转 ref. Y旋转 △02 DOF:The number of independent coordinates required to define the systems'position. 圆上泽夫道大学 Links Links:individual parts of mechanism.They are considered rigid bodies and are connected with other links to transmit motion and forces. Nodes Binary link Ternary link Quatemary link 二副元素连杆 三副元素连杆 四副元素连杆 FIGURE 2-2 Links of different order 2
2 Degree of Freedom DOF: The number of independent coordinates required to define the systems’ position. Links: individual parts of mechanism. They are considered rigid bodies and are connected with other links to transmit motion and forces. Links 二副元素连杆 三副元素连杆 四副元素连杆
圈上大￥A Link may have several components 圆上清支大华 Joints Joints:A joint is a connection between two or more links(at their nodes),which allows some motion,or potential motion,between the connected links Joints can be classified in several ways: >By the type of contact between the elements,line,point,or surface. >By the number of degrees of freedom allowed at the joint. >By the type of physical closure of the joint:either force or form closed. >By the number of links joined(order of the joint). 3
3 A Link may have several components Joints: A joint is a connection between two or more links (at their nodes), which allows some motion, or potential motion, between the connected links. Joints can be classified in several ways: By the type of contact between the elements, line, point, or surface. By the number of degrees of freedom allowed at the joint. By the type of physical closure of the joint: either force or form closed. By the number of links joined (order of the joint). Joints
国 上海文通大学 Joints lower pair:joints with surface contact(as with a pin surrounded by a hole) 国 higher pair:joints with point or line contact. 国 The main practical advantage of lower pairs over higher pairs is their better ability to trap lubricant between their enveloping surfaces 周 上游充豆大￥ Joints of various types 三州 IGURI 2-3 4
4 lower pair: joints with surface contact (as with a pin surrounded by a hole) higher pair: joints with point or line contact. The main practical advantage of lower pairs over higher pairs is their better ability to trap lubricant between their enveloping surfaces. Joints Joints of various types
圆上泽文大学 Joints of various types The revolute(R)and the prismatic(P)pairs are the only lower pairs usable in a planar mechanism. The screw(H),cylindric(C),spherical,and flat(F)lower pairs are all combinations of the revolute and/or prismatic pairs and are used in spatial(3-D)mechanisms. Name (Symbol)DoF Cont- ains Revolute 1 (R) R Prismatic 1 (P) 0 The Six Lower Pairs Helical (H) 1 RP Cylindric (C) 2 RP Spherical 3 RRR P 3 RPP 圈上泽夫道大学 Basic concepts and definitions Kinematic Chain(运动链)：an assembly of links and joints.(Interconnected in a way to provide a controlled output motion in response to a supplied input motion.) Mechanism(机构)：a kinematic chain in which at lease one link has been "grounded",or attached,to the frame of reference (which itself may be in motion);the links in the kinematic chain move upon each other with definite relative motion. >Link,Joints >Input Link,Output Link,Frame >Input motion 5
5 The revolute (R) and the prismatic (P) pairs are the only lower pairs usable in a planar mechanism. The screw (H), cylindric (C), spherical, and flat (F) lower pairs are all combinations of the revolute and/or prismatic pairs and are used in spatial (3-D) mechanisms. The Six Lower Pairs Joints of various types Kinematic Chain（运动链）: an assembly of links and joints. (Interconnected in a way to provide a controlled output motion in response to a supplied input motion.) Mechanism（机构）: a kinematic chain in which at lease one link has been “grounded”, or attached, to the frame of reference (which itself may be in motion); the links in the kinematic chain move upon each other with definite relative motion. Link, Joints Input Link, Output Link, Frame Input motion Basic concepts and definitions
国上泽发大坐 Basic concepts and definitions Machine(机器)：A combination of resistant bodies arranged to compel the mechanical forces of nature to do work accompanied by determinate motions. Machine(机器)：is a collection of mechanisms arranged to transmit forces and do work.(Reuleaux >Crank:a link which makes a complete revolution and is pivoted to ground, >Rocker:a link which has oscillatory (back andforth)rotation and is pivoted to ground >Coupler:a link which has complex motion and is not pivoted to ground. 圈上泽夫通大学 Basic concepts and definitions Take-up mechanism 挑线机构 Needle mechanism 刺布机构 12 10 8 SKId: 1 6
6 Machine（机器）: A combination of resistant bodies arranged to compel the mechanical forces of nature to do work accompanied by determinate motions. Machine（机器）: is a collection of mechanisms arranged to transmit forces and do work.（Reuleaux ） Crank：a link which makes a complete revolution and is pivoted to ground, Rocker：a link which has oscillatory (back andforth) rotation and is pivoted to ground Coupler ：a link which has complex motion and is not pivoted to ground. Basic concepts and definitions 8 5 6 7 8 9 10 12 11 12 10 P 1 4 2 3 1 2 3 Basic concepts and definitions Take-up mechanism 挑线机构 Needle mechanism 刺布机构
图上涤支大峰 OUTLINE Basic concepts and definitions How does a MECHANISM work? The kinematic diagram A simple equation-Gruebler Criterion Exceptions to Gruebler's Equation 国 上海充廷大学 How does A MECHANISM work Lower Pairs square X-section Revolute (R)joint-1 DOF Prismatic (P)joint-1 DOF Helical (H)joint-1 DOF 较链副 移动副△9 螺旋副 Ay C-do Cylindrie (C)joint-2 DOF Spherical (S)joint-3 DOF Planar(F月oint-3DOF 柱销制 球较副 平面副 FIGURE 2-3 (a)The six lower pairs Prismatic Revolute Cylindric Spherical Helical Planar(F) DOF 7
7 OUTLINE Basic concepts and definitions How does a MECHANISM work? The kinematic diagram A simple equation-Gruebler Criterion Exceptions to Gruebler’s Equation Prismatic Revolute Cylindric Spherical Helical Planar (F) DOF 1 1 2 3 1 3 Lower Pairs How does A MECHANISM work 铰链副 移动副 螺旋副 柱销副 球铰副 平面副
圈上泽支大峰 How does A MECHANISM work Higher Pairs-1 Names Degree of Typical form Comments freedom Roller rotates about this line at this Cylindrical instant in its motion.Roller does not slip on the surface on which it roller rolls. Cam rolls and slides on follower. Cam pair 2 01 Spur gears,helical gears,and other gears.(rolls slides) Gear pair 圆上海夫通大学 How does A MECHANISM work Higher Pairs-2 Names Typical form Degree of Comments freedom Ball rolls without slipping. Rolling ball Ball can rotate about any axis Ball in throughitscenterand slides along cylinder axis. cylinder Body can rotate about any axis through the contact point and slide Spatial point in any direction in the tangent contact plane. 8
8 Higher Pairs-1 How does A MECHANISM work Higher Pairs-2 How does A MECHANISM work
圈上泽文通大华 Planar VS Spatial Close VS Open In a planar mechanism,all of the A spherical mechanism is a relative motions of the rigid bodies are mechanical system in which the bodies in one plane or in parallel planes. move in a way that the trajectories of The rotational axes of hinged joints points in the system lie on concentric that connect the bodies in the system spheres. are perpendicular to this ground plane. The rotational axes of hinged joints that connect the bodies in the system pass through the center of these spheres. 圈上泽夫通大学 Planar VS Spatial Close VS Open If every link in the chain is connected to two or more links then the chain form one or more closed loops. If NOT,the chain is said to be open. 9
9 Planar VS Spatial Close VS Open In a planar mechanism, all of the relative motions of the rigid bodies are in one plane or in parallel planes. The rotational axes of hinged joints that connect the bodies in the system are perpendicular to this ground plane. A spherical mechanism is a mechanical system in which the bodies move in a way that the trajectories of points in the system lie on concentric spheres. The rotational axes of hinged joints that connect the bodies in the system pass through the center of these spheres. Planar VS Spatial Close VS Open If every link in the chain is connected to two or more links then the chain form one or more closed loops. If NOT, the chain is said to be open
圆上泽文大华 How to do kinematic analysis of a given mechanism? Fourbar slider-crank linkage 圆上泽充大学 The kinematic diagram Revolute joints:Symbols used in kinematic diagram Two motion links One motion link .向兴 Three motion link 10
10 How to do kinematic analysis of a given mechanism? Fourbar slider-crank linkage The kinematic diagram Revolute joints: Symbols used in kinematic diagram Two motion links One motion link Three motion link