MT Chap2 Structural Analysis of Planar Mechanisms

2020-02-27 171浏览

  • 1.
  • 2.2.1 Kinematic Chain and Mechanisms 1. Link A part is a minimum unit in a machine from the standpoint of manufacture, such as a rigid link, nut, bolt, gear and so on. Fig.2-1a shows a single cylinder four stroke cycle engine, and Fig.2-1b is the schematic diagram. Fig.2-1c is a coupler. The coupler consists of several parts which are connected rigidly. Fig.2-1 Coupler of the internal combustion engine(内燃机中的连杆)
  • 3.2. Kinematic Pair A kinematic pair is a joint that permits relative motion. (1) Kinematic pairs according to nature of relative motion Accordin g to the feature of relative motion between the two links, kinematic p airs may be classified as turning pairs and sliding pairs. 1) Turning pair. When one link has a turning or revolving motion rela tive to the other link, these two links constitute a turning pair or a rev olving pair. Fig.2-2 Turning pairs(转动副)
  • 4.2) Sliding pair. If two links have a sliding motion relative to each other, they form a sliding pair or prismatic pair. Fig.2-3 shows some sliding pairs and their symbols. Fig.2-3 Sliding pairs(移动副)
  • 5.(2) Kinematic pairs according to nature of contact Accordi ng to the feature of contact between the two links, kinemat ic pairs may be classified as lower pairs and higher pairs. 1) Lower pair. When a pair has surface or area contact bet ween two links, it is known as a lower pair. 2) Higher pair. When a pair has a point or line contact betw een two links, it is known as a higher pair. Fig.2-4 Higher pairs(高副)
  • 6.(3) Kinematic pair element The geometric forms of contact in a pair, such as point, line or surface, are known as pair elements. A pair is made up of two elements, one on each link being joined, such as the outside cylindrical surface of shaft 1 in Fig.2-2 and inner cylindrical surface of bearing 2 in Fig.2-2 are pair elements respectively.
  • 7.3. Kinematic Chain A kinematic chain is an assembly of links in which the relative motions of the links are possible. Kinematic chains can be classified as closed chains and unclosed chains. If every link in a kinematic chain has at least two pair elements, and links form a closed loop, this kinematic chain is called a closed chain. A closed chain at least has one loop. Fig.2-5 shows some closed kinematic chains. Fig.2-5 Closed kinematic chains(闭链)
  • 8.Fig.2-6 shows some unclosed kinematic chains. The first and the last link have only one pair element in the unclosed chain. Fig.2-6 Unclosed kinematic chains(开链)
  • 9.If the relative motion of the links in the assembly is impossible, the assembly of links is called a structure or superstructure. Fig.2-7 shows some structures. A structure may be considered as a link. Fig.2-7 Structures(桁架)
  • 10.4. Mechanism If one link of a kinematic chain is fixed to the ground, the kinematic chain becomes a mechanism. If all the pairs in a mechanism are lower pairs, the mechanism is called a lower pair mechanism. If a mechanism has one or more higher pairs, the mechanism is called a higher pair mechanism. Fig.2-8 Mechanisms in which all the pairs are lower pairs(低副机构)
  • 11.Fig.2-9 shows a higher pair mechanism in which links 1 and 2 are connected by a higher pair at point C. Fig.2-9 Mechanism including higher pair(高副机构)
  • 12.2.2 Schematic Diagram of Mechanisms 1. Schematic Diagram A simple diagram in which the links and pairs are represented by some simple lines and pair symbols to describe the composition of a mechanism is called a schematic diagram of mechanisms. The schematic diagram takes one or twoforms:a schematic diagram and scaled schematic diagram. A schematic diagram is proportional but not exactly to scale, while a scaled schematic diagram requires a “stripped down” stick diagram, “stripped down” stick diagram is usually used for further motion analysis and force analysis.
  • 13.2. Symbols of Common Used Links and Pairs The special symbols used in a schematic diagram of mechanisms are listed in Table.
  • 14.3. The Procedure of Drawing a Schematic Diagram of a Mechanism (1) Mechanism nomenclature 1) Frame. Link which is fixed in a mechanism. 2) Driving link. Link acted by the driving force in a mechanism. 3) Driven link. All the other moving links except the frame and the driving links in a mechanism. 4) Coupler or connected rod. Links which are not connected with t he frame in a mechanism. Fig.2-10 Mechanism nomenclature (机构术语) 1、 3—link connected frame (连架杆) 2—coupler (连杆) 4—frame (机架)
  • 15.(2) The procedure of drawing a schematic diagram 1) Find out the driving links and the driven links. 2) Run the mechanism slowly for a while, then stop it at a suita ble position, and observe its composition. 3) Find out the number of links and the number of pairs, and d etermine the type of pairs from input link to the output link. 4) The plane on which most links move can be selected as a dr awing plane. 5) The dimensions between two pairs and the other kinematic dimensions must be measured, then select proper scale to draw t he sketch.
  • 16.Example 2-1 Fig.2-11a shows a pump. Draw a schematic diagra m of the pump. Fig.2-11 Schematic diagram of the pump (泵的机构运动简图) 1—eccentric disk(偏心轮) 2—coupler(连杆) 3—slider(滑块) 4—frame(机架)
  • 17.Example 2-2 Fig.2-12a shows a shaper. Draw a schematic diagram of the shaper. Fig.2-12 Shaper and its schematic diagram(牛头刨床及其机构运动简图) 1、2—gear(齿轮) 3—block(滑块) 4—rocker(摆杆) 5—link(连杆) 6—slide bar(滑枕) 7—frame(机架)
  • 18.2.3 Degree of Freedom of Planar Mechanisms 1. Grueblers Equation (1) Degree of freedom of a link Degree of freedom is also called th e mobility, and it can be defined as the number of independent coor dinates required to determine its position. (2) Constraints of a kinematic pair The turning pair shown in Fig.2-1 3b has two constraints. (3) Degree of freedom of a kinematic pair It can be defined as the n umber of the independent relative motion. Fig.2-13 Constrains of pair(运动副的约束)
  • 19.(4) Degree of freedom of a planar mechanism In a planar mechanism, the fixed link has zero degree of freedom; each moving link has 3 d.o.f., each lower pair has 2 constraints and each higher pair has 1 constraint. We suppose that there are moving links n, lower pairs pl, higher pairs ph, then the degree of freedom in a planar mechanism is asfollows:F=3n-2pl-ph
  • 20.Example 2-3 Determine the degrees of freedom of the mechanisms shown in Fig.2-14. Fig.2-14 The caculation of degree of freedom (自由度计算)
  • 21.2. Conditions Having Predictable Motion in a Mechani sm The degree of freedom of a mechanism is the number of independent coordinates to define its position, and is also the number of input links which need to be provided in order to create a predictable output motion Fig.2-15 Conditions of causing definite and predictable motions(机构具有确定运动 的条件)
  • 22.3. Points for Attention When Calculating Degree of Fre edom (1) Redundant degree of freedom Sometimes, one or mor e links of a mechanism may be moved without causing any motion to the other links of the mechanism. Fig.2-16 Partial degree of freedom(局部自由度)
  • 23.(2) Multiple pin joints Two links are connected together by onl y one turning pair, which is illustrated in Fig.2-17 &2-18. Fig.2-17 Multiple pin joints(复合铰链) Fig.2-18 Examples of multiple pin joints (复合铰链的示例)
  • 24.(3) Redundant constraints Sometimes, a mechanism may have o ne or more redundant constraints which do not effect the movem ent of links, or a mechanism may have one or more links which do not introduce any extra constraint. Fig.2-19 Redundant constrain in the parallel-crank mechanism(平行四边形机构的虚约束)
  • 25.the redundant constraints andlinks:1) Two links are connected by several turning pairs and their axes are coincident. 2) Two links are connected by several sliding pairs and their g uide lines are parallel. 3) Two links are connected by several higher pairs and their c ommon normal lines are coincident. 4) Redundant links.
  • 26.Fig.2-20 Redundant constrains of turning pairs(转动副的虚约束) Fig.2-21 Redundant constrains of Sliding pairs(移动副的虚约束)
  • 27.Fig.2-22 Redundant constrains of Higher pairs(高副机构的虚约束)
  • 28.Fig.2-23 Redundant constraints (虚约束) Fig.2-24 Redundant constrain produced by connecting two equidistance points ( 连接等距点产生的虚约束)
  • 29.Example 2-4 Calculate the degree of freedom of the mechanism shown in Fig.2-25. Fig.2-25 Degree of freedom of the complex mechanism (复杂机构的自由度)
  • 30.Example 2-5 Calculate the degree of freedom of the shearing m echanism shown in Fig.2-26a. Fig.2-26 Degree of freedom of the shearing mechanism (剪床机构的自由度)
  • 31.2.4 Mechanism Analysis and Innovation 1. Link Group Analysis (1) Driving link The driving link may rotate about its axis or translate along a guideline, and it has one degree of freedom. Fig.2-27 shows two kinds of dri ving links. Fig.2-27 Driving links(原动件)
  • 32.(2) Link group Any mechanism consists of driving link, driven link and a frame. The number of driving links is equal to the number of degrees of freedom. For example, Fig.2-28 shows a one degree of freedom mechanism, and the driving link is crank AB. After the driving link AB and the frame have been removed from the mechanism, the degree of freedom of the link group BCDEF is zero. Fig.2-28 Diriding of link groups(拆分杆组)
  • 33.When there are two links and three lower pairs in the link group, this link group is called class Ⅱ link group. There is one pair which connects two links in the link group and two pairs which will connect the other links. The class Ⅱ link groups are illustrated in Fig.2-29. Fig.2-29 Class Ⅱ link groups(Ⅱ级杆组)
  • 34.When there are four links and six lower pairs in the link group, the link group is called class Ⅲ link group. There are three pairs which connect links in the link group and three pairs which will connect the other links. The common class Ⅲ link groups are illustrated in Fig.230. Fig.2-30 Class Ⅲ link groups (Ⅲ级杆组)
  • 35.Another link group in which there are four links and six lower pairs is illustrated in Fig.2-31. There are four pairs which connect links in the link group and two pairs which will connect the other links. We called this link group as class IV link group. This kind of link group is used rarely. Fig.2-31 Class Ⅳ link group (Ⅳ级杆组)
  • 36.2. Principle of Mechanism Composition Any mechanism can be designed by connecting basic link group in which the degree of freedom is zero with the driving link and the frame. This is illustrated in Fig.2-32. Fig.2-32 Shaper mechanism design (牛头刨床的组合过程)
  • 37.3. Replacement of Higher Pair by Lower Pairs When a mechanism including a higher pair must be analyzed, we can replace the higher pair by lower pairs. Therefore, we can u se the principle of link group to analyze the mechanism connected with lower pairs. As we know that a higher pair has one constraint, and a lower pair has two constraints, so that we can use a link wit h two turning pairs to replace the higher pair.
  • 38.Fig.2-33 shows some higher pair mechanisms; the higher pair can be replaced by one binary link with two turning pairs. The centers of curvatures at the contact point P of the two profiles lie at C1and C2; the link C1C2 with turning pairs at C1 and C2 replaces the higher pair. Fig.2-33 Replacement of higher pair by lower pairs (高副低代)
  • 39.4. Structural Analysis of Planar Mechanism When determining a class of a mechanism, the following proce dure must be noticed. 1) Remove the redundant degree of freedom and redundant constr aints. 2) The higher pairs are replaced by lower pairs. 3) Calculate the degree of freedom, and determine the driving links. 4) Find out the class II link groups first and remove them from the mechanism. If there is not any class II link group, the class III link g roup must be considered. 5) The last links which have been left must be the driving links, and they are equal to the number of the degrees of freedom.
  • 40.Example 2-6 Determine the class of the shearing mechanism as shown in Fig.2-26. Fig.2-34 Mechanism analysis (机构的分析)
  • 41.Example 2-7 Determine the class of the shaper mechanism sho wn in Fig.2-35. Fig.2-35 Shaper mechanism analysis (牛头刨床机构的分析)
  • 42.5. Innovative Design of Mechanism (1) Design a tandem mechanism When adding a class Ⅱ li nk group shown in Fig.2-36b to the driving link shown in Fig. 2-36a and the frame, we can obtain a four bar linkage show n in Fig.2-36c. If adding another class Ⅱ link group shown in Fig.2-36d to the link DCand the frame, we can obtain a six b ar mechanism shown in Fig.2-36e. Fig.2-36 Series mechanism consisted by class Ⅱ link groups ( Ⅱ级杆组组成的串联机构)
  • 43.If adding class Ⅲ link group to the driving link and the frame, we can obtain a class Ⅲ mechanism; see the Fig.2-37. Fig.2-37 Series mechanism consisted by class Ⅲ link groups (Ⅲ级杆组组成的串联 机构)
  • 44.(2) Design a parallel mechanism When connecting a class Ⅱ lin k group shown in Fig.2-38b to two driving links shown in Fig.238a, we can obtain a five bar linkage shown in Fig.2-38c. The fi ve bar linkage is a parallel mechanism. Fig.2-38 Parallel mechanism consisted by class Ⅱ link groups (Ⅱ级杆组组成的并联机构)
  • 45.If connecting a class Ⅲ link group to three driving links, we can obtain another parallel mechanism; see the Fig.2-39. This kind of mechanism can be used to parallel robot. Fig.2-39 Parallel mechanism consisted by class Ⅲ link groups (Ⅲ级杆组组成的并联机构)