Chapter 2 Structural Analysis of Planar Mechanisms,1. Link,2.1 Kinematic Chain and Mechanisms,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),2. Kinematic Pair,(1) Kinematic pairs according to nature of relative motion According to the feature of relative motion between the two links, kinematic pairs may be classified as turning pairs and sliding pairs. 1) Turning pair. When one link has a turning or revolving motion relative to the other link, these two links constitute a turning pair or a revolving pair. ,A kinematic pair is a joint that permits relative motion.,Fig.2-2 Turning pairs(转动副),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),(2) Kinematic pairs according to nature of contact According to the feature of contact between the two links, kinematic pairs may be classified as lower pairs and higher pairs.,1) Lower pair. When a pair has surface or area contact between two links, it is known as a lower pair. 2) Higher pair. When a pair has a point or line contact between two links, it is known as a higher pair. ,Fig.2-4 Higher pairs(高副),(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.。,3. Kinematic Chain,Fig.2-5 Closed kinematic chains(闭链),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.2-6 Unclosed kinematic chains(开链),Fig.2-6 shows some unclosed kinematic chains. The first and the last link have only one pair element in the unclosed chain.,Fig.2-7 Structures(桁架),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.2-8 Mechanisms in which all the pairs are lower pairs(低副机构),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.2-9 Mechanism including higher pair(高副机构),Fig.2-9 shows a higher pair mechanism in which links 1 and 2 are connected by a higher pair at point C.,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 two forms: 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.,2. Symbols of Common Used Links and Pairs,The special symbols used in a schematic diagram of mechanisms are listed in Tab.2-1.,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 the frame in a mechanism.,Fig.2-10 Mechanism nomenclature (机构术语) 1、 3link connected frame (连架杆) 2coupler (连杆) 4frame (机架),(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 suitable position, and observe its composition. 3) Find out the number of links and the number of pairs, and determine the type of pairs from input link to the output link. 4) The plane on which most links move can be selected as a drawing plane. 5) The dimensions between two pairs and the other kinematic dimensions must be measured, then select proper scale to draw the sketch.,Example 2-1 Fig.