How to draw a kinematic diagram 2. The Mechanism DOF 3 How to draw a kinematic diagram 2. The Mechanism DOF 3. The Planar four bar linkages

Chapter Two Planar Linkage

Chapter Two Planar Linkage General Character of a four-bar linkage 2.1）Basic Form of Four-bar Linakage 2.2）Grashof Criterion (Conditions of a Crank) 2.3）Inversions of Four-bar Linkage 2.4）Kinematic Design of Four-bar Linkage

Character of Planar Linkage 1.Advantage Bar form link, the distance of kinematic transmission can be longer Low pairing, Force Transmitted be very large Can got a very complex curve Different motions 2.Shortage:Low Efficiency, Inertia force, Not easy to design Problem to be Investigated Kinematic analysis Kinematic design

2.1 Basic form of four-bar linkage 2.1.1 Crank rocker 2.1.2 Double crank 2.1.3 Double rocker

2.1.1 Crank rocker mechanism 1）Constitution 2）Quick return Character 3）Pressure angle and transmission angle 4）Dead point position

Constitution of four bar mechanism Crank Floating link Or coupler Side links Frame

2.1.1 Crank rocker mechanism Diagram of quick return principle

Quick return character of a crank rocker Definition Coefficient of Advance return time ratio K=Vmb\r/Vma>=1 K=（180º+q）/（180º-q） Limit position：Extreme position of the driven bar crank angle between extreme positions

Quick return Character of crank-rocker Quick return is used to describe the characteristic of the driven bar If q >0 , that is:K>0 then the mechanism has quick return character Pay attention to the direction of prime mover when analyze the quick return characteristic

Pressure angle a、transmission angle Pressure angle a: without consideration of friction force, The acute angle between the acted force line of driven link and the velocity direction of acted point. Transmission angle g: the component angle of pressure Represent its transmission performance. The bigger the g，the better performance to transmit force. When Design a mechanism，g gmin Where is the smallest g?

Extreme position of the transmission angle

Dead point How to avoid the dead point? When the transmission angle is zero, this position is called dead point. You must know which is the prime move when analyze the dead point. Dead point is a special position of the mechanism. It is different from the DOF equals zero. Or the mechanism is self-locking. How to avoid the dead point? Duplicate a linkage out of 90 degrees phase With the help of a flying wheel Acting a outer force How to use the dead point Landing mechanism in airplane Clamping device on machine tool

2.1.2 double crank Use the quick return character of driven crank Parallel linkage anti-parallel linkage

2.1.3 Double rocker The formation crane landing mechanism of a air plane

2.2 Grashof Criterion 1）The question asked why there is a crank 2）Grashof criterion ( Conditions for having a crank) Suppose: l1=min{l1,l2,l3,l4} l4=max{l1,l2,l3,l4} l1+l 4 <=l2+l3 the crank should be the shortest link bar l1

2.3 Inversions form of a four-bar linkage mechanism 1) Changing the kinematic pairing a. The crank slider mechanism 2) Changing the fixed link a) guide bar mechanism b) Rocking block and fixed block mechanism 3) Enlarge the size of a pairing a) eccentric wheel mechanism

2.4 Kinematic Design of planar four-bar linkage To realize the motion of a driven link To Realize certain trace curve 1） graphical design Know the positions of a coupler， Know the positions of side likns Know the quick return coefficient 2）through the experiment 2） analytical design Know the positions of side links Know the trace point of a coupler 4） Optimization

2.4.1 Given the movement of driven link Know the speed ratio of driven link Given：the quick return coefficient K，the length of a rocker l3 It’s rocking angle f，Design this mechanism! Steps： 1）Calculate the value of q 2）draw an equilateral triangle with side length l3 and the top angle f 3）draw a right angle triangle，the right angle side has a angle 90- q 4）take the hypotenus as the diameter, draw a circumcircle 5）Taka an appropriate point, decide the length of crank and coupler

2.4.2 Give the movement of driven link Know the positions of a coupler Design a door for heat-treatment oven 1）Analyze the problem 2）The optimization of the results 3）Given the three positions of a coupler, How to solve the Problem? 4）Given four or more positions of a coupler, How to deal with the problem?

Exm.1 Concept design of a door Mechanical door Biological door Magnetic fluid door Gas door Fliud door

Exm1. Mechanical Ways of a Door Rotating door Folding door Soft door Push-pull door Horizontal axis Vertical axis double single

The open methods of vertical axis doors 、 Inward or outward?

2.4 Kinematic Design of planar four-barlinkage Given the trace points of a coupler graphical method, Experiment method, Virtual experiment method, Analytical method, synthetic method Steps to optimization 1）Describe the problem with mathematic model and the constraint equations 2）Select a appropriate method and software package 3）Analyze the calculate results.

Homework today Exercise book, pp 42, Prob. 2.16 Design a door operating mechanism, Analyze the given Conditions and How to solve it. Please give the size of your design