References WEEKS 1-2 MECHANISMS (METU, Department of Mechanical Engineering) Text Book: Mechanisms Web Page: http://www.me.metu.edu.tr/people/eres/me301/in dex.ht Analitik Çözümlü Örneklerle Mekanizma Tekniği, Prof. Dr. Mustafa SABUNCU, 2004 Mekanizma Tekniği, Prof. Dr. Eres SÖYLEMEZ, 2007 Theory of Machines and Mechanisms, J.J. Uicker, G.R.Pennock ve J.E. Shigley, 2003 1
Course Policy Two Midterms (20%) +Homework (10%) + 1 Final (50%) 2
What is a mechanism? A mechanism is a device which transforms motion to some desirable pattern and typically develops very low forces and transmits little power. Mechanisms are assemblages of rigid members connected together by joints. A machine typically contains mechanisms which are designed to provide significant forces and transmit significant power The motion is transferred from the crank driven by a motor through the coupler to the left rocker. The rotary motion is converted into rocking motion (desired motion) A windshield wiper mechanism 3
Robot Gear mechanism (Gearbox) 4
Crank mechanism Crank mechanism: It is mainly used to convert rotary motion to a reciprocating motion An engine, or motor 5
suspension system The vehicle suspension system is responsible for driving comfort and safety as the suspension caries the vehicle body and transmits all forces between the body and the road. Airplane nose wheel mechanism These systems damp the vibration. 6
Mechanisms are assemblages of rigid members (links) connected together by joints. Rigid link: A rigid link is one which does not undergo any deformation while transmitting motion. Actually, rigid links do not exist. However, as the deformation of a connecting rod, crank etc. of a reciprocating steam engine is not appreciable, they can be considered as rigid links. Flexible link: A flexible link is one which is partly deformed in a manner not to affect the transmission of motion. Example: belts, ropes (halat), chains and wires are flexible links and transmit tensile forces only. Why do we assume that all links are rigid? A 2 B If the link 2 is assumed that is flexible, it can be difficult to obtain the kinematic equation between A and B points. Mechanical press for Example Therefore, all links are designed as to be rigid 7
Theory of machines is separated into two section Dynamics is also separated into two section Kinematics: Kinematic analysis involves determination of position, displacement, rotation, speed, velocity, and acceleration of a mechanism. Kinetics: It is that branch of theory of machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts. Kinematic Synthesis: It is the determination of the mechanism parameters (dimensions of the link lengths, number of tooth on gears, etc) to realize a given motion (including velocity and acceleration) 8
TYPES OF MOTION TRANSLATION. All points on the body describe parallel paths. A reference line drawn on the body changes its linear position but does not change its angular orientation. All the particles forming the body move along parallel paths. If these paths are straight lines, the motion is said a rectilinear translation; if the paths are curved lines, the motion is a curvilinear motion rectilinear translation curvilinear motion 9
ROTATION about a fixed axis. The particles forming the rigid body move in parallel planes along circles centered on the same fixed axis. If this axis, called the axis of rotation intersects the rigid body, the particles located on the axis have zero velocity and zero acceleration GENERAL PLANE MOTION (Complex motion): Any plane motion which is neither a translation or a rotation is referred as a general plane motion. Plan motion is that in which all the particles of the body move in parallel planes. Translation and rotation are plane motions. 10
Kinematic element, is that part of a rigid body which is used to connect it to another rigid body such that the relative motion between the two rigid bodies can occur Kinematic element Kinematic element Kinematic pair (joint) is a connection between two or more kinematic elements. The types of kinematic pairs and their distribution within the mechanism determine the main characteristics of a mechanism. 11
Kinematic pair (joint) Note: DOF is Degree of Freedom 12
Wheel Planar pure-roll (R), pure-slide (P), or roll-slide (RP) joint - 1 or 2 DOF (higher pair) 13
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Kinematic pairs (joints) may be classified in several diffrent forms. Classification Mechanisms of Kinematic Pairs Type of contact Closed kinematic form Open kinematic form Lower kinematic pairs Higher kinematic pairs Force closed Form closed Contact along a surface A nut and a bolt have been assembled to each other by its geometry The spring provides contact between the follower and cam. Contact at a point or on a line Closed kinematic pairs are those in which the contact between the kinematic elements is maintained within all possible positions of a mechanism. In force closed kinematic pairs, there exist an external force ( spring force etc.) which keeps the two kinematic elements in contact. In form closed kinematic pairs, one of the kinematic elements envelopes the other. An open kinematic pair is one whose pairing and unpairing of its kinematic elements that form the joint are controlled. 15
Degree of freedom of a rigid body: The degree of freedom (DOF) of a rigid body is the number of independent parameters that define its configuration Six independent parameters are required to define the motion of the ship. DOF=6, λ=6 (spatial space) DOF=3, λ=3 (planar space) An unrestrained rigid body in space has six degrees of freedom: three translating motions along the x, y and z axes and three rotary motions around the x, y and z axes respectively. Degree of freedom a kinematic pair: The degrees of freedom (DOF) of a kinemtaic pairs defined as the number of independent movements it has. 16
Degree of freedom a kinematic pair: 17
Degree of freedom a kinematic pair: Joint with Highest freedom. Translation perpendicular to the plane is restricted. Translations within the plane and rotation in all three axes are possible the ball can rotate around the x,y and z-axes **In force closed kinematic pairs, there exist an external force ( spring force etc.) which keeps the two kinematic elements in contact. **In form closed kinematic pairs, one of the kinematic elements envelopes the other. When a Cylinder is confined between two parallel planes, there is no translation perpendicular to the planes and no rotation about an axis within the plane perpendicular to the cylinder axis. Translation about two perpendicular axes within the plane and rotation about the cylinder axis and about an axes perpendicular to the plane are possible 18
Degree of freedom a kinematic pair: Joint with Highest freedom. Translation perpendicular to the plane is restricted. Translations within the plane and rotation in all three axes are possible When a Cylinder is confined between two parallel planes, there is no translation perpendicular to the planes and no rotation about an axis within the plane perpendicular to the cylinder axis. Translation about two perpendicular axes within the plane and rotation about the cylinder axis and about an axes perpendicular to the plane are possible Three axes of rotation intersect at the center of the sphere If a pin perpendicular to the axes of translation is inserted into a slot, then rotation about the translation axis is constrained. If the slot is cut in a different direction, rotation about one axis will be constrained. Translation in two axes (in plane) and rotation (perpendicular to the plane) are possible. Rotation axes are skew (they do not intersect). The rotation and translation axes are coincident Axes of translation and rotation are perpendicular to each other. 19
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If a rigid body contains at least two kinematic elements we shall call it a link. A link may have more than two kinematic elements (but not less than two). One can classify links according to the number of kinematic elements it contains. These are binary, ternary or quarternary, etc. For the kinematic analysis we shall be interested only with the kinematic dimensions The kinematic dimensions of a link in a mechanism are those dimensions which define the relative positions of the kinematic elements on that link and when these dimensions are specified, the link dimensions are known for motion analysis. These dimensions can be distances or angles. For the manufacture of the link or for the dynamics, etc other physical dimensions such as the width, height, thickness, etc. may be important. For the kinematic analysis we shall be interested only with the kinematic dimensions. As seen with the above figure, on the link at points A and B kinematic elements form revolute joins, whereas at D there is a cylinder in slot joint. For manufacture besides the thickness, one must specify the radii ( R 1, R 2, R 3 ), the slot length and width (L 1, L 2 ), the length of the piece (L 3 ) etc. These have no importance for kinematics. Whereas the distance between revolute joints A and B (a), the angle slot makes with respect to the line AB (α) and perpendicular distance from point A to the slot axis (b)are the kinematic dimensions of this link. Once these four parameters are known, the link is kinematically defined. 21
Kinematic diagram: A kinematic diagram or kinematic scheme illustrates the connectivity of links and joints of a mechanism or machine rather than the dimensions or shape of the parts. Often links are presented as geometric objects, such as lines, triangles or squares, that support schematic versions of the joints of the mechanism or machine. Connecting rod 22
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Kinematic diagram Crank mechanism Shaping Machine (Quick Return Mechanism) 25
There are certain joints where more than two links are connected. For such cases we define the degree-of a joint as the number of links connected at the joint minus one. One must assume that there joints at this point equal to the degree of the joint, ( please do not confuse the degree of the joint with the degree-of-freedom of a joint) Degree of a joint is equal to the number of joints at that connection. Degree of freedom of a joint is the number of independent parameters required to define the position of one link relative to the other connected by that joint. 26
Kinematic chain: The links connected to each other by kinematic pairs will form a kinematic chain. If all the kinematic pairs are closed, than we have a closed kinematic chain. If one of the kinematic pair is of open type, the kinematic chain is an open kinematic chain. Kinematic chain is an idealised representation of the mechanism structure. We are not concerned with the dimensions of the links. Each link is represented as a line or as a polygon and at each vertex we have a kinematic element which joins with another element on another link. The dimensions of the edges are not important. Shaping Machine (Quick Return Mechanism) Sled element 1- The kinematic diagram of all links is drawn 2- All links are connected according to their kinematic pairs 1 closed kinematic chain. Slider element 2 3 4 1 6 5 2 5 6 3 4 27
open kinematic chain 1 2 4 2 3 3 4 1 For higher kinematic pair 2 1 2 3 3 1 28
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The degree of freedom of a mechanism (mobility) is the number of independent parameters required to define the position of every link in that mechanism Degree of freedom of a mechanism depends on: The degree of freedom of space The degree of freedom of the joints The number of links and joints The distribution of links and joints Does not depend on the shape of the links. Determination of the Degree-of- Freedom of a Mechanism F j f = λ ( 1) + j i= 1 i *** If F=0 or F<0, the mechnisms can be called static or hiperstatic respectively. 30
To increase the load carrying capacity there can be several contact points between the two links. Each contact point cannot be treated as a different kinematic pair. There can be only one kinematic element between two links. There is one kinematic element (lower kinematic pair) between two links. 31
Four-bar linkage = λ ( 1) + F j f j i i= 1 Slider crank mechanism F = 3( 1) + ( + + + ) = i= 1 Shaping Machine (Quick Return Mechanism) 4 4 4 1 1 1 1 1 F 7 i= 1 ( + + + + + + ) = 3( 6 7 1) + 1 1 1 1 1 1 1 = 1 32
Adjustable Drive Grabber Second order pin joints F = 3( 7 8 1) + 8 i= 1 ( + + + + + + + 1) 1 1 1 1 1 1 1 = 2 F = 3( 10 13 1) + 13 i= 1 13 = 1 33
F 10 = 3( 1) + ( ) = 8 10 10 1 i= 1 34
A simplified engineering drawing of the front loader assembly is as shown. Note that a lot of details are neglected. 35
The Schematic kinematic diagram of the mechanism involved for the front loader is as shown. Note that each link in practice may be composed of several different rigid bodies that are rigidly connected to each other. F = 3( 9 11 1) + 12 i= 1 11 = 2 ( ) The two degrees of freedom refer to the displacement parameters between the piston and cylinders. It can be said that two actuators need for the front loader motion 36