ME309- Notes-CH1 - Kinematics of Machinery PDF

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Kinematics of Machinery...

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King Fahd University of Petroleum & Minerals

Mechanical Engineering Department

MECHANICS OF MACHINES ME 309

Dr. Saif A. Al-Kaabi

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Mechanics of Machines Mechanics is that branch of scientific analysis that deals with motions, time, and forces. Motion covers position, displacement, rotation, speed, velocity, and acceleration. Mechanics

Statics

Dynamics

Kinematics

Kinetics

Statics deals with the analysis of systems that are either stationary or moving with zero acceleration. Dynamics deals with systems that change with time (with acceleration). Kinematics is the study of motion, quite apart from the forces which produce that motion. Kinetics is the study of forces and moments that produce the motion. Machines: a machine is a combination of fixed and moving bodies that are arranged for transforming or transferring energy (to do work) accompanied by certain determinate motions.

Dr. Saif A. Al-Kabi

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A Mechanism is a set of rigid bodies (links), connected by movable joints, with one link fixed to produce a specific motion. (Linkage ⇔ Mechanism) A Mechanism is a component of a machine. It differs from a machine in its purpose. In a machine, terms such as force, torque, work, and power describe the predominant concepts. In a mechanism, though it may transmit power or force, the predominant idea in the mind of designer is one of achieving a desired motion. Links are the individual rigid bodies that collectively form a mechanism. A Frame is a fixed link. It’s important to keep in mind that there is only ONE frame for a given mechanism or a machine. The links of a mechanism must be connected together in some manner in order to transmit motion from the driver, or input link, to the follower, or output link.

Link Link Joint

Frame

Kinematic pairs (joints): those are the connections between links in order to transmit motion. Kinematic pairs are divided into two types: Lower Pairs: have surface contact between the pair elements. Higher Pairs: have line or point contact between the elemental surfaces.

Dr. Saif A. Al-Kaabi

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Dr. Saif A. Al-Kaabi

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Pin-in-slot (fork) joint: it is a two-degree of freedom joint. It allows sliding and rotation (x and θ ).

A Planar Mechanism is one in which all the links move in a plane or in parallel planes (2-D motions). In this course, only planar mechanisms are studied. A Spatial Mechanism is one in which some links undergo motion in three-dimensional space (3-D motions). Joint

Joint

Link

Link

Dr. Saif A. Al-Kaabi

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An example of spatial mechanisms: a schematic diagram of a robotic arm.

An example of planar mechanisms.

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Kinematic Chain: a group of links joined together by pairs (joints). Kinematic chains are divided into two types: (a) Closed-loop kinematic chain: Every link in the chain is connected to at least two other links (the chain may form one or more closed loops. (b) Open-loop kinematic chain: One (or more) of the links is connected to only one other link.

Loop

Loop

A closed-loop kinematic chain.

An open-loop kinematic chain

Dr. Saif A. Al-Kaabi

A closed-loop kinematic chain.

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Some Basic Mechanisms: the four-bar linkage and the slider-crank mechanism are considered two of the simplest mechanisms that form other complicated machines and mechanisms. 1. A four-bar linkage is basically a closed planar linkage consisting of four rigid links connected by four pin joints. The four links are the frame (fixed), crank (driver), coupler, and follower (output).

Coupler

Follower Crank

Frame

Frame

2. A slider-crank mechanism consists of the crank link (input), connecting link (rod), slider (output), and the frame. Connecting rod

Crank Slider

Frame

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Frame

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Kinematic Inversion: When different links are chosen as the frame for a given kinematic chain, the relative motions between the various links are not altered, but their absolute motions (those measured with respect to the frame link) may be changed drastically. The process of choosing different links of a chain for the frame is known as kinematic inversion.

(c)

Four inversions of the four-bar mechanism: (a, b) crank-rocker mechanisms; (c) draglink mechanism; (d) double-rocker mechanism.

Consider the kiematic inversion of the four-bar mechanism as shown above where the longest link has length l, the shortest link has length s, and the other two links have lengths p and q. If the shortest link s is adjacent to the fixed link, as shown in (a) and (b), we obtain what is called a crank-rocker linkage. The drag-link mechanism (c) is obtained by fixing the shortest link s as the frame. By fixing the link opposite to s we obtain the double-rocker mechanism (d).

Dr. Saif A. Al-Kaabi

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MOBILITY: One of the first concerns in either the design or the analysis of a mechanism is the number of degrees of freedom, also called the mobility of the device. The mobility of a mechanism is the number of input parameters that must be controlled independently in order to bring the device into a particular position. It is possible to determine the mobility of a mechanism directly from a count of the number of links and the number and types of joints that it includes. To develop this relation, consider that before they are connected together, each link of a planar mechanism has 3 degrees of freedom when moving relative to the fixed link. Not counting the fixed link, therefore, an n-link planar mechanism has 3(n – 1) degrees of freedom before any of the joints are connected. Connecting a joint that has one degrees of freedom, such as a revolute joint, has the effect of providing two constraints between the connected links. If a twodegree-of-freedom joint is connected, it provides one constraint. When the constraints for all joints are subtracted from the total freedoms of the unconnected links, we find the resulting mobility of the connected mechanism. Therefore the mobility m of a planar mechanism is given by

m = 3(n – 1) – 2 j1 – j2

where m : the mobility n : number of links (including the frame) j1 : number of single-degree-of-freedom joints j2 : number of two-degree-of-freedom joints.

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Examples:

(e)

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(f)

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Cam joint

(g)

(h)

GRASHOF’S LAW (CRITERION): A very important consideration when designing a mechanism to be driven by a motor is to ensure that the input crank can make a complete revolution. Mechanisms in which no link makes a complete revolution would not be useful in such applications. For the four-bar linkage, there is a very simple test of whether this is the case: Grashof’s law states that for a planar four-bar linkage, the sum of the shortest and longest link lengths cannot be greater than the sum of the remaining two link lengths if there is to be continuous rotation between two members (links). Grashof’s law states that one of the links, in particular the shortest link, will rotate continuously relative to the other three links if and only if

s+l≤ p+q where s : length of the shortest link l : length of the longest link p and q : lengths of the remaining two links.

Dr. Saif A. Al-Kaabi

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Type of mechanism

Grashof -Crank-rocker -Drag link -Double rocker -Crossover-position Change point Non-Grashof Double rocker of The second kind (triple rocker)

Shortest link

Any Driver crank Fixed link Coupler Any

Any

Relationships between link lengths

s+l ≤ p+q s+l...