Kinematics PDF

KINEMATICS - continuation of statics and dynamics - shifts from studying general concepts with illustrative examples to developing methods and performing analyses of real designs (IMPORTANT: it entails dealing with complex objects and utilizing different t...

KINEMATICS - continuation of statics and dynamics - shifts from studying general concepts with illustrative examples to developing methods and performing analyses of real designs (IMPORTANT: it entails dealing with complex objects and utilizing different tools to analyze these objects) KINEMATICS DYNAMICS Objective Develop analysis of the various means behaviour of a The design process starts with meeting the functional of given machine requirements: transforming or mechanism motion to when subjected - Opening achieve a to dynamic - Dwelling specific kind forces - Closing needed in Of the valve as a function of time… applications To achieve: Role ensure the verify the functionality of acceptability of  Cam profile producing the needed follower the mechanism induced forces motion should be found. in parts - rocker arm, being a lever, serves as a displacement amplifier/reducer - timing of opening, dwelling, and BRANCHES OF THE THEORY OF MACHINES: closing is controlled by the speed of the camshaft 1. Kinematics - function of the spring is to keep the - focuses on the geometry of motion roller always in contact with the cam (movement of parts in a machine without considering the forces that To meet this requirement the inertial forces developed cause the motion) during the follower– valve system motion should be 2. Dynamics known, since the spring force must be larger than these - concerned with the forces and torques forces at any time that cause motion and their effects on the machine parts KINEMATICAL ANALYSIS - satisfy the functional  Kinetics - deals with the inertia forces requirements for valve displacements which arise from the combined effect DYNAMIC ANALYSIS - find forces in the system as a of the mass and motion of machine function of time (these forces are needed to continue parts (BODY IN MOTION) the design process)  Statics - deals with forces and their effects while machine parts are at rest. The design process continues with meeting the Mass of parts are assumed negligible. constraints requirements, which in this case are: (BODY IN STATIONARY) - Sizes of all parts KINEMATICS - Sealing between the valve and its seat - Deals with relative motion of different parts - Lubrication of a mechanism without taking into - Selection of materials consideration the forces producing the - Manufacturing and maintenance motions - Safety - To know displacement, velocity, and - Assembly acceleration of a part of a mechanism Kinematic and dynamic analysis is an integral part of DYNAMICS the machine design process, which means it uses input - Calculation of forces impressed upon from this process and produces output for its different parts continuation - Force: static or dynamic Machine KINEMATICS TERMINOLOGIES: - applied to a complete product Kinematics - deals with the way things - devices used to alter, transmit, and direct move. forces to accomplish a specific objective - it is the study of the - a mechanism/combination of mechanism geometry of motion - transmits and modifies the available Kinematic - determination of: mechanical energy into some kind of desired Analysis  position work  displacement Ex: Car, Tractor, Combine, Earthmoving  rotation machine, Chain saw  speed  velocity Mechanism  acceleration of a mechanism - devices performing specific functions out of machine Linkage - a mechanism where rigid parts are connected together - mechanical portion of a machine that has the function of transferring motion and forces to form a chain from a power source to an output Frame - serves as the frame of - heart of a machine reference for the motion of - transmits and modifies a motion all other parts. - number of bodies assembled that the motion - the frame is typically a part of one causes constrained and predictable that exhibits no motion motion to others Links - a member/combination of - fundamental unit members of a mechanism, - the study of this involves ANALYSIS as well as connecting other members SYNTHESIS and having motion relative to them. Analysis – study of motion and forces concerning - also known as Kinematic link different parts of existing mechanism or element Types of Link: Synthesis – design of its different parts Simple Link - contains only two joints Ex: Windshield wiper which connect it to other links Complex Link - contains more than Structure two joints - assemblage of a number of resistant bodies Rigid Link - does not undergo (members) having no relative motion between significant deformation during them and meant for carrying loads having transmission of motion. straining action Flexible link - partly deformed during transmission of motion Fluid link - the medium for motion transmission is fluid through pressure or compression only Binary Link Ternary link Quaternary link Machine/Mechanism – must have moving parts (transforms motion, produces work, or transforms energy) Structure – does not have moving parts (its function is purely structural, i.e., to maintain its form and shape under given external loads) CLASSIFICATION OF KINEMATIC PAIRS: B. HIGHER ORDER/HALF JOINTS 1. Cam Joint 1. According to the type of relative motion - a mechanical connection where a between the elements cam's shape guides a follower's a. Sliding Pair – 2 elements of a pair are movement, converting rotational connected in such a way that one can motion into linear motion or only slide relative to the other controlling movement timing in b. Turning Pair – 2 elements of a pair are mechanical systems connected in such a way that only one 2. Gear Joint can turn/revolve about a fixed axis of - Allows rotation and sliding between another link two gears as their teeth mesh c. Spherical Pair - 2 elements of a pair are connected in such a way that one Crank - a simple link that is able to complete a full element (with spherical shape) rotation about a fixed center turns/swivels about the other fixed element Rocker- is a simple link that oscillates through an angle, d. Rolling Pair- 2 elements of a pair are reversing its direction at certain intervals connected in such a way that one rolls Rocker arm- is a complex link, containing three joints, over another fixed link that is pivoted near its center e. Screw Pair – 2 elements of a pair are connected in such a way that one Bell crank- is a mechanical lever that redirects force or element can turn about the other by motion by 90 degrees using a pivoting L-shaped or T- screw threads shaped arm 2. According to the type of contact between the Actuator- is the component that drives the mechanism elements a. Lower Pair – 2 elements of a pair have Common Actuators: a surface contact when relative motion 1. Motors (electric and hydraulic) takes place and the surface of one 2. Engines element slides over the surface of the 3. Cylinders (hydraulic and pneumatic) other 4. Ball-screw motors b. Higher Pair – 2 elements of a pair have 5. Solenoids a line/point contact when elative 6. Manually operated machines utilize motion takes place and the motion human motion, such as turning a crank, as between the two elements is partly the actuator. turning and partly sliding 3. According to the type of closure Types of Constrained Motion: a. Self-Closed Pair – 2 elements of a pair are connected together mechanically 1. Completely constrained motion - motion in such a way that only required kind between a pair is limited to a definite direction of relative motion occurs 2. Incompletely constrained motion - motion b. Force-Closed Pair – 2 elements of a between a pair can take place in more than one pair are not connected mechanically direction but are kept in contact by the action of 3. Successfully constrained motion - motion is not external forces completed by the links itself but by some other means JOINTS - movable connections between links and allows relative motion between the links Point of Interest Types of Joint: - specific location on a link or component within a mechanical system where the motion, forces, A. PRIMARY/FULL JOINTS or other dynamic characteristics are 1. Revolute (Pin/Hing) particularly significant or require detailed - allows pure rotation between the two analysis links that it connects - This point is selected due to its role in the 2. Sliding (Piston/Prismatic) overall function or performance of the - allows linear sliding between the links mechanism that it connects Once kinematic analysis is performed, the displacement, velocity, and accelerations of that point are determined. Kinematics Diagram MOBILITY - “stripped-down” sketches of mechanisms - capability of a mechanism to move in certain - drawn to a scale proportional to the actual ways mechanism - measure of how many independent movements are possible - number of degrees of freedom of a mechanism and it is given the symbol M DEGREE OF FREEDOM (DOF) - quantifies the number of independent motions or movements a component or mechanism can have SPECIAL CONDITIONS:  Coincident Joints - when three links come together at a common pin, the joint must be modeled as two pins  Exceptions to the Gruebler’s Equation  Idle degrees of freedom (redundant) - a link can be moved without producing any movement in the remaining links of the mechanism Locked Mechanism  - Linkages with zero, or negative, degrees of 1. Binary Joint – 2 links are joined at the same freedom connection - unable to move and form a structure Truss - a structure composed of simple links and connected with pin joints and zero degrees of freedom 2. Ternary Joint – 3 links are joined at the same connection (equivalent to 2 binary joints) Kinematic Chain - interconnected system of links in which not a 3. Quaternary Joint – 4 links are joined at the single link is fixed same connection (equivalent to 3 binary joints) - n becomes a mechanism when one of the links in the chain is fixed fixed link - called a frame or, sometimes, a base link TYPES OF MECHANISM: COMMONLY USED LINK & JOINTS: 1. Planar Mechanism - all movements and interactions occur within a single two- dimensional plane 2. Parallel Mechanism - multiple links or arms operate in parallel configurations to achieve precise motion and force distribution 3. Spatial Mechanism - operates in three- dimensional space, allowing for complex motion in all directions 4. Spherical Mechanism - designed to move with rotational degrees of freedom constrained to a spherical surface 5. Cylindrical Mechanism - motion is constrained to a cylindrical surface or involves components with cylindrical movement 6. Flexure Mechanism - uses flexible components to achieve motion or force transmission, often eliminating the need for traditional joints 7. Compliant Mechanism - uses the flexibility of materials to achieve movement and force transfer, relying on deformation rather than traditional joints. 8. Cam Mechanism - a rotating cam drives a Four-bar Mechanism follower to produce specific, often complex, - simplest and most common linkage motion profiles - combination of four links, one being 9. Gear Mechanism - uses gears to transmit designated as the frame and motion and torque between rotating shafts connected by four pin joints with varying speed and direction - because the four-bar mechanism has 10. Ratchet Mechanism - allows movement in one one degree of freedom, it is direction while preventing movement in the constrained or fully operated with one opposite direction, often used for locking or driver incremental movement TYPES OF JOINTS IN A CHAIN  Parallelogram Mechanism Quick-return Mechanism Scotch Yoke Mechanism VECTOR SCALAR Definition A quantity with A quantity with both magnitude only 1 magnitude and direction Examples  Velocity  Mass (kg) (m/s)  Time (s)  Force (N)  Distance (m)  Displacement  Energy (J) (m) Application  Plowing  Determining Force and the Speed of Direction Rotating  Sprayer Shaft Boom  Angular Velocity Displacement  Conveyor  Power Belt Output Acceleration  Mass of Slider-crank Mechanism - consists of a combination of in Grain Moving Parts four links, with one being designated as the frame Elevators Special Purpose Mechanism: Straight-Line TYPES OF VECTORS (basis on orientation) Mechanisms 1. Parallel Vectors - vectors having a similar direction 2. Equal vectors - Two parallel vectors are said to be equal vectors, if they have same magnitude 3. Anti-parallel vectors - if they are in opposite directions  4. Negative vectors - Two anti-parallel vectors Limiting Positions – the configuration of a are said to be negative vectors, if they have mechanism that places one of the follower same magnitude links in an extreme position 5. Collinear Vectors - Two vectors are said to be collinear vectors, if they act along a same line 6. Co-initial Vectors - Two or more vectors are said to be co-initial vectors, if they have common initial point 7. Co-terminus Vectors - Two or more vectors are said to be co terminus vectors, if they have common terminal point 8. Coplanar Vectors- Three or more vectors are said to be coplanar vectors, if they lie in the same plane 9. Non-coplanar Vectors- Three or more vectors are said to be non-coplanar vectors, if they are distributed in space TYPES OF VECTORS (basis on effect) 1. Polar Vectors- Vectors having straight line effect (Displacement, Velocity, Acceleration , Force) 2. Axial Vectors - Vectors having rotational effect (Angular momentum, Angular velocity, Angular acceleration, Torque) SCALAR PROPERTIES: 1. Operations: Addition, subtraction, multiplication, and division Position – A point on a mechanism is the spatial location of that point Displacement – end product of motion  Linear Displacement – straight line distance between an original position of a point on a mechanism and some later position  Angular Displacement – angular distance between two positions of a rotating link Position Analysis:  Graphical Analysis  Analytical Analysis