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New York City College of Technology EMT 1220L- Fundamentals of Digital System Lab

Lab Report Experiment #1: Slider Crank Mechanism Author: Cristhian Urgiles Partner: Rabia Arif Semester: Fall 2017 Date: September 11, 17 Professor: John Razukas

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Table of Contents Objective of the Experiment ………………………………………….........3 Schematic Diagrams ……………………………………………………….4 Digital Photos ………………………………………………………...........5 Data……………………………………………………….........................6-8 Graphs........................................................................................................9-11 Questions & Answers ………………………………………………...........12 Conclusion ………………………………………………………................13 Internet Research…………………………………………………..........14-27 Signed Data Sheet.........................................................................................28

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Objective of the Experiment The objective of the experiment was to construct a Slider Crank Mechanism to transform Uniform Rotational Motion of the Crank into Linear Reciprocating Motion of the Slider. We will then prove that the Slider Stroke is equal to two times the crank length by measurement. We then plot the Crank Angle vs. Slider Displacement and analyze the graph to determine the slider will have Maximum and Minimum Linear Velocities and Accelerations.

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Schematic Diagram

Coupler

Crank

Slider

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Digital Photos

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DATA Cr ankAng l eVs .Sl i de rDi s pl ac e me nt Cr a n kAn g l e ( De g r e e s ) 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 1 8 0

Sl i d e rDi s p l a c e me n t ( I n c h e s ) 0 1 / 3 2 2 / 3 2 5 / 3 2 1 0 / 32 1 6/ 3 2 2 0 / 32 3 0 / 32 15 / 3 2 19 / 3 2 11 6/ 3 2 12 5/ 3 2 2 24 / 3 2 26 / 3 2 29 / 3 2 21 2/ 3 2 21 3/ 3 2 21 4/ 3 2

Cr a n kAn g l e ( De g r e e s ) 1 9 0 2 0 0 2 1 0 2 2 0 2 3 0 2 4 0 2 5 0 2 6 0 2 7 0 2 8 0 2 9 0 3 0 0 3 1 0 3 2 0 3 3 0 3 4 0 3 5 0 3 6 0

Sl i d e rDi s p l a c e me n t ( I nc h e s ) 21 3/ 3 2 21 2/ 3 2 21 0/ 3 2 28 / 3 2 24 / 32 2 12 8 / 3 2 12 1 / 3 2 11 4/ 3 2 15 / 3 2 1 2 4 / 32 18 / 3 2 1 2 / 32 8 / 3 2 4 / 3 2 1 / 3 2 0

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Cr ankAngl eVs .Ve l o c i t y Crank Angle (Degrees) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Velocity 0 0.173648178 0.342020143 0.500000000 0.642787610 0.766044443 0.866025404 0.939692621 0.984807753 1.000000000 0.984807753 0.939692621 0.866025404 0.766044443 0.642787610 0.500000000 0.342020143 0.173648178 0

Crank Angle (Degrees) 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360

Velocity -0.173648178 -0.342020143 -0.5 -0.642787610 -0.766044443 -0.866025404 -0.939692621 -0.984807753 -1.000000000 -0.984807753 -0.939692621 -0.866025404 -0.766044443 -0.642787610 -0.5 -0.342020143 -0.173648178 0

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Cr ankAngl eVs .Ve l o c i t y Crank Angle (Degrees) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Acceleration 1 0.984807753 0.939692621 0.866025404 0.766044443 0.64278761 0.5 0.342020143 0.173648178 6.12574E-17 -0.173648178 -0.342020143 -0.5 -0.64278761 -0.766044443 -0.866025404 -0.939692621 -0.984807753 -1

Crank Angle (Degrees) 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360

Acceleration -0.984807753 -0.939692621 -0.866025404 -0.766044443 -0.64278761 -0.5 -0.342020143 -0.173648178 -1.83772E-16 0.173648178 0.342020143 0.5 0.64278761 0.766044443 0.866025404 0.939692621 0.984807753 1

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Crank Angle Vs. Slider Displacement

Slider Displacement (inches)

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Slider Displacemen

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0 0

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Crank Angle (Time in Degrees) Graphs

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Crank Angle Vs. Slider Velocity Slider Velocity (meters per second)

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Velocity

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Crank Angle (Time in Degrees)

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Slider Acceleartion (meters per second squared)

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Crank Angle Vs. Slider Acceleration 1.5

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0.5

Acceleration

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Crank Angle (Time in Degrees)

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Questions & Answers 1. Draw the data box of link lengths versus stroke. What conclusion can be made about Stroke? The stroke is 2 times the crank length. Link Lengths (inches) Vs. Stroke (inches) Crank Coupler Stroke 1 1.25 4.25 2.5 2 1.5 4.5 2.5 2. From you observations, if the length of the Slider Stroke and the total length of the Crank plus Coupler are known, explain how the length of the Crank and the length of the Coupler can be calculated. We subtract the length of the crank from the length of the coupler and then add the crank thus calculating the length of the coupler. L, (coupler Length) R, (Crank Length) L=(R+L)-(Stroke/2) L+R= the length of both coupler and crank. The stroke is 2 times the crank ∴ the crank is equal to the stroke divide by two. 3. The resulting graph from the experiment will look similar to the following example. From Math, what type of curve or family of curves does this resemble? What is the equation? The graph is a Cosine curve. The equation is y=1 −cos x 4. If in the experiment the crank were to be turned by a motor moving at a constant speed (also known as angular velocity) measured in revolutions per minute (RPM), then the graph can be described from Physics as a Displacement versus Time curve. The slope of a Displacement versus Time curve at any point is equal to Acceleration. By studying the graph, determine in terms of Physics where (degrees of crank rotation) the Slider will have Maximum Linear Velocity and where the Slider will have Maximum Acceleration. Sketch the Velocity and Acceleration Curves. Maximum Linear Velocity: Occurs at 90 degrees. Maximum Acceleration: Occurs at 360 degrees. Velocity an Acceleration curves are found on the Graphs section of the lab report (see table of contents). 12

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Conclusion In conclusion we know a slider crank mechanism transforms rotational motion into linear reciprocating motion. We also proved that the slider stroke is equal two times the crank length using our data to compare with the computations using the formula. Furthermore, the total distance covered by the slider between the two extreme positions is the path length.

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Internet Research Linear Displacement Displacement is the change in position of an object. Mathematically displacement is defined as the difference between the value of the final position and the value of the initial position ( △ x=x f −x 0 ). Since displacement is a vector, it has direction and magnitude. In the example below the professor moved from left to right. An arrow pointing to the right represents the +2.0m displacement of the professor relative to Earth. September 2017. Khan Academy URL:

https://www.khanacademy.org/science/physics/one-dimensional motion/displacement-velocity-time/a/what-is-displacement

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Angular Displacement Angular displacement is displacement covered in terms of an angle. It is the distance that an object moves in a rounded path. The length of the arc of curved path represents it. Angles are measured in radians; therefore the unit of angular displacement is radians. For example in the picture below the angular displacement is theta ( θ ). September 2017 Tutorvista URL: http://physics.tutorvista.com/motion/linear-velocity.html

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Linear Velocity Linear Velocity is the velocity of the object travelling in a straight line. A body moves with linear velocity when its direction is not changing. Linear velocity depends on the distance an object travels with respect to x time. Thus the linear formula is v = t , where v is the linear velocity, x is

the distanced covered and t is time. Linear velocity is given in units of meters per second. September 2017 Tutorvista URL: http://physics.tutorvista.com/motion/linear-velocity.html

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Angular Velocity Angular velocity is the velocity of object traveling in curved path. It is defined as ratio of the angle traversed to the amount of time it takes to θ traverse that angle. Mathematically angular velocity is defined as ω= t ,

where ω is the angular velocity, θ is the angle the object traversed and t is the time in which the object is transverse. Angular velocity can also be defined as the rate of change of angular displacement with respect to time. Angular velocity is given in units of radians per second. `

September 2017 Tutorvista URL: http://physics.tutorvista.com/motion/linear-velocity.html

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Linear Acceleration Linear Acceleration is the acceleration by a moving body with uniform acceleration in a straight line. There are three equations for linear acceleration. Those are as follow: v =u+at , where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken. This equation is used to find the velocity of a body within a given time. The

second equation is

1 2 s=ut + a t , where s is the distance traveled by an 2

object, u is the initial velocity of the object, a is the acceleration and t is the time taken. The last equation is v 2=u 2+ 2as , where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance traveled.

September 2017 Tutorvista URL: http://www.tutorvista.com/physics/linear-accelerationequation

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Angular Acceleration Angular acceleration is the rate of change of angular velocity. Angular acceleration of a rotating body is the same as that of any particle of the body. △w Mathematically angular acceleration is defined as a= , where a is the △t

angular acceleration, w is the change in angular velocity and t is the change in time. September 2017 Tutorvista URL: http://www.softschools.com/formulas/physics/angular_acceleration_formula /153/

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Slider Crank Mechanism Slider Crank Mechanism is designed to convert uniform rotational motion of the crank into linear reciprocating motion of the slider or viceversa. It is composed of a crank, a coupler and a slider. In the picture below, part A, crankshaft, is connected to part B, crankpin, which is then connected to a rod, part 3. Part 3 extend to part C. The three bearings shown as circles at A, B, and C allow the connected members to rotate freely with respect to one another. September 2017 Britannica URL: https://www.britannica.com/technology/slider-crank-mechanism

Toggle Linkage 20

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Toggle linkage is an assemblage of at least two links, pitmans, bars, or struts and at least three pivots, an end of one link being connected to an end of the other link by a pivot that is common to both links. Each of the links also has a pivot at the end remote from the common pivot, which common or intermediate pivot is movable from a first position at which the common pivot is not in line with the other two pivots to a second position at which the common pivot is substantially in line with the other two pivots, or which common pivot is movable from said second position to said first position. September 2017 Definedterm URL: https://definedterm.com/toggle_linkage

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Linkage “Dead Points” Linkage “Dead Points” is when a side link such as AB in the figure below, becomes aligned with the coupler link BC. Then it can only be compressed or extended by the coupler. In this figure, a torque applied to the link on the other side, CD, cannot induce rotation in link AB. This link is referred to as a linkage “dead point”. September 2017 Yi Zhang URL:https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt5.html - HDR73

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Flywheel The flywheel is used to increase the machine's momentum. A heavy revolving wheel is used in a machine to provide greater stability. Acting as a backup to the available power during interruptions in the delivery of power to the machine. September 2017 Quizlet URL:https://quizlet.com/83453171/a2-aqa-physics-rotationaldynamics-flash-cards/

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Inverted Mechanism Inverted mechanism is the motion of the members of the mechanism by fixing different links in turn. When a different link is chose as the frame link, different characteristics of the motion are shown on the mechanism. September 2017 Slideshare URL:https://www.slideshare.net/chetanjaganure14/inversions-ofmechanisms

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Sinusoidal Wave Sinusoidal wave is a waveform that shows periodic oscillations in which the amplitude of displacement at each point is relative to the sine of the phase angle of the displacement is known as the sinusoidal wave. It may be visualized as a sine curve. Electrical machines and generators use to generate a Sinusoidal Waveform for our mains supply. September 2017 Electronic-Tutorials URL:http://www.electronics-tutorials.ws/accircuits/sinusoidalwaveform.html

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Cam Cam is defined as a machine element having a curved groove, which, by its oscillation or rotation motion, giving a specified motion to another element called the follower. The cam has an important function in the operation of many classes of machines, especially the automatic type, such as printing presses, shoe machinery, textile machinery, gear-cutting machines, and screw machines. In any class of machinery in which automatic control and accurate timing are paramount, the cam is an indispensable part of mechanism. The possible applications of cams are unlimited, and their shapes occur in great variety. September 2017 Yi Zhang URL: https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt6.html

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Four Stroke Engine A Four Stroke Engine is an internal combustion engine in which the piston finishes four different strokes while turning a crankshaft. The full travel of the piston along the cylinder, in either direction is referring to as a stroke. September 2017 Wordpress URL:https://xorl.wordpress.com/2011/03/05/the-basics-of-4-strokeinternal-combustion-engines/

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