Crank and slider - this is lab report PDF

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CRANK AND SLIDER MECHANISM

Title

Objective To obtain the displacement, velocity and acceleration diagram for the motion of a crank and connecting rod assembly. Problem statement In this lab we will investigate the kinematics of some simple mechanisms used to convert rotary motion into oscillating linear motion and vice-versa. This bench top unit demonstrates the conversion of smooth rotary motion into reciprocating motion. The input angle is set on a ball bearing mounted crank disc and read off on an angle measuring scale integrated into the base plate. Crank radius and connecting rod length can both be adjusted, each have three positions. The simple insertion of a bolt enables the swivelling cylinder to be locked, thus a crank drive with either a fixed or oscillating cylinder can be demonstrated. Apparatus Crank and Connecting rod apparatus.

Connecting rod

Piston Crank

apparatus

Theory There are three types of planar rigid body motion. Translation: This type of motion occurs when a line in the body remains parallel to its original orientation throughout the motion. When the paths of motion for any two points on the body are parallel lines, the motion is called rectilinear translation. If the paths of motion are along curved lines which are equidistant, the motion is called curvilinear translation. Rotation about a fixed axis: When a rigid body rotates about a fixed axis, all the particles of the body, except those which lie on the axis of rotation, move along circular paths. General plane motion: When a body is subjected to general plane motion, it undergoes a combination of translation and rotation. The translation occurs within a reference plane, and the rotation occurs about an axis perpendicular to the reference plane. From theory, The piston displacement is given by, 2 2 X =r (1−cos θ ) + L ( sin θ ) / ( 2 n )

The piston velocity is given by, V =ωr [ ( sin θ+( sin 2 θ ) /2 n ) ] Where r is the crank radius, of the link to the crank radius.

L

is the length of the link,

n

is the ratio

Crank Mechanism: The slider-crank mechanism is a simple four bar mechanism in which the rocker is replaced by a slider. Thus, the four links in the slider-crank mechanism are: Crank, Coupler/Connecting Rod, Slider and the Ground link. A simple slider-crank mechanism is shown below:

The Slider-Crank mechanism can be used whenever there is a need of converting rotational motion to translational motion. The common applications of slider-crank mechanism are the internal combustion engines, Bull Gear, loco-motive etc. Crank and connecting rod: The Crank and Connecting rod are the fundamental components of any internal combustion engine, the piston moves up and down in the cylinder while the connecting rod converts this translation to rotation of the crank.

Procedure      

Take the apparatus of crank slider mechanism. Set the apparatus to its mean position. Note that deflection is at zero degree and set the reference point for the displacement. The crank is rotated by 20  increment and recorded the value of displacement. Note carefully the value of displacement at different deflections. Repeat the experiment at least two times to get the mean reading of displacement.

 The reading for every 5 degrees of the crank rotation was recorded.  The readings were recorded in the table provided. Crank Movement Crank Movement Crank Movement Crank Movement θ θ θ θ (inch) (inch) (inch) (inch) 0 10 20 30 40 50 60 70 80 90

0 0.16 0.23 0.58 0.84 1.11 1.46 1.72 2.08 2.46

100 110 120 130 140 150 160 170 180 190

2.85 3.25 3.68 4.11 4.48 4.65 4.83 4.98 5 5

Experimental Data & Observation

200 210 220 230 240 250 260 270 280 290

4.95 4.85 4.68 4.52 4.21 3.78 3.43 2.98 2.55 2.22

300 310 320 330 340 350 360

1.96 1.52 1.12 0.65 0.42 0.12 0

Displacement Graphs Excel Graphs

Displacement -Graph 6

Displacement

5 4 3 2 1 0

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Software Graph Displacement-graph

Displacement

Displacement Graph Analysis The displacement in this graph is like a linear. As the displacement graph has zero value and start but with further movement of crank it changes. But at the top of the displacement graph it shows that the crank is its maximum point. Its look like piston movement. From this graph we easily understand all concept of piston motion.one point in this graph is that we in a minute look

to our whole system progress. So, this graph explain about in what proportional rotary motion is converted to reciprocating motion. Description about the displacement as the crank rotates. The type of displacement when the crank rotates is reciprocating motion, also called reciprocation. It is a repetitive up-and-down or back-and-forth linear motion. It is found in a wide range of mechanisms, including reciprocating engines and pumps. The two opposite motions that comprise a single reciprocation cycle are called strokes. A crank can be used to convert circular motion into reciprocating motion, or conversely turn reciprocating motion into circular motion. For example, inside an internal combustion engine (a type of reciprocating engine), the expansion of burning fuel in the cylinders periodically pushes the piston down, which, through the connecting rod, turns the crankshaft. The continuing rotation of the crankshaft drives the piston back up, ready for the next cycle. The piston moves in a reciprocating motion, which is converted into circular motion of the crankshaft, which ultimately propels the vehicle or does other useful work. The vibrations felt when the engine is running are a side effect of the reciprocating motion of the pistons as the crank and connecting-rod usually are not enclosed. Reciprocating motion is close to, but different from sinusoidal simple harmonic motion. The point on the camshaft which connects the connecting rod rotates smoothly at a constant velocity in a circle. Thus, the horizontal displacement of that point is indeed exactly sinusoidal. However, during the cycle, the angle of the connecting rod changes continuously. So, the horizontal displacement of the "far" end of the connecting rod differs from sinusoidal

Velocity Graphs Excel Graph

Velocity-Graph Software

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Velocity

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V

-0.03 -0.04 -0.05 Angle

Graph Velocity Graph Analysis In this graph its clearly analyse that velocity increase at some extent but after some angular displacement the velocity increases and maximum at largest value of displacement but in the next with just some displacement it is going to decrease and become zero.it means that when there is change in displacement occur then there velocity is produced.in the graph you see that there is much lower difference in between the angular displacement and angular velocity. The reason behind this so simple that velocity is produced in the direction of displacement. So, due to this the graph of

velocity is much like the displacement.

Acceleration Graphs Excel Graph

Acceleration-Graph 0.03

Acceleration

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Acceleration-graph

Acceleration

Acceleration Graph Analysis It is clearly informed that when there is change in velocity then acceleration is form. As you know the acceleration is the time rate of change of velocity. In this graph, we see that when velocity change and it decreases then there produce a negative acceleration that is called as retardation or deceleration. This graph shows at different point in what way acceleration changes. At the start velocity is zero and acceleration is also zero but with the interval of some angle velocity changes so, acceleration also changes.one more important thing is that this graph is between angle and acceleration which mean acceleration is produced due to change in angular velocity.

Comparison between EXCEL and Software graphs

The graphs which we draw with the help of excel actually in between angle and displacement, velocity and angle and acceleration and angle but software draw graphs between time and displacement, velocity and acceleration. So, there may be some difference on these both graph that clearly shows in the above graphs.one more thing is that in software graphs are plotted with the help of a ideal mechanism. Therefore, there result would be valuable and more accurate than that of experimental value that we get from the experimental observation. The piston was under simple harmonic motion since it was under the oscillating motion. It has a maximum displacement due to the increasing and decreasing of the piston velocity and acceleration of the mechanism itself. The higher the value of the ratio would give a better shape and form of simple harmonic motion of the plotted graph. The maximum displacement occurs at the steepest slope among the plotted graph in. Based on it, it is quite hard to find by just looking at the graphs. So, finding the best steepest slope of the plotted graphs will assume. It is found that the maximum displacement is about 5inch and it occurred at an angle about 190° to 200°.

Reasons why the maximum acceleration is important. When the velocity of an object changes, it is said to be acceleration. Acceleration is the rate of change of velocity with time. The acceleration is often used to describe a state of increasing speed. Acceleration in Physics is much more than just increasing speed. Any change in the velocity of an object results in acceleration, increasing speed what people usually mean when they say acceleration, decreasing speed also called deceleration or retardation, or changing direction. A change in the direction of motion results in an acceleration even if the moving object neither speed up nor slowed down. That's because acceleration depends on the change in velocity and velocity is a vector quantity, one with both magnitude and direction. Acceleration occurs anytime an object's speed increases or decreases, or it changes direction. The maximum acceleration is where the objects accelerate to a higher speed with time.

Discussion

Explain how a crank and slider system works. This mechanism is composed of three important parts. The crank which is the rotating disc, the slider which slides inside the tube and the connecting rod which joins the parts together. As the slider moves to the right the connecting rod pushes the wheel round for the first 180 degrees of wheel rotation. When the slider begins to move back into the tube, the connecting rod pulls the wheel round to complete the rotation As the slider moves to the right the connecting rod pushes the wheel round for the first 180 degrees of wheel rotation. When the slider begins to move back into the tube, another mechanism that has a very wide usage in machine design is the slider-crank mechanism. It is mainly used to convert rotary motion to a reciprocating motion or vice versa. The slider-crank mechanism is shown and the parameters that are used to define the angles and the link lengths are given. As in the four-bar mechanism, the extended and folded dead centre positions are when the crank and the coupler are collinear (coupler link is commonly called connecting rod in slider-crank mechanisms). Full rotation of the crank is possible if the eccentricity, c, is less than the difference between the connecting rod and the crank lengths and the crank length is less than the connecting rod length. Connecting rod pulls the wheel round to complete the rotation. A crank is an arm attached at right angles to a rotating shaft by which reciprocating motion is imparted to or received from the shaft. It is used to convert circular motion into reciprocating motion, or vice versa. The arm may be a bent portion of the shaft, or a separate arm or disk attached to it. Attached to the end of the crank by a pivot is a rod, usually called a connecting rod. The end of the rod attached to the crank moves in a circular motion, while the other end is usually constrained to move in a linear sliding motion. In this case a person's arm or leg serves as the connecting rod, applying reciprocating force to the crank. There is usually a bar perpendicular to the other end of the arm, often with a freely rotatable handle or pedal attached.

Comment or suggest any cause of errors Instrument resolution (random) All instruments have finite precision that limits the ability to resolve small measurement differences. One of the best ways to obtain more precise

measurements is to use a null difference method instead of measuring a quantity directly. Null or balance methods involve using instrumentation to measure the difference between two similar quantities, one of which is known very accurately and is adjustable. The adjustable reference quantity is varied until the difference is reduced to zero. The two quantities are then balanced, and the magnitude of the unknown quantity can be found by comparison with the reference sample. With this method, problems of source instability are eliminated, and the measuring instrument can be very sensitive and does not even need a scale Failure to calibrate (systematic) Whenever possible, the calibration of an instrument should be checked before taking data. If a calibration standard is not available, the accuracy of the instrument should be checked by comparing with another instrument that is at least as precise, or by consulting the technical data provided by the manufacturer. Parallax (systematic or random) This error can occur whenever there is some distance between the measuring scale and the indicator that used to obtain a measurement. If the observer's eye is not squarely aligned with the pointer and scale, the reading may be too high or low.

Practical applications of a crank and slider mechanism.       

Reciprocating engine Rotary engine Winch Hand Pump Piston motion equations Sun and planet gear Nothing grinder

Conclusion In conclusion, the result obtained by this experiment shows that the pattern of the angular velocity is constant. Through this experiment, the characteristic of the mechanism is learnt as if the mechanism is meant to be used in the complex and complicated motions applications such as foot pump and engine. The graph of results plotted helps the calculations of the

maximum displacement, velocity and acceleration. From the result obtained, the experimental errors are minor errors in the range of 0.5mm to 1.5mm. This concludes that the error might be parallax error during the reading. For the improvement for better and accurate result, the reading must be taken more than one time until a fixed reading is obtained.

Reference   

http://journals.sagepub.com https://prezi.com/ursk_fgyvcut/dynamics-planar-rigid-body-motion/ http://www.academia.edu...