Crank And Slotted Lever 5l4y4a
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Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
CRANK AND SLOTTED LEVER QUICK RETURN MOTION EXPERIMENT
OBJECTIVES The objective of this experiment is to investigate the kinematics motion of a Crank and Slotted Lever Quick Return mechanism. The investigation is to show that it is indeed a quick return mechanism and to evaluate the increase in efficiency that this would offer if applied to a machine tool.
THEORY Definition of a Mechanism A mechanism is a simplified model, usually in the form of a line diagram, which is used to reproduce the motion occurring in a machine. The purpose of this reproduction is to enable the nature of the machine. The purpose of this reproduction is to enable the nature of the motion to be investigated without the encumbrance of the various solid bodies which form the machine elements
The various parts of the mechanism are called links or elements. Where two links are in and a relative motion is possible, then they are known as a pair. An arbitrary set of a links which form a closed chain that is capable of relative motion, and that can be made into a rigid structure by the addition of a single link, is known as a kinematics chain. To form a mechanism from a kinematics chain one of the links must be fixed. However as any of the links can be fixed, it follows that there are as many mechanism as there are links in the chain. The technique obtaining different mechanism by fixing the various links in turn is known as inversion.
Kinematics Pairs The relative motion between two links of a pair can take different form. Three types of a pairs are known as lower pairs and these are the frequently occurring ones: Sliding
: such as occurs between a piston and a cylinder
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
Turning
: such as occurs with a wheel on an axle
Screw motion : such as occurs between a nut and a bolt All other cases are considered to be combinations of sliding and rolling are called higher pairs. Strictly screw motion is a higher pair as it combines turning and sliding.
Slider – Crank Mechanism The slider- crank mechanism is well known as the basis of a reciprocating engine. As shown in the diagram below it consists of three turning pairs and one sliding pair
2
3 4
1
In the above diagram, the link 1 is fixed. If we now fix link 2, that is consider an inversion of the mechanism, we obtain the mechanism shown below. This is known as Whiworth’s Quick Return Mechanism. 4
1
3
2
Expansion of a Revolute Pairs Consider the four bar linkage shown below:-
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
R3
3
B
R2
2
4
R1
A
R4 OB
The revolute pair R3 can be expanded so that it becomes a block, 3. When the crank 2 form a complete revolution the block, 3, only transverses a small are from E1 to E2.
E1 R3
B
R2
2
E2 R1
A
R4 OB
The motion of 3 is still described by means of an angle referred to B. The curved slider is thus still a revolute form and 3 are described by an angle and not by linear distance. The curved slider remains a revolute pair as long as its radius of curvature is finite. If the radius of a curvature of a revolute pair becomes infinite, i.e. its center of rotation is at
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
infinity. Then the revolute pair becomes prismatic pair variable change from an angular measurement to a linear distance measurement. For Bar Chains:R2
3
R3
2 4
R1 R4 OB R2
3
R3 R4
4
2
R1
OB
R2
3
R3
R4 4
2
R1
OB at ∞
Thus a prismatic pair may be considered as a revolute pair whose center is at infinity in the direction perpendicular to the generatrix.
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
Here we can see that a four bar mechanism when taken to the limit can be shown to become slider-crank mechanism. This is very useful in the synthesis of a planar mechanism as the properties of a four bar mechanism become the properties of the slidercrank mechanism.
Now consider the crank and slotted lever quick return motion.
OB at ∞
It is evident that we have a four bar chain with a prismatic pair as a limiting case of a revolute pair. Superimposed upon this is an inversion of the slider-crank chain.
θ
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
The crank radius, OB is 40 mm. The slotted lever length, AC, is 240 mm. It is a matter of a trigonometry to develop an expression for x in of the crank angle, θ, and the length of the links. On the apparatus x is 70 mm when θ is 0° and 180°.
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
APPARATUS Crank and Slotted Lever Quick Return Mechanism
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
PROCEDURES 1. Set the crank so that the pointer is at zero on the scale. Note the crosshead position, x. 2. Rotate the crank by 10° increments and for every increment, note the corresponding crosshead position, x.
RESULTS 1. Find an expression for theoretical distance (x) in term of θ. 2. Plot a graph of experimental crosshead position, x, versus crank angle. 3. Plot on the same graph, a graph of theoretical crosshead position versus crank angle. 4. On both graphs, show the return and cutting stroke. 5. Plot a graph of crosshead velocity versus crank angle. On the graph, show the return and cutting stroke.
DISCUSSION 1. How well does the experimental result agree with the predictions from the theory? 2. What rotation angle is required for the cutting and return strokes? 3. Discuss the motion of the slider and that it is indeed a quick return mechanism. 4. What is the increase in efficiency (in term of the time required for each stroke in one revolution of crank) obtainable in the mechanism?
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
RESULT SHEET Crank and Slotted Lever Quick Return Motion Experiment
Crank Angles, θ (degrees) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360
Experimental Slider position, x, (mm)
Theoretical Slider position, x, (mm)
CRANK AND SLOTTED LEVER QUICK RETURN MOTION EXPERIMENT
OBJECTIVES The objective of this experiment is to investigate the kinematics motion of a Crank and Slotted Lever Quick Return mechanism. The investigation is to show that it is indeed a quick return mechanism and to evaluate the increase in efficiency that this would offer if applied to a machine tool.
THEORY Definition of a Mechanism A mechanism is a simplified model, usually in the form of a line diagram, which is used to reproduce the motion occurring in a machine. The purpose of this reproduction is to enable the nature of the machine. The purpose of this reproduction is to enable the nature of the motion to be investigated without the encumbrance of the various solid bodies which form the machine elements
The various parts of the mechanism are called links or elements. Where two links are in and a relative motion is possible, then they are known as a pair. An arbitrary set of a links which form a closed chain that is capable of relative motion, and that can be made into a rigid structure by the addition of a single link, is known as a kinematics chain. To form a mechanism from a kinematics chain one of the links must be fixed. However as any of the links can be fixed, it follows that there are as many mechanism as there are links in the chain. The technique obtaining different mechanism by fixing the various links in turn is known as inversion.
Kinematics Pairs The relative motion between two links of a pair can take different form. Three types of a pairs are known as lower pairs and these are the frequently occurring ones: Sliding
: such as occurs between a piston and a cylinder
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
Turning
: such as occurs with a wheel on an axle
Screw motion : such as occurs between a nut and a bolt All other cases are considered to be combinations of sliding and rolling are called higher pairs. Strictly screw motion is a higher pair as it combines turning and sliding.
Slider – Crank Mechanism The slider- crank mechanism is well known as the basis of a reciprocating engine. As shown in the diagram below it consists of three turning pairs and one sliding pair
2
3 4
1
In the above diagram, the link 1 is fixed. If we now fix link 2, that is consider an inversion of the mechanism, we obtain the mechanism shown below. This is known as Whiworth’s Quick Return Mechanism. 4
1
3
2
Expansion of a Revolute Pairs Consider the four bar linkage shown below:-
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
R3
3
B
R2
2
4
R1
A
R4 OB
The revolute pair R3 can be expanded so that it becomes a block, 3. When the crank 2 form a complete revolution the block, 3, only transverses a small are from E1 to E2.
E1 R3
B
R2
2
E2 R1
A
R4 OB
The motion of 3 is still described by means of an angle referred to B. The curved slider is thus still a revolute form and 3 are described by an angle and not by linear distance. The curved slider remains a revolute pair as long as its radius of curvature is finite. If the radius of a curvature of a revolute pair becomes infinite, i.e. its center of rotation is at
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
infinity. Then the revolute pair becomes prismatic pair variable change from an angular measurement to a linear distance measurement. For Bar Chains:R2
3
R3
2 4
R1 R4 OB R2
3
R3 R4
4
2
R1
OB
R2
3
R3
R4 4
2
R1
OB at ∞
Thus a prismatic pair may be considered as a revolute pair whose center is at infinity in the direction perpendicular to the generatrix.
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
Here we can see that a four bar mechanism when taken to the limit can be shown to become slider-crank mechanism. This is very useful in the synthesis of a planar mechanism as the properties of a four bar mechanism become the properties of the slidercrank mechanism.
Now consider the crank and slotted lever quick return motion.
OB at ∞
It is evident that we have a four bar chain with a prismatic pair as a limiting case of a revolute pair. Superimposed upon this is an inversion of the slider-crank chain.
θ
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
The crank radius, OB is 40 mm. The slotted lever length, AC, is 240 mm. It is a matter of a trigonometry to develop an expression for x in of the crank angle, θ, and the length of the links. On the apparatus x is 70 mm when θ is 0° and 180°.
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
APPARATUS Crank and Slotted Lever Quick Return Mechanism
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
PROCEDURES 1. Set the crank so that the pointer is at zero on the scale. Note the crosshead position, x. 2. Rotate the crank by 10° increments and for every increment, note the corresponding crosshead position, x.
RESULTS 1. Find an expression for theoretical distance (x) in term of θ. 2. Plot a graph of experimental crosshead position, x, versus crank angle. 3. Plot on the same graph, a graph of theoretical crosshead position versus crank angle. 4. On both graphs, show the return and cutting stroke. 5. Plot a graph of crosshead velocity versus crank angle. On the graph, show the return and cutting stroke.
DISCUSSION 1. How well does the experimental result agree with the predictions from the theory? 2. What rotation angle is required for the cutting and return strokes? 3. Discuss the motion of the slider and that it is indeed a quick return mechanism. 4. What is the increase in efficiency (in term of the time required for each stroke in one revolution of crank) obtainable in the mechanism?
Universiti Tenaga Nasional, 2006 Mechanical Design and CAD Laboratory
RESULT SHEET Crank and Slotted Lever Quick Return Motion Experiment
Crank Angles, θ (degrees) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360
Experimental Slider position, x, (mm)
Theoretical Slider position, x, (mm)
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