Loci - Paper 2 Flashcards
What is a locus?
A locus is the path traced by a point as it moves according to defined conditions.
What is the plural of helix?
Helices
What is a helix?
A helix is the locus generated by a point that moves at uniform velocity around the outside surface of a cylinder while at the same time advancing at uniform velocity, either up or down the surface of the cylinder, in the direction of the axis.
What is always constant in a helix?
The ratio between the rotational motion and the linear motion is always constant.
List 2 ways a helix can be described.
Left handed or right handed.
When is a helix referred to as right handed?
When a cylinder is viewed axially, and the point moves away from the observer in a clockwise direction.
When is a helix referred to as left handed?
When a cylinder is viewed axially, and the point moves away from the observer in an anti-clockwise direction.
What is the first step of the method for constructing a helix?
- Draw the front view and the auxiliary view of the cylinder.
What is the second step of the method for constructing a helix?
- Divide the circumference of the auxiliary view of the cylinder into 12 equal sized (30°) segments.
What is the third step of the method for constructing a helix?
- Number the segments. Make the segment that contains the starting point 0.
What is the fourth step of the method for constructing a helix?
- Project the divisions from the circumference of the auxiliary view of the cylinder onto the front view.
What is the fifth step of the method for constructing a helix?
- Divide the front view into the required number of pitches.
What is the sixth step of the method for constructing a helix?
- Divide each pitch of the cylinder into 12 equal segments.
What is the seventh step of the method for constructing a helix?
- The divisions create a grid. Number the segments.
What is the eighth step of the method for constructing a helix?
- Locate the starting position of the point in the front view and determine the direction in which it moves.
What is the ninth step of the method for constructing a helix?
- Trace the locus of the point by neatly linking up the corresponding numbered points on the grid.
What is the auger?
The auger consists of two parallel helices of different diameters wrapped around a central shaft.
What is another name for an auger?
The helicoid.
What type of pitch does a square thread have?
It has a large pitch.
What is a square thread used for?
It is used as a transmission thread.
Where do you find a square thread?
On the lead screw of a metal working lathe and jacks for lifting objects.
Describe the similarity in construction between a square thread and a square sectioned spring?
The square thread is similar in construction to the square sectioned spring except the thread is drawn around a core.
Is the thread on a square thread left or right handed?
It can be either left or right handed.
Where does the square spring get its name?
It gets its name from the cross-section of the spring which is square.
How do you construct a square spring?
By drawing four helices that wind around a common invisible core.
Where does the round spring get its name from?
It gets its name from the cross section of the spring being round.
How do you construct a round spring?
By drawing a series of circles and helices tangential to the circles.
What is the chute?
A chute is similar in construction to a single start thread but without a central core and with the top open.
What is a cam?
A cam is a mechanical device used in many industrial applications to convert rotational motion into reciprocating motion.
What does a cam system consist of?
It consists of a shaft, which is connected to a motor that rotates at a uniform speed. An irregular shaped disk is attached to the shaft and called a cam.
How does a cam work?
As the cam rotates, its outer edge, referred to as the cam profile, imparts movement to a follower, which rests on the profile.
What causes the rise and fall of the follower?
The rise and fall or reciprocating movement of the follower is caused by the irregular shape of the profile of the cam.
What is a displacement graph?
A graph on which the movement of the follower is plotted.
What does a displacement graph show?
It’s a line or a curve showing the stroke or displacement of a follower as ordinates or heights, drawn off the base line on a graph.
What does the baseline of a displacement graph represent?
It represents one full revolution or 360° of the cam.
What does the baseline of a displacement graph indicate?
It indicates the time or the angular displacement of the follower through one revolution of the cam.
What does the vertical axis of the displacement graph indicate?
It indicates the vertical displacement, or the rise and fall of the follower.
What must be done before the cam profile can be constructed?
Since the motion of the cam follower is of primary importance, the exact positions of the follower must be plotted on a displacement graph before the cam profile can be constructed.
How must the horizontal axis of the displacement graph be drawn?
The horizontal axis of the graph must be drawn to the predetermined scale, which is then divided into a number of equally spaced segments.
What does each segment on the horizontal axis of the displacement graph represent?
Each segment represents a set number of degrees of rotation of the cam.
How must the completed displacement graph be labeled?
It must be labeled as DISPLACEMENT GRAPH and must include the horizontal scale.
What is the dwell angle?
The dwell angle or rest period is when there is no linear movement of the follower and is indicated on the profile as an arc.
List the 3 types of movement used when drawing a displacement graph.
Uniform motion
Simple harmonic motion
Uniform acceleration and retardation
What is another name for uniform motion?
Constant velocity or straight line motion.
What is uniform motion?
This motion is used at slow speeds because of the abrupt changes in motion at the beginning and the end of the motion period.
What is uniform motion used for?
It is typically used for the feed control of machine tools.
How is uniform motion indicated on a displacement graph?
It is indicated as straight lines.
What construction method do you use to create the uniform motion section of a displacement graph?
Equal increments of lift or fall are set against equal increments of angular displacement. The slope of the line must be constant over the angle of displacement.
How should simple harmonic motion be indicated on a displacement graph?
When plotted on a displacement graph the curve appears as a sine curve.
What is step one of the construction method you use to create the simple harmonic movement section of a displacement graph?
- Draw a semi-circle on the end of the displacement graph with a diameter equal to the linear movement of the follower.
What is step two of the construction method you use to create the simple harmonic movement section of a displacement graph?
- Divide the semi-circle into a convenient number of equal parts and divide the angle through which the cam rotates during this motion into the same number of divisions.
What is step three of the construction method you use to create the simple harmonic movement section of a displacement graph?
- Form a grid by dropping verticals through the angular divisions and horizontal lines through the divisions of the semi-circle.
What is step four of the construction method you use to create the simple harmonic movement section of a displacement graph?
- Draw the graph line through the points of intersection.
What type of curve is formed by uniform acceleration and retardation motion?
The curve that is formed is parabolic in form.
What is step one of the construction method you use to create the uniform acceleration and retardation motion displacement graph?
- The angular displacement of the cam and the lift of the follower are divided into an equal number of divisions.
What is step two of the construction method you use to create the uniform acceleration and retardation motion displacement graph?
- For half of these divisions the follower is accelerated and during the second half the follower is retarded.
What is step three of the construction method you use to create the uniform acceleration and retardation motion displacement graph?
- Once the points have been determined then either a French curve or a flexi curve is used to draw in the curve.
How do the acceleration and the retardation segments of the curve compare with each other?
The acceleration and the retardation segments of the curve are uniform.
List 3 types of cam followers.
The knife-edged or wedge-end follower.
The roller-ended follower.
The flat-ended follower.
When do you use a wedge-ended follower?
It is used for low speed, low force applications and is effective in situations that require abrupt changes in the cam profile.
What is problematic about the wedge-ended follower?
A problem with the wedge-ended follower is that it wears rapidly due to the pressure and friction exerted on a small surface area.
What is the advantage of a flat follower over a wedge-ended follower?
The flat follower wears better than the wedge-ended follower but the surface area is greater resulting in the creation of more friction.
Which positions does the displacement graph show for the wedge-ended follower versus the roller-ended follower?
It shows the positions of the bottom of a wedge-ended follower, but the centre of a roller-ended follower.
What is the consequence of this difference of position that is being recorded on a displacement graph for wedge and roller ended followers?
As a result, the profile of a roller-ended follower cam will be the radius of the roller smaller than that of a wedge-ended follower cam.
When do you place the camshaft on a drawing?
Af the follower has been drawn.
Which measurement is crucial when drawing a cam and follower?
The distance between the cam profile and the centre of the camshaft.
Study the photo on this answer card carefully to see the difference between the roller-ended follower and the wedge-ended follower.
Study the photo:
What is step one of drawing the cam?
- Draw the camshaft according to the given information and in the correct position.
What is step two of drawing the cam?
- Determine the rotational direction of the cam.
What is step three of drawing the cam?
- Through the centre of the camshaft, divide the cam area into divisions (degrees) used in the displacement graph.
What is step four of drawing the cam?
- Transfer the motion from the displacement graph onto the centre line of the follower.
What is step five of drawing the cam?
- using the center of the camshaft as a centre point, strike the heights of the follower position onto the corresponding generator, in the opposite direction of the rotation of the cam.
What is step six of drawing the cam?
- The profile of the cam is drawn as a smooth continuous curve through the points, using either a French curve or a flexi curve, as an aid.
List the features of a mechanism.
Connecting rod or link
Crank
Pivot
Pin-joint
Locus
What is the connecting rod or link?
A rigid joining piece of a mechanism pivoted at each end.
What is a crank?
A rotating or oscillating link.
What is a pivot?
The join between a link and a fixed point.
What is a pin joint?
The join between a link and a crank.
What is a locus?
The path traced by a point on a mechanism as it moves through its cycle.
What is a sliding link?
A sliding link is a simple mechanism that has one end of the link always in contact with the OY axis and the other end always in contact with the OX axis.
Give an example of a sliding link.
A point located on a ladder that is propped against a wall. If the lower end of the ladder slides out, but remains in contact with the ground at all times, while the upper end remains in contact with the wall, the locus of a point on the ladder will generate a slider link.
What is step one of the method to draw a graph for a sliding link?
- Divide line AB, which lies on the OY axis into any number of parts.
What is step two of the method to draw a graph for a sliding link?
- With radius AB, strike arcs from each of the divisions along the OY axis, to cut the OX axis.
What is step three of the method to draw a graph for a sliding link?
- Join the points 1, 2, 3… along the OY axis to the corresponding point 1’, 2’, 3’… on the OX axis.
What is step four of the method to draw a graph for a sliding link?
- Plotting the locus of point P - with radius BP, strike off the distances BP along each of the lines (1,1’;2,2’; 3,3’; …) from the OX axis.
What is step five of the method to draw a graph for a sliding link?
- Trace a neat locus through each point using a French curve.
What is a slider and crank mechanism?
It is a mechanism that is used to convert rotary motion to linear motion or vice versa.
How do you draw the locus of a slider and crank mechanism?
One rotation of the crank is divided into twelve 30° segments. The components of the mechanism are then drawn in the 12 positions to determine the locus of a point on a mechanism.
Only 4 positions are shown in the image.
What is this diagram?
The schematic diagram of the mechanism showing all the necessary construction to determine the locus of point P.
What is a four-bar chain?
A simple mechanism which consists of two cranks AB and CD, joined by the rod BD. The fourth link is between the two pivot points A and C.
What is a slotted link and crank?
The slotted link and crank consists of a rod attached to a crank, with the movement of the rod constrained to pass through a point.
What does a linked crank consist of?
The linked cranks consist of cranks AB and CD joined by rod BD.
What is Watts’ quick-return mechanism used for?
It is used to reduce time wasted during the recovery stroke on a machine.
Where would you find a Watts’ quick return mechanism?
An example of this machine can be found on a metalwork shaping machine.
What is the function of a safety guard?
To protect the machine operator from injury.
Where can a safety guard be found?
On any machine that has moving parts.
How is a safety guard produced?
By constructing a parallel curve equal to the required distance away from the mechanism around the outer edges of the loci.
