Page 66 - Engineering drawing from first principles using AutoCAD

Geometrical applications 59

U GROUP means that the program has just removed the last line, but the expression will
change according to your last drawing operation, and that may be a circle, erasure, break,
etc. Just experiment by drawing some random lines, arcs, breaks and erasures on the
screen and then cycle through the UNDO feature and clean them, one by one off the
screen, noting the 'U' references.

REDO operates in the reverse order, so experiment again to understand the sequence.
1. Figure 2.28 shows two lines L1 and L2 drawn at random and an arc which crosses both at
any two points A and B. I wish to break the arc and trim the two parts back to the lines Ll
and L2.
2. Choose the BREAI( command and click on the arc at any two points between A and B. A
gap appears and there are two short lines to trim back to L1 and L2.
3. Choose the Trim command in the Modify menu. Click the two lines you want to
remain, namely L1 and the arc above line Ll. Press <Enter> then click on the small line
you wish to delete. Repeat for the other side.
4. Alternatively, choose the TRIM command and click on lines Ll and L2. Press <Enter> and
click once on the arc between the two lines which is then deleted cleanly.
5. Now assume that a third line L4 is inserted between Ll and L2 and you wish arc L3 to be
extended from above to meet it.
6. Choose Extend in the Modify menu. Click on L4 and the required arc L3 above. Press
<Enter> and then click on the arc L3 which will then be extended as required.

Loci and mechanisms
A locus is a curve traced out by a point, line or surface moving according to a mathe-
matically defined condition. Figure 2.29 shows a simple case where a link connected to a
rotating wheel at end X is designed to slide through a swivel fitting at point P. The
engineer requires to know the path traced out by point Y at the end of the link. The
reason for this interest may be that a protective safety guard is needed to cover the
machinery, or that this is the first part of a mechanical system of levers and all aspects of
the movement must be known.

Set out the diagram to the dimensions shown and divide the circle into 12 equal parts.
The length of the link is 270mm. Draw a line from the 8 o'clock position through
point P and mark the position of point Y. I find that it is easiest just to draw a circle of
270mm radius and use the BREAI( command to delete the unwanted part of the
circumference. The radii will be set to repeat the procedure. Marking the intersection
with a small 'donut' of inside diameter 0.5mm and outside diameter 1.0mm is
sufficient. Repeat the procedure for the other points from 3 to 9 o'clock. Since the
required curve will be symmetrical, the plotted points can be positioned on the other
side of the centre line using the MIRROR command. Draw a polyline through the
intersection points and modify this polyline with the EDIT POLYLINE option in the
Modify menu to give a curve. Study the curve. Clearly, the most accurate curve will be
plotted using more points. I have added just one between 4 and 5 o'clock. Experiment
and note the results. It is also possible that one half of the curve will be better than the
other. If this is the case, just delete the worst half and MIRROR the best to obtain two
symmetrical parts.

Archimedian spiral

An Archimedian spiral is the locus of a point which moves around a centre at uniform
angular velocity and at the same time moves towards or away from the centre. A typical
example can be found in amusement arcade pin ball machines. In Fig. 2.30 a ball is