GEOMETRIC CONSTRUCTION. C H A P T E R F O U R. OBJECTIVES. 1. Identify the geometry that makes up basic 2D drawings. 2. Use board drafting or 2D CAD skills to create technical figures. 3. Describe the advantages of CAD contrasted with drawing with manual instruments.
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C H A P T E R F O U R
1. Identify the geometry that makes up basic 2D drawings.
2. Use board drafting or 2D CAD skills to create technical figures.
3. Describe the advantages of CAD contrasted with drawing with manual instruments
Triangle and T-Square System
From endpoints A and B, draw construction lines at 30°, 45°, or 60° with the given line. Then, through their intersection, C, draw a line perpendicular to the given line to locate the center D…
Inclined lines can be drawn at standard angles with the 45° triangle and the 30° x 60° triangle. The triangles are transparent so that you can see the lines of the drawing through them. A useful combination of triangles is the 30° x 60° triangle with a long side of 10" and a 45° triangle with each side 8" long.
With only a 30° x 60° triangle and a 45° triangle, you can draw
any angle in 15° increments
of the triangle in
each case is resting
on the blade of the
T-square. Twenty-four 15° sectors are possible with just these two triangles used singly or in combination.
For measuring or setting off angles other than those obtainable with triangles, use a protractor.
Plastic protractors are satisfactory for most angular measurements
Nickel silver protractors are available when high accuracy
BISECTING AN ANGLE
TRANSFERRING AN ANGLE
When the Point Is Not on the Line
When the Point Is on the Line
DRAWING A TRIANGLE WITH SIDES GIVEN
DRAWING A RIGHT TRIANGLE WITH
HYPOTENUSE AND ONE SIDE GIVEN
Many angles can be laid out directly with the triangle or protractor.
You can use the AutoCAD Polygon
command to draw squares. The Rectangle command is another quick way to make a square in AutoCAD.
Each side of a hexagon is equal to the radius of the circumscribed circle
Use a compass
Given an inscribed circle, or distance “across flats”, use a T-square or straightedge and a 45° triangle to draw the eight sides tangent to the circle.
Given a circumscribed square, (the distance “across flats”) draw the diagonals of the square. Then, use the corners of the square as centers and half the diagonal as the radius to draw arcs cutting the sides
This method uses the principle that any right triangle inscribed in a circle cuts off a semicircle.
Another method, slightly longer, is to reverse the procedure. Draw two nonparallel chords and draw perpendicular bisectors. The intersection of the bisectors will be the center of the circle.
AutoCAD software provides a convenient object snap for finding tangency.
For small radii, such as 1/8R for fillets and rounds, it is not practicable to draw complete tangency constructions. Instead, draw a 45° bisector of the angle and locate the center of the arc by trial along this line
Connecting Two Parallel Lines
Connecting Two Nonparallel Lines
The conic sections are curves produced by planes intersecting a right circular cone.
Four types of curves are produced: the circle, ellipse, parabola, and hyperbola, according to the position of the planes.
If a circle is viewed with the line of sight perpendicular to the plane
of the circle…
…the circle will appear as a circle, in true size and shape
The intersection of like-numbered lines will be points on the ellipse. Locate points in the remaining three quadrants in a similar manner. Sketch the ellipse lightly through the points, then darken the final ellipse with the aid of an irregular curve.
These ellipse guides are usually designated by the ellipse angle, the angle at which a circle is viewed to appear as an ellipse.
The curves are largely successive segments of geometric curves, such as the ellipse, parabola, hyperbola, and involute.
For many purposes, particularly where a small ellipse is required, use the approximate circular arc method.
The curve of intersection between a right circular cone and a plane parallel to one of its elements is a parabola.
A helix is generated by a point moving around and along the surface of a cylinder or cone with a uniform angular velocity about the axis, and with a uniform linear velocity about the axis, and with a uniform velocity in the direction of the axis
An involute is the path of a point on a string as the string unwinds from a line, polygon, or circle.
A cycloid is generated by a point P on the circumference of a circle that rolls along a straight line
Like cycloids, these curves are used to form the outlines of certain gear teeth and are therefore
of practical importance in machine design.