Descriptive Geometry: course of lectures
Course lectures is generated according to the requirements of Federal State Standard for Higher Education for Bachelor’s Degree students.Established on meeting of Mechanical Engineering and Technological Equipment Department (Minute №3 at the 07th of October, 2014) for students taught the program 131000.62 – Oil and Gas Engineering.
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17 b) Figure 2.8. Traces of line AB: a) in space; b) on the projection planes When the vertical projection A2B2 of line is prolonged until it intersects OX, the point of intersection M2 is the vertical projection of the required point M from which the horizontal pro-jection M1 may be determined by means of the ordinate. The point M whose distance from H is a minimum is that which the line AB in space pierces plane H, and is termed the horizontal trace of that line. When the projection A1B1 of line is prolonged until it intersects OX, the point of intersection N1 is the horizontal projection of the required point N from which the vertical projection N2 may be determined by means of the ordinate. The point N whose distance from V is a minimum is that which the line AB in space pierces plane V, and is termed the vertical trace of that line. 2.4. True length of line definition There are no projections of general line define its true length because gives projections are shorter then itself (Figure 2.9a). In this case that line (AB) is the hypothenuse of the right-angled triangles ABB1, hence is greater then the bases AB1 or this equivalent, the projection A1B1. Thus, another base of the triangular is the difference between height of points A and B (ΔZAB=ZA – ZB) that may be defined on the vertical projection A2B2. If this section is drawn on the horizontal projection at the right angle to the A1B1 the hypothenuse of that triangle may be found as a line A1B*. This line is the true length of AB and the angle between A1B* and A1B1 is the true angle of line intersection with H plane (Figure 2.9b). The similar way of draw the true length of CD on the vertical projection (Figure 2.9c). But in this case the difference between depth of points C and D should be drawn on the vertical projection of CD. This difference may be found on the horizontal projection of the line as it shown on the...
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