ISOMETRIC PROJECTION Contents Introduction Principle of Isometric Projection Isometric Scale Construction of Isometric Scale Isometric View (Isometric Drawings) Methods to draw isometric projections/isometric views Difference between isometric projection and Isometric view Isometric views of planes Isometric views of solids Triangular prism Triangular Pyramid Examples Assignment Importance of this Chapter Isometric projection of the object helps us to visualize the three dimensions of the object in one view It helps in conveying the real shape of the object to the viewers.
INTRODUCTION The orthographic views we discussed are very valuable in providing us true heights, widths and depths of objects. However the formats of object representation previous chapter are two dimensional. Seeing objects in three dimensional will be more useful. A three-dimensional drawing of sketch shows the entire object in one view. The object is not scattered among top, front and side views. A three dimensional pictorial greatly enhances one s ability to visualize the object, especially if one does not understand orthographic projection. There is often a need to illustrate for a non technical person some object under discussion and the three dimensional format is probably the best way to present the object. PRINCIPLES OF ISOMETRIC PROJECTION NOTE When lines are drawn parallel to isometric axes, the lengths are foreshortened to 0.816 times the actual lengths. In isometric projection (isometric means equal measure ), it is necessary to place the object such that its principal edges or axes make equal angles with the plane of projection and therefore foreshortened equally. In this position the edges of a cube would be projected equally and would make equal angles with each other 120 0.
The isometric projection of solid is represented on vertical plane of projections. The solid is such that its three mutually perpendicular edges make equal inclinations with the plane of projection. When a cube is resting on one of its corner on HP, and its solid diagonal in the front view is perpendicular to VP, then the front view of the cube represents the Isometric projection of the cube. (Refer the figure). Consider a cube resting on HP, with two of its square faces making equal inclinations with the VP. o c is the solid diagonal (Refer the figure 1 & 2). Tilt the solid on one corner g and make the solid diagonal parallel to HP. Draw the corresponding top view in this position, the solid diagonal oc in the top view is parallel to VP. (Refer the figure 3 & 4). Rotate the solid diagonal oc in the top view perpendicular to VP and the project corresponding front view which represents isometric projection of cube. The lengths of their projections are equal to the lengths of the edges multiplied by 0.816, approximately (for information refer the isometric scales). Thus the projected lengths are about 80% of the true lengths. The projections of the axes OB, OD, and OG make angles of 120 0 with each other and are called the isometric axes. Any line parallel to one of these axes is called as an isometric line; a line that is not parallel to these axes is called a nonisometric line. It should be noted that the angles in the isometric projection of the cube are either 120 0 or 60 0 and that all are projections of 90 0 angles. In an isometric projection of a cube, the faces of the cube and any planes parallel to them are called isometric planes. NOTE There are three isometric planes containing any two isometric axes and planes parallel to these planes are termed Isometric planes. The planes no parallel to any of the any of the Isometric planes are termed Non-Isometric planes
Construction of Isometric scale Method 1: The isometric scales are drawn by the following two methods. Draw a horizontal line BD and another line BP at 45 0 to horizontal. From B, draw line BA inclined at 30 0 to BD. Mark divisions of true lengths on the line BP. From each division draw vertical lines to BA.
The divisions obtained on the line BA gives the isometric lengths on isometric scale. Method 2: Draw a horizontal line AB of any length. From A draw line making an angle of 15 0 with AB. From B draw line making an angle of 45 0 with AB, cutting the line 15 0 line at C. Mark divisions of true length on the line AB. From each division draw parallel lines to BC. Thus the divisions obtained on the line AC give the isometric length on isometric scale.
ISOMETRIC VIEW (ISOMETRIC DRAWING) The view drawn with the true scale is called isometric view, while the view drawn with the use of isometric scale is called Isometric projection. In isometric view of any rectangular solid resting on the ground, each horizontal face will have its sides parallel to the two sloping axes; each vertical face will have its vertical sides parallel to the vertical axis and the other sides parallel to one of the slopping axes. In other words, the vertical edges are shown by vertical lines, while the horizontal edges are represented by lines, making 30 0 with the horizontal. These lines are very conveniently drawn with the T-square and a 30 0 60 0 set square. Refer the given figure. The procedure for drawing isometric views of planes, solids and objects of various shapes is explained in stages by means of illustrative problems. In order that he construction of the view may be clearly understood, construction have not been erased. They are, however, drawn fainter than the outlines. In an isometric view, lines for the hidden edges are generally not shown. In the solutions accompanying the problems, one or two arrows have been shown. They indicate the directions from which if the drawing is viewed, the given isometric views would be obtained. NOTE Isometric projection are commonly used to prepare the pictorial view of smaller Objects and it is used in mechanical, production, automobile, aerospace Engineering to show the machine parts.
METHODS TO DRAW ISOMETRIC PROJECTIONS/ISOMETRIC VIEWS Projections or drawings which are not parallel to one of the isometric axes are called Non isometric lines. An important rule is that the measurements can be made only on the drawings of isometric lines. Conversely, measurements cannot be made on the drawings of nonisometric lines. For example, the diagonals of the face of a cube are nonisometric lines; although they are equal in length, their isometric drawings will not be equal of length. There are two basic methods for drawing the isometric projections/views. (1) Boxing method (2) Offset (or) Co-ordinate method Boxing method When an object contains many nonisometric lines, it is drawn by the boxing method or the offset method. When the boxing method is used, the object is enclosed in a rectangular box, which is drawn around it in orthographic projection. The box is then drawn in isometric and the object located in it by its points of contact as in the given figure. It should be noted that the isometric views of lines that are parallel on the object are parallel. This knowledge can often be used to save a large amount of construction, as well as to test for accuracy might be drawn by putting the top face into isometric and drawing vertical lines equal in length to the edges downward from each other. It is not always necessary to enclose the whole object in a rectangular crate. The pyramid would have its base enclosed in a rectangle and the apex located by erecting a vertical axis from the centre.
Offset (or) Co-ordinate method When an object is made up of planes at different angles, it is better to locate the ends of the edges by the offset method rather than by boxing. When the offset method is used, perpendiculars are extended from each point to an isometric reference plane. These perpendiculars, which are isometric lines, are located on the drawing by isometric coordinates, the dimensions being taken from the orthographic views. In the given figure line AB is used as a base; first to locate points on the base; then verticals from these points e, f and g. NOTE This method can be used for any object, however it may be complicated. DIFFERENCE BETWEEN ISOMETRIC PROJECTION AND ISOMETRIC VIEW S. No Isometric Projection Isometric View 1 Isometric dimensions are considered. Isometric Length = 0.816 x True length True dimensions are considered 2 Volume is less Volume is more. (22.5% enlarged) Consider the following isometric projection and isometric view of a cube kept in vertical position to make the difference between them.
ISOMETRIC VIEWS OF PLANES The construction of isometric views of standard planes ( triangle, square, rectangle, quadrilateral, circle, semi- circle, arcs, hexagonal, fillets) is explained below. Triangle Consider the triangle as shown in the given fig. To draw the isometric view of triangle coinciding with the right isometric plane from the point a draw a vertical line ap Then from a draw the line ab = AB.
(isometric view ) making an angle 30 to horizontal line. Then complete the triangle abc with the help of these two lines (ap, ab). Similarly to draw the isometric view of triangle coinciding with the left isometric plane from the point b draw a vertical line bq. Then from b draw the line ba = BA making an angle 30 to horizontal line (150 anticlockwise direction). Then complete the triangle abc with the help of these two lines (bq,ba). To draw the isometric view of triangle coinciding with the top isometric plane from the point a draw a line ab with an angle of 30 to horizontal line. Then from a draw the line ap = AP ( isometric view ) making an angle 30 to horizontal line (150 anticlockwise direction). Then complete the triangle abc with the help of these two lines (ap, ab). Square Consider the square as shown in the given fig. Draw the orthographic view of the square with side of units. To draw the isometric view of square coinciding with the right isometric plane from the point d draw a vertical line ad. Then from d draw the line dc = DC (isometric view ) making an angle 30 to horizontal line. Then complete the rhombus abcd with the help of these two lines (ad, dc). Similarly to draw the isometric view of square coinciding with the left isometric plane from the point c draw a vertical line cb. Then from c draw the line cd = CD making an angle 30 to horizontal line (150 anticlockwise direction ). Then complete the rhombus abcd with the help of these two lines (cb, cd).
To draw the isometric view of square coinciding with the top isometric plane from the point d draw a line dc with an angle of 30 0 to horizontal line. Then from d draw the line ad = AD (isometric view) making an angle 30 0 to horizontal line (150 0 anticlockwise direction). Then complete the square abcd with the help of these two lines (ad, dc). Rectangle: Consider the rectangle an show in the given fig. Draw the orthographic view of the rectangle. To draw the isometric view of rectangle coinciding with the right isometric plane from the point a draw a vertical line ad. Then from a draw the line ab =AB (isometric view) making an angle 30 0 to horizontal line then complete the rhombus abcd with the help of these two lines (da, dc). Similarly to draw the isometric view of rectangles coinciding with the left isometric plane from the point c draw a vertical line cb. Then from c draw the line cd = CD making an angle 30 0 to horizontal line (150 0 anticlockwise direction). Then complete then rhombus abcd with the help of these two lines (cb, cd). To draw the isometric view of rectangle coinciding with the top isometric plane from point a draw a line ab with an angle of 30 0 to horizontal line. Then from a draw the line ad =AD (isometric view) making an angle 30 0 to horizontal line (150 0 anticlockwise direction) then complete the rectangle abcd with the help of these two line (cb, cd). Quadrilateral: Consider the quadrilateral as shown in the given fig
Refer the given fig. to draw the isometric views of quadrilateral inn three planes. Pentagon Consider the pentagon as shown in the fig 16.16. Refer the fig.16.16. to draw the isometric views of pentagon in all three planes. Circle A Circle on any isometric plane will be an ellipse, it will be shown as the isometric projection of the true curve and it is by using the following two methods. i. Method of points ii. Four-centre method Assuming a circular lamina of dia d units which is to H.P. (i) Method of points
Draw the circle with 0 as centre. Enclose the circle in a square box 1 2 3 4 in the orthographic view. Give notations fort the point of intersection of circle with the square edges as A,B,C,D Draw diagonals of square 13, 24 cutting the circle at E,F,G,H. Now join HE and get 5, 6 if extended on to the square similarly get 7, 8 by joining and 1 2 3 4 in isometric on this mark a, b, c, d which are the midpoints of the square. To get the point E in isometric first mark 6 on the edge 23 such that distance of 26 in orthographic view is equal to 26 In isometric Now draw 56 parallel to 12. On this mark points e and h such that 6e = 6E and 5h =5H Follow the same to get f, g. Join the points a, b, c, d, e, f, g, h, in sequence by free hand is the required isometric view of the circle. Follow the same procedure to draw the isometric view of the circle on isometric left and isometric top planes. NOTE The isometric projection of a circle is always an ellipse. (ii) Four center method The procedure to draw the isometric view of a circle by four-center method are as follows;
Draw the square 1234 in isometric, which is a rhombus. mark points a,b,c,d on the mid points of the square edges. Joint 2 with c, d. Similarly join 4 with a & b. Now with 2 as center 2c as radius draw an arc cd. Similarly with 4 as center 4a as radius draw an arc ab. Now with 0 1, intersection of 4a and 2d, as center 0 1 a, as radius draw the arc ad. Also with 0 2, intersection of 4b and 2c, as center 0 2 c as radius draw the arc bc. Thus completing the circle in isometric. Follow the same procedure to draw isometric left and top planes. the isometric circle coinciding with the Note For easy and quick construction of the ellipse it is preferable to adopt the four centre method. Semi - circle Consider semi-circle with dia of d units which is parallel to H.P. This isometric view of semi-circle is drawn by the following two methods. (i) Method of points (i) Method of points (ii) Four-center method Refer the fig. to draw the isometric view of Side and top plane. right side, left
(ii) four-center method Refer the fig to draw the isometric view of right side, left side and top plane. Arcs Consider an arc which is parallel to H.P. As shown in the fig.
The following steps are used to draw the isometric view of an arc. Refer the fig.to draw the orthographic view of an arc ac and draw the box abcd. Then draw the isometric view of arc coinciding with right isometric plane from the point A draw a vertical line AD. Then from A draw the line AB=ab making an angle of 30 0 to horizontal line. Then draw an arc with B as centre and AB as radius. Similarly, draw the isometric view of arc in left and top planes. Fillets Consider a fillet with radius of r which is parallel to H.P as shown in the fig. Refer the fig to draw the isometric right, left, top view of fillets. ISOMETRIC VIEWS OF SOLIDS Triangular prism Draw the isometric view of triangular prism of 30mm side and 50mm long when it rests on its base on ground with a side of the base parallel to XY line. Step 1 : Step 2 : Draw the orthographic views of given prism ( i. e. plan and elevation). Redraw the plan in isometric axes and draw verticals. Step 3 : complete the rectangular box and mark the triangular face on the Left face of the box and plan of the top. Step 4 : Join all the corners of triangle prism to get the isometric view as
Shown in the fig. 16.7.2 Triangular pyramid Draw the isometric view of triangle pyramid of side 30mm and 50mm height. It rests with one of its base edges parallel to V.P and the axis perpendicular to H.P. Step 1: Draw the orthographic views of the triangle pyramid. Step 2 : Enclose the plan in a rectangle and number the corners as 1,2,3,4,5. Step 3 : Redraw the rectangle 1, 2, 3,4, 5 those formed an isometric axes. Step 4 : Set out the corners 1,5,3 on the plan. Fix the center and draw a vertical line. mark the height of the pyramid and fix 0 as apex of the axis. Step 5 : Join all the corners of the base to the apex and complete final isometric view as shown in the fig.
EXERCISES: 1. Draw the isometric view of the block, two views of which are shown in the figure. 2. Draw the isometric view of the block, three views of which are shown in the figure.
3. Draw the isometric view of the block, three views of which are shown in the figure. 4. Draw the isometric view of the block, three views of which are shown in the figure.
5. Draw the isometric view of the block, three views of which are shown in the figure. 6. Draw the isometric view of the block, three views of which are shown in the figure.
7. Draw the isometric view of the block, two views of which are shown in the figure. 8. Draw the isometric view of the block, three views of which are shown in the figure.
9. Draw the isometric view of a square-headed bolt 30mm diameter and 90mm long, with a square neck 20mm thick and ahead, 40mm square and 20mm thick. 10. The front view of a stool having a square top and four legs is shown in the figure, draw its isometric view.
11. Draw the isometric view of the following objects, orthographic views of which are shown in the following figure.