DEVELOPMENT BY TRIANGULATION

TRIANGULAR  DEVELOPMENT Triangulation  is  slower  and  more  difficult  than parallel line or radial line development, but it is more practical for many types of figures. Additionally, it is the only method by which the developments of warped surfaces may  be  estimated.   In  development  by triangulation, the  piece  is  divided  into  a  series  of triangles as in radial Line development. However, there is no one single apex for the triangles. The problem becomes one of finding the true lengths of the varying oblique lines. This is usually done by drawing a true, length  diagram.

A BRIEF LOOK AT PARALLEL LINE DEVELOPMENT THE VIEW ON THE LEFT SHOWS THE DEVELOPMENT OF A TRUNCATED CYLINDER. PARALLEL LINES

A BRIEF LOOK AT RADIAL LINE DEVELOPMENT RADIAL LINES OF A CONE

Triangulation Development In this method of development the surface of the object is divided into a number of triangles. The true sizes of the triangles are found and they are drawn in order, side by side, to produce the pattern. It will be apparent that to find the true sizes of the triangles it is first necessary to find the true lengths of their sides. TRUE LENTHS REBATEMENT OR ROTATION METHOD TREE METHOD

EXAMPLE 1 REBATEMENT METHOD Before starting with the development you must find the true lengths of sides ‘oa’, ‘ob’, ‘oc’ and ‘od’. The base lines, lines ‘ab’, ‘bc’, ‘cd’ and ‘da’ are all true lengths since they are all parallel or perpendicular to the reference line HP/VP.

The rotation method is used to find the true length of line ‘oa’.

True lengths of the other lines are worked out. Notice how the drawing is becoming cluttered with lines.

To draw the development, you start by drawing one triangle first. In the example, triangle ‘oab’ is drawn first. Draw second triangle, triangle ‘obc’. Draw third triangle, triangle ‘ocd’. Draw last triangle, triangle ‘oda’. Do not forget to use the true lengths of the lines.

EXAMPLE 1 TRUE LENGTH TREE METHOD

EXAMPLE 2 ROTATION METHOD Develop the given oblique cone. Divide the oblique cone into a number of triangles. The most convenient number is twelve since you can easily divide the base into twelve divisions and join the divisions to the apex. Use the rotation method to find the true lengths of all lines. Using the true lengths of the sides, draw the triangles one at a time. Do not forge to start from the shortest side.

Method 2 TRUE LENGTH TREE METHOD

TRUNCATED OBLIQUE CONE

Transition Piece Often in industry it is necessary to connect tubes and ducts of different cross-sectional shapes and areas, especially in air conditioning, ventilation and fume extraction applications. The required change in shape and area is achieved by developing a transition piece with an inlet of a certain shape and cross-sectional area, and an outlet of a different shape and area; for example square-to-round.

EXAMPLE 1 Develop the given square to square transition piece. The rotation method is used to find the lengths of the sides.

The true length tree is used to find the true lengths of the sides.

EXAMPLE 2 Develop the given circle to rectangle transition piece. The rotation method is used to find the true lengths of the lines.

The true length tree is used to find the true lengths.

EXAMPLE 3 The true length tree is used to find the true lengths.

EXAMPLE 4 CIRCLE TO SQUARE

EXAMPLE 5 CIRCLE TO RECTANGLE