Projections of Solids: Hexagonal Pyramid with Axis Inclined to Both HP and VP (Step by Step)

Learn how to draw the projections of a hexagonal pyramid resting on a corner of its base, with its axis inclined to both HP and VP, step by step on a grid sheet using a mini drafter, set square, compass and pencil. PROBLEM A hexagonal pyramid of base side 25 mm and axis length 60 mm is placed on one of the corners of its base on HP, such that the two base edges containing the resting corner make equal inclinations with HP. Draw the projections of the pyramid if the axis is inclined at 40° to HP and 30° to VP. METHOD (three-stage / change of position method) • Stage I – Axis perpendicular to HP: base on HP, with the resting corner on a line parallel to XY so that the two edges at that corner become equally inclined to HP. • Stage II – Tilt the pyramid about the resting corner so that the axis makes 40° with HP (the base line is drawn at 50° to XY). • Stage III – Turn the pyramid about a vertical line, keeping 40° to HP, so that the axis makes 30° with VP. The top view of the axis makes an apparent angle β ≈ 40.7° with XY, found with the true-length locus construction. • Redrawing the top view at β: every corner of the stage II top view is fixed by its distance along the axis from the base centre and its perpendicular distance from the axis. These are transferred onto the new axis pr with the compass (used as a divider) and the set square, then the points are joined. KEY RESULTS • Apparent angle of the axis in the top view: β ≈ 40.7° • Hidden edges in the final top view: oa, ab, af • Hidden edges in the final front view: oe, de, ef CHAPTERS 0:00 Introduction 0:09 The problem 0:32 The three-stage approach (3D animation) 1:05 Setting up the sheet and instruments 1:19 Stage I – Top view (hexagon with compass) 2:07 Stage I – Front view 2:32 Stage II – Tilting the front view (axis 40° to HP) 3:10 Stage II – Top view 3:56 Stage III – Finding the apparent angle β 4:33 Stage III – Redrawing the top view at β (divider, set square, compass) 5:33 Checking by rotation and joining the final top view 5:59 Stage III – Final front view 6:44 Result and summary INSTRUMENTS USED Mini drafter, 45° set square, compass, HB pencil, grid sheet. Useful for first-year engineering students studying Engineering Graphics / Engineering Drawing (Projections of Solids). #EngineeringGraphics #EngineeringDrawing #ProjectionsOfSolids #HexagonalPyramid #OrthographicProjection