SPECIAL CURVES: ELLIPSE

  

HOW TO CONSTRUCT AN ELLIPSE USING THE FOCAL POINT/INTERSECTING ARC METHOD

i. Draw the major axis AB (80mm)

ii.  Bisect AB at P and mark CD equals the minor axis (50mm)

iii. With center C  and radius AP, mark F1 and F2.

iv. From F1 mark 1,2,3 and 4 at any equal spacing towards the center P.

v. With centers F1 and F2, radius A1, and B1 draw arcs to intersect at 1 in each of the four-quadrant. Repeat with points 2-4 to get points 2-4.

vi. Join all the intersecting points with a curve to give the required ellipse.

COUNT AND LEAVE 12 LINES FOR THE CONSTRUCTION.

SPECIAL CURVE

HOW TO CONSTRUCT A CYCLOID WITH A TANGENT AT A POINT ON THE CYCLOID.

i. Draw the circle and divide it into 12 equal parts.

ii. Draw horizontal lines from each point 1,2,3...12

iii. From 0 with radius 0-1 step off 12 equal division 1,2,3...12

iv. Erect perpendicular from each point 1,2,3...12 to intersect the center line of the circle at C1, C2, C3...C12

v. With center C1, C2, C3...C12 and radius OC, construct circles to intersect the corresponding horizontal.

vi. Join the points of intersection with a curve to give the required cycloid.

vii. Measure the given dimension for where the point of tangency should be and draw a circle of the same radius as the original circle.

viii. Mark point P where the circle intersects with the center line and draw a line from P to T. Draw a vertical line from point P to the baseline at M and draw a line from M passing through T and extend it upward.

ix. Construct a perpendicular at point T and draw the tangent to the cycloid.

COUNT AND LEAVE 12 LINES FOR THE CONSTRUCTION.

HOW TO CONSTRUCT AN EPICYCLOID

i. With O as the center and radius R of the larger circle draw a big arc (R60)

ii. Draw a line OA to cut the big arc at B.

iii. With B as the center and radius of the smaller circle mark point C on line OA. (R25)

iv. With C as the center and radius of the smaller circle draw the smaller circle to touch the big arc at B.

v. Divide the smaller circle into 12 equal parts 1, 2, 3...12

vi. With radius 1-2 of the smaller circle, step off 12 equal division 1, 2, ...12 on the big arc.

vii. Radiate lines from point O through points 1, 2, ...12

viii. Draw a series of arcs from points 1, 2, ...12 on the smaller circle around the big arc.

ix. Draw the center arc from C to intersect the radial lines at C1, C2, ...C12.

x. Draw a curve to join all the points of intersection to give the epicycloid.

COUNT AND LEAVE 17 LINES FOR THE CONSTRUCTION.

HOW TO CONSTRUCT AN HYPOCYCLOID

The method of construction is similar to that of cycloid only that the smaller circle rolls without slipping around the inside of a larger circle.

COUNT AND LEAVE 17 LINES FOR THE CONSTRUCTION.

HOW TO CONSTRUCT A PARABOLA, GIVEN THE SPAN AND HEIGHT

i. Divide AB, CD, half span BE, and half span ED into 6 equal parts.

ii. With center E radiate lines 1, 2 ...6.

iii. Draw vertical lines from the points on BD to intersect their corresponding radial lines to mark the curve points.

COUNT AND LEAVE 12 LINES FOR THE CONSTRUCTION.

HOW TO DRAW A HYPERBOLA  WHEN GIVEN THE ORDINATE, THE VERTEX, AND THE TRANSVERSE AXIS.

i. Indicate O and mark the ordinate each side of it OA and OB.

ii. At O draw a perpendicular to AB and mark the vertex V and the transverse axis VVL.

iii. Divide OA, OB, and the two perpendicular at A  and B into the same number of equal parts. Radiate lines. The intersection of the lines gives the points for the hyperbolic curve.

LINK MECHANISM

A simple link mechanism is an assembly of bodies (links) connected to manage forces and movement for other uses in a system. Mechanical linkages are usually designed to transform a given input force and movement into the desired output force and movement.

The simple link mechanism system consists of a fixed point, links, joints, and rods connecting to other links. The links are called cranks or levers.  The joints are referred to as fulcrums or pivots. The connecting rod is also called a coupler. The fixed point may be the ground or frame on which the cranks are mounted. Each link is connected to one or more other links by a rod with a joint.

View the links below to have an idea of a simple link mechanism.

https://technologystudent.com/cams/link1.htm

https://www.pinterest.com/pin/gearsmechanisms--7036943152858170/

https://makeagif.com/gif/4-bar-linkage-mechanism-animation-HiZfHy