Geometric Construction

Unit C BY: K. L. TATRO CENTRAL HIGH SCHOOL EAST

Points and Lines

  A Point represents a location in space or in a drawing and has no width, height, or depth.

A Line is defined as “that which has length without breadth.” A straight line is the shortest distance between two points.

Lines Horizontal Perp Lines Points Indefinite Definite

Angles

 An angle is formed by two intersecting lines.

3 6 0 ° 1 8 0 ° 9 0 ° Less t han 9 0 ° STRAIGHT ANGLE RIGHT ANGLE ACUTE ANGLE COMPLETE CIRCLE More t han 9 0 ° OBTUSE ANGLE 9 0 ° A° B° COMPLEMENTARY ANGLES A° 1 8 0 ° B° SUPPLEMENTARY ANGLES

Regular Polygons

   MORE THAN THREE SIDE CONSTRUCTED AROUND A CIRCLE POLYGON MAY BE INSCRIBED (POINTS TOUCH) OR CIRCUMSCRIBED (FLATS TOUCH) ALL SIDES ARE EQUAL IN LENGTH AND IN ANGLE INSCRIBED PENTAGON SQUARE HEXAGON OCTAGON TRIANGLE CIRCUMSCRIBED

Polygons …

   ANGLES IN REGULAR POLYGONS ARE FOUND BY DIVIDING A CIRCLE (360 0 ) BY THE NUMBER OF SIDE Except a triangle, then we use 180 0 E.g. Hexagon has 6 sides. 360/6=60. Therefore we use a 60 0 triangle to complete a hexagon Circumscribed Inscribed

Creating a Perpendicular Bisecting Line..

    Bisect = 2 equal parts Perpendicular = 90 o to its counterpart From each end of the given line, draw an arc that is greater than half Connect the two intersections from each of the created arcs R4 .3 9 4 5 R4 .3 9 4 5

Using a ruler to divide…

Dividing 6 equal spaces 1 2 3 4 5 6 7 ANY ANGLE ANY ANGLE CONNECT OF LINE WITH LAST MARK. TRANSFER MARKS AT SAME ANGLE

Dividing a given space..

    Dividing horizontal space Place ruler so that it touches each end at a number that you can divide.

Put dots on those points Draw vertical lines through those dots 1 2 3 4 5 6 7 8 9 10 11 12

Dividing a given space vertically

    Dividing vertical space Place ruler so that it touches the top and bottom line at a number that you can divide.

Put dots on those points Draw horizontal lines through those dots

Tangent Lines

 A line that touches a circle or arc in a point of tangency. Is this tangent?

Creating a tangent arcs and circles Draw a line the distance of the radius away from the given line (the line we want to be tangent to) then create a circle using the radius line to mark the center of the circle radius

Creating a circle or arc to two given lines

Draw a line the distance of the radius away from each given line. Where the two lines cross, that is where you will place the middle of the circle. R R

Creating a circle or arc to a line and an arc.

R R •Create a line tangent to the given straight.

•Mark the radius away from the edge of the circle you want to be tangent to.

•Draw an arc from the given circle’s mid-point that represents a distance of the radius away from the edge •Draw the circle using the point of crossing as the mid point

Handout: Arcs tangent to a circle and a line.

DRAWING A 2" EXCLUSIVE ARC TANGENT TO A CIRCLE AND A LINE (REMEMBER, IF DIAMETER IS GIVEN, YOU NEED TO CONVERT TO RADIUS) TO DRAW AN EXCLUSIVE ARC THAT IS TANGENT TO AN ARC AND A LINE, START BY MEASURING OUT THE DISTANCE NEEDED (ARC RADIUS) FROM THE OBJECT THAT YOU ARE GOING TO BE TANGENT TO. MAKE SURE THAT YOUR RULER POINTS TO THE CENTER. FROM THE CENTER POINT OF THE CIRCLE, DRAW AN ARC THE DISTANCE FROM THE CENTER TO THE POINT THAT WAS MADE AT THE RADIUS DISTANCE.

2.000

4 3 2 1 0 NOW MEASURE THE RADIUS DISTANCE AWAY FROM THE LINE THAT YOU ARE TRYING TO BE TANGENT TO. THEN DRAW A PARALLEL LINE AT THAT DISTANCE AWAY. DRAW IT SO THAT IT IS BETWEEN THE CIRCLE AND THE EXSISTING LINE. LIGHT CONSTRUCTION ARC FROM THE POINT IN WHICH THE CONSTRUCTION ARC AND THE CONSTRUCTION LINE CROSS, PLACE YOUR COMPASS NEEDLE THERE, SET AT THE RADIUS, AND DRAW THE REQUIRED ARC (OR CIRCLE). 4 3 2 1 0

Handout: Exclusive Arcs…..

DRAWING A 2" EXCLUSIVE ARC TANGENT TO TWO CIRCLES (REMEMBER, IF DIAMETER IS GIVEN, YOU NEED TO CONVERT TO RADIUS) TO DRAW AN EXCLUSIVE ARC THAT IS TANGENT TO TWO CIRCLES, START BY MEASURING OUT THE DISTANCE NEEDED (ARC RADIUS) FROM THE OBJECT THAT YOU ARE GOING TO BE TANGENT TO. MAKE SURE THAT YOUR RULER POINTS TO THE CENTER. FROM THE CENTER POINT OF THE CIRCLE, DRAW AN ARC THE DISTANCE FROM THE CENTER TO THE POINT THAT WAS MADE AT THE RADIUS DISTANCE.

REPEAT THIS PROCESS FOR THE OTHER CIRCLE.

2.000

4 3 2 1 0 4 3 2 1 2.000

0 LIGHT CONSTRUCTION ARC FROM THE POINT IN WHICH THE CONSTRUCTION ARCS CROSS, PLACE YOUR COMPASS NEEDLE THERE, SET AT THE RADIUS, AND DRAW THE REQUIRED ARC (OR CIRCLE).

Handout: Inclusive Arcs

DRAWING A 6" INCLUSIVE (INSIDE) ARC TANGENT TO THE TWO CIRCLES (REMEMBER, IF DIAMETER IS GIVEN, YOU NEED TO CONVERT TO RADIUS) TO DRAW AN INCLUSIVE ARC THAT IS TANGENT TO TWO CIRCLES, START BY MEASURING OUT THE DISTANCE NEEDED (ARC RADIUS) FROM THE OBJECT THAT YOU ARE GOING TO BE TANGENT TO (FROM THE . SIDE THAT THE ARC WILL BE MADE). MAKE SURE THAT YOUR RULER CROSSES THROUGH THE CENTER. REPEAT THIS FOR THE NEXT CIRCLE.

6 5 4 3 6.000

2 1 0 LIGHT CONSTRUCTION ARC FROM THE POINT IN WHICH THE CONSTRUCTION ARCS CROSS, PLACE YOUR COMPASS NEEDLE THERE, SET AT THE RADIUS, AND DRAW THE REQUIRED ARC (OR CIRCLE). 6.000

Homework

    Worksheets Exercise 3.14

Figure 4.76 (handout) Exercise 3.12

Figure 3.14

 Find center and draw the outer circle.

Figure 3.14

 Add the centerlines for the 6 circles @ 60 0 between each

Figure 3.14

 Draw in the 6 needed circles

Figure 3.14

  Mark lines at 15 0 increments Draw teeth so that each line intersects the next at 90 0 Each line is at 90 o to the next

Figure 3.14

   Finish with the hub and keyway Darken final object and leave construction lines of they are light Add border and title block

Questions?

Remember that all drawings are done in a formal sketch fashion.. That means to sketch with some aides, and that there is some built in assumption of error for accuracy, but not concepts….

Earn 15 points extra credit by completing the 6 page handout out marked Chapter 5: Geometric Construction.