ࡱ> @B?M ;bjbj== ."WW;l 2$8 XTHHHH.HHxH 9 @~^@.Q0Y,&"HSteps in constructing the Limaon of Pascal Set the Straightedge Tool to Line tool (to draw an infinite line) Press and hold down the SHIFT button to help you to draw a horizontal line with the Tool Select and then Hide the two points used in constructing this line This prevents the line from moving from its horizontal orientation Construct 3 random points on the (infinite) line Label these points C, F and R Set Line Style to Thick Lines and set the Straightedge Tool to Segment tool Draw the segment CF Set Line Style to Dashed Lines and with the Compass tool construct a circle, centre F, radius FR Construct a point on this circle Label this point K Select the circle (To be called The Generating Circle) From the Edit Menu choose Action Button and then choose Hide/Show Press and hold down the SHIFT Button and select point K and then the circumference of the generating circle From the Edit Menu choose Action Button and then choose Animation From the Path Match dialogue box select the required speed Normally is fine and click the Animate Button Press and hold down the SHIFT Button and select points C, K and F in this order Run the crostrap.gss script. This will draw an isosceles trapezium through the points C, K and F and will also give the 4th point in this trapezium Label this 4th point in the isosceles trapezium as point D Make the line segmentS CD, KD and FK thick by setting the Line Style to Thick Lines Construct a point anywhere on the line segment KD Label this point E Press and hold down the SHIFT Button and select points C, E and D in this order Run the crostrap.gss script. This will draw an isosceles trapezium through the points C, E and D and will also give the 4th point in this trapezium Label this 4th point in the isosceles trapezium as point G Make the line segment EG thick by setting the Line Style to Thick Lines (Notice now that the trapeziums CDKF and CGED will be similar its a nice little proof to do) Set Line Style to Dashed Lines Construct, using the Compass tool in the Toolbox, a circle with centre C and radius CD Set the Straightedge Tool to Ray tool Draw a ray from C through G. This ray should extend through the circle CD Construct the point of intersection of the ray and the circle. Label this point of intersection as point H Hide both the ray and the circle Hide the line segment CG Set Line Style to Thick Lines and set the Straightedge Tool to Segment tool Draw the line segment CH Set Line Style to Dashed Lines and set the Straightedge Tool to Line tool Draw a segment between points H and D With the Selection Arrow tool, shaped like an arrow (The Translate tool), double click on the segment HD This will prepare it to become a mirror line Press and hold down the SHIFT button and select segments CH and CD and also the point C From the Transform Menu choose Reflect (This Reflection is the CRITICAL step that allows the full range of correct movement for the linkage) Label the reflection of C as the point J. Hide the line segment HD Set Line Style to Dashed Lines and set the Straightedge Tool to Line tool Draw a line extended in both directions through points J and D Construct a point anywhere on the line through J and D Label this point P Hide the full, dotted line through J and D Set Line Style to Thick Lines and set the Straightedge Tool to Segment tool Join point D to P, then join point J to P If the Generating Circle is hidden, unhide it Press and hold down the SHIFT Button and then click on, in order:- Point P, Point K and then anywhere on the circumference of the Generating Circle From the Construct Menu click on Locus (NOTICE that if the resulting locus is poorly formed then from the Display Menu choose Preferences and then click on the More Button. Then in the Number of Samples in Locus Objects: text box enter the value 500. This will improve the quality of the locus formed) Select the Locus Set Line Style to Thin Lines and set the colour to red or blue (anything NOT black!) With the Locus still selected, from the Edit Menu choose Action Button and then choose Hide/Show Select Point P and then press CTRL + T. This will put a trace on point P as it moves. Make sure that point P has the same colour as that of the locus. Hide, show or colour things as you wish Points that can be moved to alter the shape of the Limacon are P, E, C, F and R NB. If point E is slid too close towards point K then point G will slide past point H. The mechanism will still work. Therefore to make the diagram more complete put it into this position and draw a thick line segment between H out to G.    - / AHY^9:; jU6]H*,-.tUk:! \ G  d  & F;d = e  < U 2"CKu8l} & F5GH89;$a$ & F ,1h. 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