阿基米德螺旋（Archimedes helix）.doc

阿基米德螺旋（Archimedes helix） A formula curve is a curve determined by a mathematical expression. The expression of the formula can be expressed in Cartesian coordinates or polar coordinates. 8.1 Archimedes helix The standard polar coordinate equation of the Archimedes helix is P =at+P0 In style: The a - Archimedes helix coefficient, mm/ degrees, indicates the increase (or decrease) of the polar diameter at 1 degrees per revolution; T - the polar angle, the unit of degree, indicates the total degree of rotation of the Archimedes helix; P O - when the t=0 degree of the polar radius, mm. Example Fig. 8-1 is a cam with a Archimedes helix. The P1 point P2 is the first Archimedes spiral, and the P3 P4 is the second section of the Archimedes helix. 1. drawing 1) make circles C1 and C2 Click the basic curve button in the toolbar menu, click the function button, select the circle menu 1: Center immediately _ radius, tip center point, Lose 0, 0 (return), when prompted to enter the radius, lose 10 (carriage return), make R=10 circle C1, prompt the input radius, lose 12 (return), make R=12 circle C2, Press the right mouse button to close. Because the graphics size is too small, in order to see more clearly, you can zoom the displayed graphics to the screen size. Click the dynamic zoom button in the toolbar above the screen, When you press the left mouse button to push the cursor from the top of the screen, the graph will zoom in. 2) make the spiral line between point P1 and point P2 The mapping is required before the first calculate the number of lines of Archimedes spiral A and polar angle t=0 degrees when the polar radius P o. (1) calculate the Archimedes helix coefficient P2 between point P1 and point a The maximum diameter of the P1 point is 10, the maximum diameter of the P2 point is 12, the P1 to P2 points turn 90 degrees, and the maximum increase in the polar diameter is a at each turn of 1 degrees, so the Archimedes helix coefficient of the section is A= (12-10) / 90=0.0222