曲线方程（Curvilinear equation）.doc

曲线方程（Curvilinear equation） Proe curve equation (collections) Click build curve icon, select from the equation of construction, and then choose to create a curve coordinate system, and then choose to create a curve coordinate system (Descartes, cylindrical, spherical coordinates three), then the two dialog - a DOS dialog, one is not operation. Notepad dialog box. In the Notepad dialog, there is already a note indicating the format of the equation and the form of the coordinate system. Then the following equations are added to the notes, and the notepad file is saved to generate the equations. In the following equation of the curve, X=a*t, y=b*t, z=c*t (where a, B are constants or functions) are Descartes coordinate equations. R=a*t, theta=b*t, z=c*t, for cylindrical coordinate equations. Rho=a*t, theta=b*t, phi=c*t, for the spherical coordinate equations. 0. sine curve X=50*t Y=10*sin (t*360) Z=0 1. disc spring R = 5 Theta = t*3600 Z = (sin (3.5*theta-90)) +24*t 2. leaf lines A=10 X=3*a*t/ (1+ (t^3)) Y=3*a* (t^2) / (1+ (t^3)) 3. Helical curve R=t Theta=10+t* (20*360) Z=t*3 4. butterfly curves Rho = 8 * t Theta = 360 * t * 4 Phi = -360 * t * 8 5. involute R=1 Ang=360*t S=2*pi*r*t X0=s*cos (ANG) Y0=s*sin (ANG) X=x0+s*sin (ANG) Y=y0-s*cos (ANG) Z=0 6. standard helix Equation: x = 4 * cos (t * (5*360)) Y = 4 * sin (t * (5*360)) Z = 10*t 7. logarithmic curve Equation: z=0 X = 10*t Y = log (10*t+0.0001) 8. spherical spiral Equation: rho=4 Theta=t*180 Phi=t*360*20 9. double arc cycloid Equation: l=2.5 B=2.5 X=3*b*cos (t*360) +l*cos (3*t*360) Y=3*b*sin (t*360) +l*sin (3*t*360) 10. Star Line Equation: a=5 X=a* (COS (t*360)) ^3 Y=a* (sin (t*360)) ^3 11. heart line Equation: a=10 R=a* (1+cos (theta)) Theta=t*360 12. inner helix Equation: theta=t*360 R=10+10*sin (6*theta) Z=2*sin (6*theta) 15. Fermat curve (a bit like thread) Mathematical equations: R * r = a*a*theta Cylindrical coordinates Equation 1:, theta=360*t*5 A=4 R=a*sqrt (theta*180/pi) Equation 2:, theta=360*t*5 A=4 R=-