Patent ID: 7860592

Claim:
A method for designing industrial products by using a computer, comprising: generating a three-dimensional clothoid curve by the computer; and designing a shape of said industrial products using the three-dimensional clothoid curve by the computer, wherein each of a pitch angle and a yaw angle in a tangential direction of said three-dimensional clothoid curve is given by a quadratic expression comprising of a curve length or a curve length variable, wherein the three-dimensional clothoid curve is generated using the following expressions: P = P 0 + ∫ 0 s ⁢ u ⁢ ⅆ s = P 0 + h ⁢ ∫ 0 S ⁢ u ⁢ ⅆ S , 0 ≤ s ≤ h , 0 ≤ S = s h ≤ 1 ; u = E k ⁢ ⁢ β ⁢ E j ⁢ ⁢ α ⁡ ( i ) = [ cos ⁢ ⁢ β sin ⁢ ⁢ β 0 sin ⁢ ⁢ β cos ⁢ ⁢ β 0 0 0 1 ] ⁡ [ cos ⁢ ⁢ α 0 sin ⁢ ⁢ α 0 1 0 - sin ⁢ ⁢ α 0 cos ⁢ ⁢ α ] ⁢ { 1 0 0 } = { cos ⁢ ⁢ β cos ⁢ ⁢ α sin ⁢ ⁢ β cos ⁢ ⁢ α - sin ⁢ ⁢ α } ; α = a 0 + a 1 ⁢ S + a 2 ⁢ S 2 ; β = b 0 + b 1 ⁢ S + b 2 ⁢ S 2 , ⁢ wherein P = { x y z } , P 0 = { x 0 y 0 z 0 } shows a positional vector at each point on the three-dimensional clothoid curve and its initial value, respectively, the expressions for the three-dimensional clothoid curve when implemented: assume that the length of the curve from a starting point is s and its whole length is h, said whole length being a length from the starting point to an end point, and produce a dimensionless value S, which is called the curve length variable; i, j and k are unit vectors in the x-axis, y-axis and z-axis directions, respectively; and the u is a unit vector showing a tangential direction of the curve at a point P; the E kβ and the E jα are rotation matrices and represent an angular rotation of angle β about the k-axis and an angular rotation of angle α about the j-axis, respectively, wherein the E kβ is referred to as a yaw rotation, while the E jα is referred to as a pitch rotation; the unit vector in the i-axis direction is rotated by an angle α about the j-axis, before being rotated by an angle β about the k-axis, thus producing a tangent vector u in which a 0 , a 1 , a 2 , b 0 , b 1 and b 2 are constants.