US 7,860,592 B2Granted

Design method for industrial product using clothoid curve, industrial products designed by the design method, and method and device for numerical control using the clothoid curve

AssigneeThk Co., Ltd.

InventorsFumihiko Kimura, Hiroshi Makino, Yoshikazu Matsuo

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Abstract

A trajectory of motion of the mechanical element is designed by using a three-dimensional curve, referred to as a three-dimensional clothoid curve, in which each of a pitch angle and a yaw angle in a tangential direction is given by a quadratic expression of a curve length or a curve length variable. A trajectory of a machine tool or a contour shape of a workpiece is expressed by using a three-dimensional curve, referred to as a three-dimensional clothoid curve, in which each of a pitch angle and a yaw angle in a tangential direction is given by a quadratic expression of a curve length or a curve length variable to control motion of the machine tool based on the three-dimensional curve.

Claims8

Dependent claims

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 Ekβ and the Ejα 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 Ekβ is referred to as a yaw rotation, while the Ejα 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 a0, a1, a2, b0, b1 and b2 are constants.

203 more elements

A computer-readable recording medium, which is for designing a shape of an industrial product, recorded thereon a program which when executed enables a computer to operate as means to design the shape of the industrial product by using a three-dimensional clothoid curve in which each of a pitch angle and a yaw angle in a tangential direction 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 Ekβ and the Ejα 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 Ekβ is referred to as a yaw rotation, while the Ejα 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 a0, a1, a2, b0, b1 and b2 are constants.

199 more elements

Dependencies are inferred from the claim text.

Facts

Application: 10/590,704Filed 14 Feb 2005
Priority: JP 2004-05555427 Feb 2004
Published: US 2007/0293962 A120 Dec 2007
Granted: 28 Dec 2010
Term ends: Not estimatedThe source records don’t support an estimate.

Classification5 codes

G05B 19/4103
Characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and…:…
G05B 2219/35146
Nc in input of data, input till input file format: enter data, calculate 3-D curve or surface, sculptured surface, okisurf
Y02P 90/02
Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation: total factory control, e.g. smart factories,…
G05B
Control or regulating systems in general