Optics: measuring and testing – Position or displacement
Reexamination Certificate
2001-06-13
2004-01-13
Shafer, Ricky D. (Department: 2872)
Optics: measuring and testing
Position or displacement
C356S622000, C356S139030, C356S139070, C250S559290
Reexamination Certificate
active
06678059
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to an apparatus for measuring 6-degree-of-freedom motions of a rigid body by using a three-facet reflector wherein the measurement of the 6-degree-of-freedom displacements of an object, particularly an object in motion with a high-speed, can be made with ease and with accuracy, and specially the measuring precision is excellent.
BACKGROUND OF THE INVENTION
Generally, there are various ways for expressing the position and orientation of a body situated in a three dimensional space.
In one of widely used methods, the position is expressed as a position vector on rectangular coordinate system for three dimensional space and the orientation is expressed by means of Euler's angle expression, in which the rotated angle for an object relative to the x, y and z axis of a reference coordinate system is expressed as &ggr;, &bgr; and &agr; respectively, the rotated angles being called as the roll, pitch and yaw.
Referring to
FIG. 1
, which shows the rectangular coordinate as defined in the three dimensional space, the position and orientation of an arbitrary object for which measurement is to be taken and which moves with 6-degree-of freedoms are illustrated. The coordinate system O
w
is the reference coordinate system to express the motion of an object
1
. For a portion of the object
1
in the drawing, the coordinate systems O
w
and O
s
are defined. The coordinate system O
s
is the coordinate system fixed on the rigid body and moving integrally with the object
1
.
Further, the coordinate system O
w′
maintains the same orientation as the reference coordinate system O
w
and shares the origin with the coordinate system O
s
. In the drawing, the vector
T
w
→
=
[
t
x
t
y
t
z
]
T
is the position vector for expressing the position of the object
1
defined by the coordinate system O
s
. Further, the equation:
T
s
w
=
[
c
α
c
β
c
α
s
β
s
γ
-
s
α
c
γ
c
α
s
β
c
γ
+
s
α
s
γ
t
x
s
α
c
β
s
α
s
β
s
γ
+
c
α
c
γ
s
α
s
β
c
γ
-
c
α
s
γ
t
y
-
s
β
c
β
s
γ
c
β
c
γ
t
z
0
0
0
1
]
,
(
Equation
1
)
wherein stand for and other abridgements have the similar meanings, is the matrix defined by t
x
, t
y
, t
z
, &ggr;, &bgr; and &agr;, which expresses the position and orientation of the coordinate system O
s
moved relative to the reference coordinate O
w
. As the coordinate system O
s
is fixed to the object
1
, this matrix can be used to show the position and orientation of the object.
As described above, the determination of the position and orientation of an object in the three dimensional space may be regarded as the problem of determining the 6 values for t
x
, t
y
, t
z
, &ggr;, &bgr; and &agr;.
The three-facet reflector used for the measuring apparatus in the present invention was initially suggested in a patent application (Korean patent application No. 99-00977) previously filed. The disclosure in the patent application was intended to determine six-degree-of-freedom motions by attaching a three-facet reflector on the slider of a hard disk drive (HDD). However, while a laser beam was needed to enter the apex of the three-facet reflector for the given purpose, a specific method therefor was not proposed in the disclosure.
Further, the mathematical equations proposed there were derived on the base of the hypothesis that the apex of a three-facet reflector and the laser light spots formed on three position-sensitive detectors form the same one plane. As the hypothesis is not precise in view of the fact, however, the equations can not be applied to the practice. Therefore, that exclusive patent application is not sufficient to achieve the goal.
There is also known a method for measuring six-degree-of-freedom displacements of an object (Korean patent application No. 00-24654) by using the three-facet reflector as proposed in the above-described patent. The arrangement of the apparatuses as proposed in that patent is shown in FIG.
2
. On the object, a mirror in the form of a trigonal pyramid as the three-facet reflector
110
is mounted. The three-facet reflector
110
is supplied with a laser beam at its top apex so as to produce three branches of reflected beams, which are detected by three laser beam position-sensitive detectors PSD's
121
,
122
and
123
. The position-sensitive detectors
121
,
122
and
123
comprise ordinary sensor elements for outputting the locations of centroids for incident laser beams in the form of voltage signal, so that the coordinates of sets of three positions from three position-sensitive detectors
121
,
122
and
123
may be used to determine the six-degree-of-freedom displacements tx, ty, tz, &ggr;, &bgr; and &agr; of the three-facet reflector
110
. As indicated in the drawing, the laser source follows with two degrees of freedom, as the three-facet reflector
110
makes movement. In order to follow the movement of three-facet reflector
110
, the two-degree-of-freedom position of the light source is controlled, so that the intensity of laser beam incident to the three position-sensitive detectors
121
,
122
and
123
may be maintained the same, by comparing the intensity of laser beam incident to the respective position-sensitive detectors
121
,
122
and
123
. This invention is pertinent to the application filed by the present inventors, which realized the laser-tracing method not embodied in the previous patent application (No. 99-00977). However, this method is still insufficient to follow high-speed movements.
FIG. 3
shows the arrangement of a special apparatus as disclosed in Korean patent application No.00-24653, which functions to determine six-degree-of-freedom movements of a HDD slider based on the principle disclosed in Korean patent application No.00-24654. Arms of a two-stage swing arm
140
run parallel to each other and connected to a pivot
14
at the rear end, so that the two-stage swing arm
140
can rotate around the axis of the pivot
14
. The lower arm member includes an E-block
16
, suspension
18
and flexure piece
19
, to the underside of which piece a slider
20
is fixed. The actuator for driving the slider
20
in the form of a voice coil motor(VCM)
12
is disposed on the rear part of the two-stage swing arm
140
. The upper arm member of the swing arm
140
is composed of a rigid body resisting an elastic deformation. A three-facet reflector
110
is fixed on the upper side of the slider
20
. Right above the apex of the three-facet reflector
110
there is formed a light permeating hole
143
on the leading edge of the upper arm member, while the first reflector
151
and the second reflector
152
are fixed on the top face of the upper arm member of the swing arm
140
. A laser beam which has passed the first and second reflectors
151
and
152
arrives at the three-facet reflector
110
through the hole
143
and then the ray reflected thereon is projected to three position-sensitive detectors
121
,
122
and
123
. In this invention, a two stage swing arm is proposed, so that the laser beam may be projected constantly in the apex of a three-facet reflector which moves together with the HDD slider, because ex
Byun Yong Kyu
Cho Hyung Suck
Park Noh Yeol
Park Won Shik
Korean Advanced Institute of Science and Technology
Shafer Ricky D.
Vidas Arrett & Steinkraus
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