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Claims  |
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What is claimed is:
1. A method for controlling motion of a function element carried by a
manipulator and having associated therewith a workpoint, the motion being
described by an arc defining a path to be traversed by the workpoint and
by a velocity of the workpoint, the arc being defined by input signals
representing coordinates of three reference positions on the arc including
the arc end positions, the velocity of the workpoint being defined by
further input signals, the manipulator including movable members for
effecting motion of a wrist and a servomechanism circuit for controlling
the motion of the movable members, the method comprising the steps of:
(a) calculating work plane orientation angles in response to the input
signals representing the arc reference positions, the work plane
orientation angles defining the attitude of a plane in which the arc lies;
(b) producing arc intermediate position signals in response to the work
plane orientation angles and the input signals defining the arc reference
positions, and the velocity of the workpoint, the arc intermediate
position signals representing an intermediate position on the arc to which
the work point is to be moved in a predetermined time;
(c) producing machine coordinate signals in response to the arc
intermediate position signals, the machine coordinate signals defining the
motion of the machine members between their positions at the current
location of the workpoint and the location of the workpoint defined by the
arc intermediate position;
(d) applying the machine coordinate signals to the servomechanism circuit
to move the workpoint to the arc intermediate position; and
(e) iterating steps (b) through (d) to move the workpoint through the arc.
2. The method according to claim 1 wherein the step of producing arc
intermediate position signals further comprises the steps of:
(a) calculating an arc angle between the arc end positions;
(b) calculating an arc length included by the arc angle;
(c) calculating an angular increment to be traversed by the workpoint in a
predetermined time interval; and
(d) calculating the coordinates of a position on the arc located away from
the present position of the workpoint by the angular increment.
3. The method according to claim 2 wherein the step of producing machine
coordinate signals further comprises the steps of:
(a) producing a servointerrupt signal representing an incremented time
interval.
(b) calculating coordinates of a workpoint location on a linear path
between two successive arc intermediate positions in response to the
servointerrupt signal, the input signals representing velocity, and the
arc intermediate position signals; and
(c) transforming the workpoint location to machine coordinate signals.
4. A method for controlling motion of a function element carried by a wrist
of a manipulator and having associated therewith a workpoint and a tool
vector, the motion being described by an arc defining a path to be
traversed by the workpoint, by a desired line of approach of the tool
vector, and by a velocity of the workpoint, the arc being defined by input
signals representing coordinates of three reference positions on the arc
including the arc end positions, the line of approach being defined by
input signals representing the orientation of the wrist at the reference
positions, the velocity of the workpoint being defined by further input
signals, the manipulator including movable members for effecting motion of
the wrist and a servomechanism circuit for controlling the motion of the
movable members, the method comprising the steps of:
(a) calculating work plane orientation angles in response to the input
signals representing the arc reference positions, the work plane
orientation angles defining the attitude of a plane in which the arc lies;
(b) producing arc intermediate position signals in response to the work
plane orientation angles and the input signals defining the arc reference
positions and the velocity of the workpoint, the arc intermediate position
signals representing an intermediate position on the arc to which the
workpoint is to be moved in a predetermined time;
(c) producing intermediate wrist orientation signals in response to the
input signals representing the wrist orientation and the tool vector, the
intermediate wrist orientation signals defining the attitude of the
function element at the arc intermediate position;
(d) producing machine coordinate signals in response to the intermediate
wrist orientation signals and the arc intermediate position signals, the
machine coordinate signals defining the motion of the machine movable
members between their current positions and the positions defined by the
arc intermediate position signals and the intermediate wrist orientation
signals;
(e) applying the machine coordinate signals to the servomechanism circuit
to move the work point to the arc intermediate position and to move the
function element to the attitude defined by the intermediate orientation
signal; and
(f) iterating the steps (b) through (e) to move the workpoint through the
arc while maintaining the tool vector on the desired line of approach.
5. The method according to claim 4 wherein the step of producing arc
intermediate position signals further comprises the steps of:
(a) calculating the arc angle between the arc end positions;
(b) calculating an arc length included by the arc angle;
(c) calculating an angular increment to be traversed by the workpoint in a
predetermined time interval; and
(d) calculating the coordinates of a position on the arc located away from
the present position of the workpoint by the angular increment.
6. The method according to claim 5 wherein the step of producing
intermediate wrist orientation signals further comprises the steps of:
(a) calculating process angles at the arc reference positions, the process
angles defining the line of approach of the tool vector at the arc
reference positions;
(b) calculating process angles at the arc intermediate position in response
to the angular increment and the process angles at the arc reference
positions;
(c) calculating a work plane orientation matrix in response to the work
plane orientation angles, the work plane orientation matrix defining a
transformation from a reference frame on the arc and including a normal to
the work to a reference frame having a coincident origin and being
parallel to a coordinate system from which the input signals are
referenced;
(d) calculating a process angle orientation matrix in response to the
process angles at the arc intermediate position, the process angle
orientation matrix defining a transformation from a reference frame at the
workpoint and including the line of approach to a reference frame at the
workpoint parallel to the coordinate system from which the input signals
are referenced;
(e) calculating a tool vector orientation matrix in response to the input
signals defining the tool vector, the tool vector orientation matrix
defining a transformation from a reference frame at the workpoint and
including the tool vector to a reference frame at the workpoint parallel
to the coordinate system from which the input signals are referenced;
(f) calculating a wrist orientation matrix in response to the work plane
orientation matrix, the process angle orientation matrix and the tool
vector orientation matrix; and
(g) calculating the wrist orientation angles in response to the wrist
orientation matrix.
7. The method according to claim 4 wherein the step of producing machine
coordinate signals further comprises the steps of:
(a) producing a servointerrupt signal representing an incremental time
interval;
(b) calculating coordinates of a workpoint location on a linear path
between two successive arc intermediate positions in response to the
servointerrupt signal and the arc intermediate position signals;
(c) calculating wrist orientation angles to be associated with the work
point location in response to the servointerrupt signal, the arc
intermediate position signals and the intermediate wrist orientation
signals; and
(d) transforming the workpoint location and the wrist orientation angles to
machine coordinate signals.
8. A method for controlling motion of a function element mounted to a
faceplate of a wrist of a manipulator and having associated therewith a
workpoint and a tool vector, the motion being described by an arc defining
a path to be traversed by the workpoint, by a desired line of approach of
the tool vector, and by a velocity of the workpoint, the arc being defined
by input signals representing coordinates of three reference positions on
the arc including the arc end positions, and further input signals
defining the desired line of approach at each arc reference position, the
velocity of the workpoint being defined by further input signals, and the
tool vector being defined by further input signals, the manipulator
including movable members for effecting motion of the wrist and a
servomechanism circuit for controlling the motion of the movable members,
the method comprising the steps of:
(a) calculating work plane orientation angles in response to the input
signals representing the arc reference positions, the work plane
orientation angles defining the attitude of a plane in which the arc lies;
(b) producing process angle signals in response to the input signals
defining the line of approach of the tool vector and the input signals
defining the tool vector and in response to the work plane orientation
angles, the process angle signals defining the attitude of the desired
line of approach of the tool vector at each reference position;
(c) producing arc intermediate position signals in response to the input
signals defining the reference positions and the velocity of the workpoint
and in response to the work plane orientation angles, the arc intermediate
position signals representing an intermediate position on the arc to which
the workpoint is to be moved in a predetermined time;
(d) producing intermediate wrist orientation signals in response to the
process angle signals and the work plane orientation angles, the
intermediate wrist orientation signals defining the attitude of the tool
vector at the position represented by the arc intermediate position
signals;
(e) producing machine coordinate signals in response to the intermediate
wrist orientation signals and the arc intermediate position signals, the
machine coordinate signals defining the motion of the movable machine
members between their current positions and the positions defined by the
arc intermediate position signals and the intermediate wrist orientation
signals;
(f) applying the machine coordinate signals to the servomechanism circuit
to move the workpoint to the arc intermediate position and to move the
function element to the attitude defined by the intermediate wrist
orientation signals; and
(g) iterating steps (c) through (f) to move the workpoint through the arc
while maintaining the tool vector on the desired line of approach.
9. The method according to claim 8 wherein the input signals defining the
line of approach of the tool vector represent orientation angles of the
wrist and the step of producing process angle signals further comprises
the steps of:
(a) calculating a work plane orientation matrix in response to the work
plane orientation angles, the work plane orientation matrix defining a
transformation between a frame of reference located on the arc and
including a normal to the work plane and a frame of reference having a
coincident origin and being parallel to a coordinate system from which the
input signals are referenced;
(b) calculating a wrist orientation matrix in response to the input signals
representing the orientation angles of the wrist, the wrist orientation
matrix defining a transformation from a frame of reference at the
workpoint and including an axis parallel to a normal to the faceplate to a
frame of reference at the workpoint and parallel to the coordinate system
from which the input signals are referenced;
(c) calculating a tool vector matrix in response to the input signals
defining the tool vector, the tool vector matrix representing a
transformation from a frame of reference at the workpoint and including
the tool vector to a frame of reference at the workpoint and parallel to
the coordinate system from which the input signals are referenced;
(d) calculating a process angle orientation matrix in response to the work
plane orientation matrix, the wrist orientation matrix and the tool vector
matrix: and
(e) calculating the process angles in response to the process angle
orientation matrix; and
(f) iteratively repeating the steps (a) through (e) for each arc reference
position.
10. The method according to claim 9 wherein the step of producing arc
intermediate position signals further comprises the steps of:
(a) calculating an arc angle included between the arc end positions:
(b) calculating an arc length included by the arc angle;
(c) calculating an angular increment to be traversed by the workpoint in a
predetermined time interval; and
(d) calculating the coordinates of a position on the arc located away from
the present position of the workpoint by the angular increment.
11. The method according to claim 10 wherein the step of producing
intermediate wrist orientation signals further comprises the steps of:
(a) calculating process angles at the arc intermediate positions;
(b) calculating a wrist orientation matrix in response to the work plane
matrix, the process angle matrix, and the tool vector matrix; and
(c) calculating the wrist orientation angles in response to the wrist
orientation matrix.
12. The method according to claim 11 wherein the step of producing machine
coordinate signals further comprises the steps of:
(a) producing a servointerrupt signal representing an incremental time
interval;
(b) calculating coordinates of a workpoint location on a linear path
between two successive arc intermediate positions in response to the
servointerrupt signal, the input signals representing the velocity of the
workpoint and the arc intermediate position signals;
(c) calculating wrist orientation angles to be associated with the work
point location in response to the servointerrupt signal, the arc
intermediate position signals and the intermediate wrist orientation
signals; and
(d) transforming the workpoint location and the wrist orientation angles to
machine coordinate signals.
13. The method according to claim 8 wherein the input signals defining the
line of approach of the tool vector represent desired process angles and
the tool vector orientation angles and the step of calculating
intermediate wrist orientation angles further comprises the steps of:
(a) calculating process angles at the arc intermediate position;
(b) calculating a process angle matrix in response to the process angles,
the process angle matrix defining a transformation from a reference frame
at the workpoint including the desired line of approach to a reference
frame at the workpoint parallel to a coordinate system from which the
input signals are referenced;
(c) calculating a tool vector orientation matrix in response to the tool
vector orientation angles the tool vector orientation matrix defining a
transformation from a frame of reference at the workpoint including the
tool vector to a frame of reference at the workpoint parallel to the
coordinate system from which the input signals are referenced;
(d) calculating a work plane orientation matrix at the intermediate
position in response to the work plane orientation angles, the work plane
orientation matrix defining a transformation from a frame of reference on
the arc and including a normal to the work plane to a frame of reference
having a coincident origin and being parallel to the coordinate system
from which the input signals are referenced;
(e) calculating a wrist orientation matrix in response to the process angle
orientation matrix, the tool vector orientation matrix and the work plane
orientation matrix; and
(f) calculating the wrist orientation angles in response to the wrist
orientation matrix.
14. A method for controlling motion of a function element mounted to a face
plate of a wrist of a manipulator and having associated therewith a
workpoint and a tool vector, the motion being described by an arc defining
a path to be traversed by the workpoint, by a desired line of approach of
the tool vector, and by a velocity of the workpoint, the arc being defined
by input signals representing coordinates of three reference positions on
the arc including the arc end positions, and further input signals
representing process angles and tool vector orientation angles together
defining the line of approach of the tool vector at the arc reference
positions, the velocity of the workpoint being defined by further input
signals, and the tool vector being defined by still further input signals,
the manipulator including movable members for effecting motion of the
wrist and a servomechanism circuit for controlling the motion of the
movable members. The method comprising the steps of;
(a) producing arc intermediate position signals in response to the input
signals defining the reference positions and the velocity of the
workpoint, the arc intermediate position signals representing an
intermediate position on the arc to which the workpoint is to be moved in
a predetermined time;
(b) producing intermediate wrist orientation signals in response to the
input signals representing process angles and the arc intermediate
position signals, the intermediate wrist orientation signals defining the
attitude of the function element at the position represented by the arc
intermediate position signals, the intermediate wrist orientation signals
being produced by;
(i) calculating process angles at the intermediate position;
(ii) calculating a process angle orientation matrix in response to the
process angles, the process angle orientation matrix defining a
transformation from a frame of reference at the workpoint and including
the desired line of approach to the frame of reference at the workpoint
parallel to a coordinate system from which the input signals are
referenced;
(iii) calculating a tool vector orientation matrix in response to the input
signals representing tool vector orientation angles, the tool vector
orientation matrix defining a transformation from a frame of reference at
the workpoint and including the tool vector to a frame of reference at the
workpoint parallel to the coordinate system from which the input signals
are referenced;
(iv) calculating a wrist orientation matrix in response to the process
angle orientation matrix and the tool vector matrix; and
(v) calculating the wrist orientation angles in response to the wrist
orientation matrix;
(c) producing machine coordinate signals in response to the intermediate
wrist orientation signals and the arc intermediate position signals, the
machine coordinate signals defining the motion of the machine members
between their current positions and the positions defined by the arc
intermediate position signals and the intermediate wrist orientation
signals;
(d) applying the machine coordinate signals to the servo mechanism circuit
to move the workpoint to the arc intermediate position and to move the
function element to the attitude defined by the intermediate wrist
orientation signals; and
(e) iterating steps (a) through (d) to move the workpoint through the arc
while maintaining the tool vector on the desired line of approach.
15. A method for controlling motion of a function element mounted to a face
plate of a wrist of a manipulator and having associated therewith a
workpoint and a tool vector, the motion being described by an arc defining
a path to be traversed by the workpoint, by a desired line of approach of
the tool vector, and by a velocity of the workpoint, the arc being defined
by input signals representing coordinates of three reference positions on
the arc including the arc end positions, and further input signals
representing orientation angles defining the line of approach of the tool
vector at the arc reference positions, the velocity of the workpoint being
defined by further input signals, and the tool vector being defined by
still further input signals, the manipulator including movable members for
effecting motion of the wrist and a servomechanism circuit for controlling
the motion of the movable members, the method comprising the steps of:
(a) producing process angle signals representing angles of the desired line
of approach of the tool vector at each reference position by:
(i) calculating a wrist orientation matrix in response to the input signals
representing the orientation angles, the wrist orientation matrix defining
a transformation from a frame of reference at the workpoint and including
an axis parallel to a normal to the face plate to a frame of reference at
the workpoint parallel to a coordinate system from which the input signals
are referenced;
(ii) calculating a tool vector orientation matrix in response to the input
signals defining the tool vector, the tool vector orientation matrix
defining a transformation from a frame of reference at the workpoint and
including the tool vector to a frame of reference at the workpoint
parallel to the coordinate system from which the input signals are
referenced;
(iii) calculating a process angle orientation matrix in response to the
wrist orientation matrix and the tool vector orientation matrix;
(iv) calculating the process angles in response to the process angle
orientation matrix; and
(v) iterating the steps (i) through (iv) for each arc reference positions;
(b) producing arc intermediate position signals in response to the input
signals defining the reference positions and the velocity of the
workpoint, the arc intermediate position signals representing an
intermediate position on the arc to which the workpoint is to be moved in
a predetermined time;
(c) producing intermediate wrist orientation signals in response to the
process angle signals and the arc intermediate position signals, the
intermediate wrist orientation signals defining the attitude of the
function element at the positions represented by the arc intermediate
position signals;
(d) producing machine coordinate signals in response to the intermediate
wrist orientation signals and the arc intermediate position signals, the
machine coordinate signals defining the motion of the machine members
between there current positions and the positions defined by the arc
intermediate position signals and the intermediate wrist orientation
signals;
(e) applying the machine coordinate signals to the servo mechanism circuit
to move the workpoint to the arc intermediate position and to move the
function element to the attitude defined by the intermediate wrist
orientation signals; and
(f) iterating steps (b) through (e) to move the workpoint through the arc
while maintaining the tool vector on the desired line of approach.
16. The method according to claim 15 wherein the step of producing arc
intermediate position signals further comprises the steps of:
(a) calculating an arc angle included between the arc end positions;
(b) calculating an arc length included by the arc angle;
(c) calculating an angular increment to be traversed in a predetermined
period of time; and
(d) calculating the coordinates of a position on the arc located away from
the present position of the workpoint by the angular increment.
17. The method according to claim 16 wherein the step of producing
intermediate wrist orientation signals further comprises the steps of:
(a) calculating process angles at the arc intermediate position;
(b) calculating a wrist orientation matrix in response to the process angle
matrix and the tool vector matrix; and
(c) calculating the wrist orientation angles in response to the wrist
orientation matrix.
18. The method according to claim 17 wherein the step of producing machine
coordinate signals further comprises the steps of:
(a) producing a servointerrupt signal representing an incremental time
interval;
(b) calculating coordinates of a workpoint location on a linear path
between two successive arc intermediate positions in response to the
servointerrupt signal, the arc intermediate position signals and the input
signals representing workpoint velocity;
(c) calculating wrist orientation angles to be associated with the
workpoint location in response to the servointerrupt signal, the arc
intermediate position signals and the intermediate wrist orientation
signals; and
(d) transforming the workpoint location and the wrist orientation angles to
machine coordinate signals.
19. An apparatus for controlling motion of a function element mounted to a
faceplate of a wrist of a manipulator and having associated therewith a
workpoint and a tool vector, the motion being described by an arc defining
a path to be traversed by the workpoint, by a desired line of approach of
the tool vector and by a velocity of the workpoint, the arc being defined
by input signals representing coordinates of three reference positions on
the arc including the arc end positions, the line of approach being
defined by further input signals, the velocity of the workpoint being
defined by further input signals, the manipulator including movable
members for effecting motion of the wrist and a servomechanism circuit for
controlling the motion of the movable members, the apparatus comprising:
(a) means for calculating work plane orientation angles in response to the
input signals representing the arc reference positions, the work plane
orientation angles defining the attitude of a plane in which the arc lies;
(b) means for producing arc intermediate position signals in response to
the input signals defining the arc reference positions, the velocity of
the workpoint, and the work plane orientation angles, the arc intermediate
position signals representing an intermediate position on the arc to which
the workpoint is to be moved;
(c) means for producing machine coordinate signals in response to the arc
intermediate position signals, the machine coordinate signals defining the
motion of the machine movable members between their current positions and
the positions defined by the arc intermediate position signals.
20. The apparatus of claim 19 wherein the means for producing arc
intermediate position signals further comprises:
(a) means for calculating an arc angle included between the arc end
positions;
(b) means for calculating an arc length included by the arc angle;
(c) means for calculating an angular increment to be traversed in a
predetermined period of time; and
(d) means for calculating the coordinates of a position on the arc located
away from the present position of the workpoint by the angular increment.
21. The apparatus according to claim 20 wherein the means for producing
machine coordinate signals further comprises:
(a) means for producing a servointerrupt signal representing an incremental
time interval;
(b) means responsive to the servointerrupt signal and the arc intermediate
position signals for calculating coordinates of a workpoint location on a
linear path between two successive arc intermediate positions; and
(c) means for transforming the work point location to machine coordinate
signals.
22. The apparatus according to claim 21 wherein the input signals defining
the line of approach of the tool vector represent orientation angles of
the wrist and the apparatus for producing intermediate wrist orientation
signals further comprises means for producing process angle signals in
response to the work plane orientation angles, and the input signals
representing the wrist orientation angles and the tool vector, the process
angle signals representing angles of the desired line of approach of the
tool vector at each arc reference position.
23. The apparatus according to claim 22 wherein the apparatus for producing
process angle signals further comprises:
(a) means responsive to the work plane orientation angle calculating means
for calculating a work plane orientation matrix defining a transformation
from a frame of reference on the arc and including a normal to the work
plane to a frame of reference having its origin coincident and being
parallel to a coordinate system from which the input signals are
referenced;
(b) means responsive to the input signals representing the orientation
angles of the wrist for calculating a wrist orientation matrix, the wrist
orientation matrix defining a transformation from a reference frame at the
workpoint and including an axis parallel to a normal to the faceplate to a
reference frame at the workpoint parallel to the coordinate system from
which the input signals are referenced;
(c) means responsive to the input signals defining the tool vector for
calculating a tool vector orientation matrix, the tool vector orientation
matrix defining a transformation from a reference frame at the workpoint
and including the tool vector to a reference frame at the workpoint
parallel to the coordinate system from which the input signals are
referenced;
(d) means responsive to the work plane orientation matrix, the wrist
orientation matrix, and the tool vector matrix for calculating a process
angle orientation matrix; and
(e) means responsive to the process angle orientation matrix for
calculating the process angles.
24. The apparatus according to claim 23 wherein the means for producing
intermediate wrist orientation signals further comprises:
(a) means responsive to the angular increment for calculating process
angles at the arc intermediate position;
(b) means responsive to the work plane orientation matrix, the process
angle orientation matrix, and the tool vector orientation matrix for
calculating a wrist orientation matrix; and
(c) means responsive to the wrist orientation matrix for calculating the
wrist orientation angles.
25. The apparatus according to claim 19 further comprising means for
producing intermediate wrist orientation signals in response to the input
signals representing the line of approach of the tool vector, the
intermediate wrist orientation signals defining the attitude of the
function element at the arc intermediate positions. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
This invention relates generally to the field of controlled path motion for
manipulators. Such manipulators may carry a tool, such as a welding
electrode requiring manipulation to a series of points along a workpiece.
A typical manipulator of that type may be constructed as generally
described in Holmes et al U.S. Pat. No. 4,598,380. Such a manipulator may
be computer controlled to move a tool along straight line paths between a
series of reference points, the coordinates of which are input to the
computer during a teaching phase. Teaching of the reference points may be
carried out as generally taught by Corwin, Jr. et al U.S. Pat. No.
3,920,972, and path control may be carried out as taught in Hohn U.S. Pat.
No. 3,909,600 or in Magnuson U.S. Pat. No. 4,506,335.
In some applications, such as welding, it is necessary to cause movement of
a tool along a circular arc or other curved path. Prior art methods of
tool manipulation require that a large number of reference points be
taught to the computer in order to achieve tool movement along a
reasonably smooth path. Such teaching requires that the manipulator be
correctly oriented as well as positioned at each such point.
It is therefore seen that there is a need for an improved method for moving
a tool along a curved path. It is desired that the teaching phase for such
manipulation require movement of the tool to only a relatively few points,
that the work plane not be constrained to a horizontal or vertical
orientation and that the tool maintain a desired process orientation as it
moves along its working path.
SUMMARY OF THE INVENTION
The present invention provides an improved method of moving a tool tip
along a curved path. The method may be practiced in a tool positioning
system comprising a face plate for supporting a tool, wrist means for
rotatably supporting the face plate, arm means for movably supporting the
wrist means, servo means responsive to movement commands and rotation
commands for causing controlled movement of the wrist means and controlled
rotation of the face plate, and means for generating the movement commands
and the rotation commands, in response to input signals representing the
location of three reference positions on the curved path together with a
desired tool attitude relative to the path at each reference position.
The method uses information defining the shape of the curved path, the
position of the tool centerpoint or workpoint and orientation of the wrist
at three reference positions along the path, and desired attitude of the
tool relative to the path to calculate and store the coordinates of the
tool centerpoint and the orientation angles of the wrist for intermediate
positions on the curved path. The machine advances the tool centerpoint on
straight line paths between these intermediate positions while linearly
interpolating the change in tool attitude to generate movement commands
for the manipulator axes.
In the preferred embodiment a planar circular arc is chosen as the curved
path. A teaching means is operated to position and orient the tool at
three reference positions along that arc. At each reference position, the
tool orientation is dictated by a desired line of approach described by
three process angles. In the preferred embodiment the method may comprise
the steps of computing the coordinates of the center point of a circle
defined by the arc, calculating arc angles for each of the work points and
iteratively using those arc angles for calculation of the coordinates of
the work points. The desired process angles may be calculated by linear
interpolation between the reference process angles.
It is therefore an object of the present invention to provide an improved
method for controlling a manipulator to move a tool along a curved path.
Other and further objects and advantages of the present invention will be
apparent from the accompanying drawings and description.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic illustration of an industrial manipulator and a
control therefor.
FIG. 2 is a block diagram of the control of FIG. 1.
FIG. 3(a) is a schematic representation of the manipulator positioned
within the rectangular coordinate system which defines the coordinates of
the programmed locations.
FIG. 3(b) and 3(c) show the axes of motion of the manipulator wrist and the
associated orientation angles defined by the input signals.
FIG. 4(a) is a schematic illustration of the movement of a tool tip along a
circular path within a work plane.
FIG. 4(b) illustrates the geometry of intermediate points along an arc.
FIG. 5(a) is a flow chart of the overall cycle of operation of a
manipulator in the automatic mode.
FIG. 5(b) is a generalized flow chart of procedures for producing arc
intermediate point signals.
FIG. 6 is a flow chart of a routine for computing the center of a circular
arc.
FIG. 7 illustrates the geometry associated with computation of the center
of a circular arc.
FIG. 8 is, an illustration of reference arc angles and the vectors
associated therewith.
FIG. 9 is a flow chart of a routine for computing arc angles and length.
FIG. 10 is a flow chart of a routine for computing a tool vector
orientation matrix.
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