JPS6254303A - Robot controller - Google Patents

Abstract

PURPOSE:To omit teaching by detecting reaction force applied to a leading tool while executing force reduction control of robot moving parts, and controlling a motor to apply pressing force and thrust corresponding to the size and direction of the reaction force to the tool. CONSTITUTION:A control device of a robot is constituted of a central processing part 23 such as a microcomputer and a servocontrol part for an arm driving motor 6 which consists of a position resistor 24 or the like. In addition, a control switching circuit 30 for switching play back control operation and free operation, a force sensor 15, a reaction force detecting part 32, and a pressing force/thrust arithmetic part 33. The arithmetic part 33 calculates the pressing force and thrust required for copy control in accordance with the size of X and Y directional components detected by the detecting part 32 and inputs the calculated values to the central processing part 23. Consequently, the central processing part 23 outputs a current command values Sa, Sb to control the driving current of the motor 6.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a robot control device capable of performing tracing control in which the robot performs work while tracing the outer shape of a workpiece.

[Conventional technology]

In recent years, various industrial robots have come to be used on factory production lines, and assembly robots are also being put into practical use.

By the way, using such conventional industrial robots,
For example, when performing work such as polishing the outer circumference of a workpiece using copying control, the outline of the workpiece is taught in advance so that the tool attached to the robot will follow the outline of the workpiece during playback. .

[Problem that the invention seeks to solve]

However, in such conventional tracing control using robots, it is necessary to teach the outline of the workpiece in advance, and it is difficult to faithfully follow the outline of the workpiece, and there are problems in that it is not possible to respond to misalignment or deformation of the workpiece. There was a point.

Furthermore, there is also the problem that new teaching is required when the shape of the workpiece is changed.

SUMMARY OF THE INVENTION An object of the present invention is to solve these problems and provide a robot control device that does not require teaching and can perform work by faithfully following the outer shape of a workpiece.

Means for Solving Problem c] Therefore, the present invention drives the movable part of the robot according to a command value based on the deviation between the speed command value and the speed feedback value from the speed detection system of the movable part of the robot. In a robot control device that controls the drive current of a motor.

2. Control switching means that sets the movable part to a relaxed state by setting the command value based on the deviation between the speed command value and the speed feedback value to zero regardless of the actual value.

A reaction force detection means for detecting the reaction force from the workpiece applied to the tool attached to the movable part of the robot, and a necessary pressing force depending on the magnitude and direction of the reaction force detected by the reaction force detection means. and a calculation means for calculating a thrust and a thrust, and the motor is configured to apply the suppressing force and thrust calculated by the calculation means to the tool while the command value based on the deviation is set to zero by the control switching means. The drive current of the workpiece is controlled to allow the tool to work while tracing the outer shape of the workpiece.

[For production]

By setting the command value based on the deviation between the speed command value and the speed feedback value to zero by the control switching means,
Playbank control is no longer performed, and the motor drive current temporarily becomes zero6. Therefore, the movable parts (arms, etc.) of the robot driven by the motors maintain their current postures.

It becomes a relaxed state where it can be moved freely by external force.

When the tool attached to the movable part contacts the workpiece (workpiece), the reaction force detection means detects the reaction force from the workpiece applied to the tool, and depending on the magnitude and direction of the reaction force, the reaction force is detected by the reaction force detection means. The necessary pressing force and thrust are calculated by the calculation means.

Then, by controlling the driving current of the motor so as to apply the calculated pressing force and thrust to the tool, the tool performs the work while faithfully following the outer shape of the workpiece.

〔Example〕

Embodiments of the present invention will be described below based on the drawings.

First, with reference to FIG. 2, the configuration and operation of the robot used in this embodiment will be explained.

In the figure, reference numeral 1 is a horizontally articulated robot, which includes a base 3 that is erected and fixed in the vertical Z direction on a pedestal 2, and a tacho generator 4 and a pulse generator 5 are connected to the output shafts of the base 3. DC servo motor (hereinafter referred to as
A first arm 7, which is a movable part that rotates in the direction of arrow 01 on the A DC servo motor (hereinafter simply referred to as "motor") 1 with a pulse generator and a pulse generator attached to its output shaft
The second arm 11 is a movable part that rotates in the direction of arrow θ2 on the XY plane by a driving force of 0.

Then, an air cylinder 12 is attached to the tip of this second arm 11, and a grinder 16 is attached to the lower end 12a of the piston via a force sensor 15, and the air cylinder 12 is moved up and down (up and down) in the vertical direction, ie, the arrow ZItZ2 direction. (movement) and
The grinder 16 rotates the polishing disk 16a in the direction of arrow θ3 by the driving force of a built-in motor (not shown).

The piston of the air cylinder 12 has an upwardly protruding portion 12b having a dog 13 fixed to its tip.

As the piston rises, the dog 13 moves up and down along the guide rod 14. When the dog 13 rises to the upper limit as shown in Figure 1, the upper limit switch 21 is turned on, and when the dog 13 descends to the lower limit, the lower limit switch 21 is turned on. Make it.

Note that both limit switches 21 and 22 are fixed to a stay (not shown) attached to the second arm 11.

This horizontally articulated robot 1 has a structure that can support the weight of each arm 7°11 in the direction of arrow Z1. ．． Even if the second arms 7 and 11 can be freely moved by external force, their postures will not collapse.

This first. By using a speed reducer with relatively high reverse transmission efficiency (for example, a bevel gear) to transmit the driving force of the motors 6 and 10 to the second arm 7 and 11, the motors 6 and 10 can be brought into a free state. By simply doing this, you will be able to move it freely using external force.

On the other hand, 17 is a conveyor, on which the workpiece 18 that has been positioned and fixed by the workpiece clamp is placed, and the robot 1
The work area is conveyed at a predetermined speed in the direction of arrow Y (direction perpendicular to the plane of the paper).

20 is a workpiece detector fixed at a predetermined working position;
While the robot 1 is waiting at a predetermined standby position,
The arrival of the workpiece 18 is detected.

Note that as the workpiece detector 20, for example, a reflective photoelectric switch or the like can be used.

The force sensor 15 is, for example, as shown in FIG.

A large-diameter sensor holding cylinder 153 is fixed to a disk-shaped mounting plate 151 via a small-diameter stopper holding cylinder 152, and each eccentric part of a cross-shaped sensor mounting plate 154 is fixed to this sensor holding cylinder 153. The cylindrical main body 16b of the grinder 16 is vertically penetrated and fixed to the center of the sensor mounting plate 154 as a detection shaft.

The sensor mounting plate 154 has four sensor elements (for example, strain sensor elements such as semiconductor strain cages) 151 to 15d.
A pair of stopper bolts 155 are screwed into the stopper holding cylinder 152 to regulate the angle of inclination of the grinder main body 16b as a detection shaft.

In this force sensor 15, when the grinder is tilted by an external force with respect to the sensor holding cylinder 153, the sensor mounting plate 154 is distorted depending on the direction and degree of the tilt.
The resistance value of each sensor element 15a to ISd changes depending on the amount of strain.

Therefore, by fixing the mounting plate 151 of the force sensor 15 to the lower end of the piston of the air cylinder 12 shown in FIG. can be detected.

Next, an embodiment of the control device for the robot 1 shown in FIG. 2 will be described with reference to FIG.

In the figure, reference numeral 23 denotes a central processing unit such as a microcomputer, which is in charge of overall control of the robot 1, and includes 5 position command registers 242 position control units 25. Speed control section 26. A first arm 7 consisting of a current control section 27, etc.
Although not shown, a servo control unit for the motor 6 that drives the motor 6 is also included.

A second arm 1 configured in exactly the same way as this servo control section
In addition to controlling the servo control unit for the motor 10 that drives the grinder 1 and the drive circuit such as the solenoid valve for the air cylinder 12, it also controls the drive and stop of the grinder 16.

It also controls the drive current of each motor during tracing control, which will be described later.

Next, during normal playback control in the servo control section for the motor 6, the target position command value of the first arm 7 from the central processing section 23 is written into the position register 24 while being updated one after another.

The position control unit 25 uses the target position command value of the first arm 7 written in the position command register 24 and the position feedback pulse from the pulse generator 5 attached to the output shaft of the motor 6 to control the motor using the current value counter 2S. A count value (current value) indicating the current position of the first arm 7 obtained by counting up or down depending on the rotation direction of the arm 6 is input, and a speed command value based on the deviation is output. Each time the target position command value and the current value match and positioning is completed, this is notified to the central processing unit 23, and the central processing unit 23 uses this to measure the timing for outputting the next target position command value.

The speed control unit 2 receives a speed command value from the position control unit 25 that is input via a control switching circuit 30, which is a control switching means to be described later, and the speed of the first arm 7 attached to the output shaft of the motor 6. A current command value is output based on the deviation from the speed feedback value from the tacho generator 4 as a detection system.

The current controller 27 includes a current detector 28 that detects the current command value from the speed controller 26 and the drive current flowing through the motor 6.
A drive current based on the deviation from the current feedback value from the first arm 7 is applied to the motor 6 that drives the first arm 7.

Therefore, the position command register 242 position control section 25.
Speed control section 26. In the servo control unit for the motor 6 that drives the first arm 7, which includes a current control unit 27 and the like, a control switching circuit 30 converts the speed command value from the position control unit 25 and the speed feedback value from the tacho generator 4. As long as the output is output to the speed control section 2 as is, playback control (positioning control) of the first arm 7 can be performed based on the target position command value from the central processing section 23.

The servo control unit (not shown) for the motor 10 that drives the second arm 7 is configured in exactly the same way as the servo control unit for the motor 6, and the control switching circuit 30 also controls the speed command value and the speed feedback value (tacho generator 8 As long as the value from the central processing unit 23 is output as is to the speed control unit, the second arm 11 can be playback controlled (positioning controlled) based on the target position command value from the central processing unit 23. - The drive circuit for the air cylinder 12 consists of a known cylinder operation circuit, and its electromagnetic directional control valve is connected to the central processing unit 23.
The grinder 15 shown in FIG. 2 is moved up and down in the directions of arrows ZI and Z2 by switching in accordance with a command from the operator.

The control switching circuit 30 switches four movable contact pieces 30a, 30b by exciting a relay coil Ry.

30c and 30d (the two 30c and 30d are not shown) are fixed contacts a1 r a2 r a 3 r, respectively.
a 4 to fixed contact) 11 pb2 +b3 rb4
(a3 ra4 +b3.b4 are also not shown)
The movable contact pieces 30a, 30b and the fixed contacts alzbl and a2°b2 used in the servo control section for the motor 6 are composed of an electromagnetic relay having four transfer switching contacts that switch to the speed. Control unit 26
is connected to the input side of the fixed contact al t 82
are connected to ground, the fixed contact b1 is connected to the output side of the position control section 25, and the fixed contact b2 is connected to the tachogenerator 4.

In addition, the remaining movable contact pieces 3oc, 30d and fixed contacts a3, a4 and b3. b4 is connected between the position control unit and tachogenerator 8 in the servo control unit for the motor 10, and the speed control unit in exactly the same way as the movable contact pieces 50a, 30b and the fixed contacts al+82 and bl+b2.

Note that the diode D connected to the 'rt1 end of the relay coil Ry is a flywheel diode.

When the relay coil R'y is energized, the control switching circuit 30 switches between each movable contact piece 30. 30d to the fixed contacts b1 to b4 as shown in the figure, and the actual speed command value and speed feedback value are passed through as they are to the motor 6.
Each servo control unit for 10 is operated for original playback control.

Then, when the power to the relay coil Ry is cut off, each movable contact piece 30a to 30d is switched to the fixed contact point a1 to a4 side, and both the speed command value and the speed feedback value are related to the playback control before the switching. value to an independent zero value (ground value) and thereby the speed control 26 in the servo control for the motor 6 driving the first arm 7 and also for the motor 10 driving the second arm 11. The current command values output from the speed control sections in the servo control sections (not shown) are set to zero regardless of the movement of the motors 6 and 10.

In this way, if the current command value is set to zero regardless of the actual speed command value and speed feedback value, the position and speed feedback control becomes ineffective, and the motor 6.10 becomes free, thereby causing the first. The second arm 7.11 can be freely pivoted in the X-Y plane by external forces. This state is called r-cut state J.

Note that the relay coil Ry of this control switching circuit 30 is activated when the upward limit switch 21 in FIG. 2 is turned off.
That is, the air cylinder 12 in FIG. 2 is energized when the grinder 16 is lowered.

Further, if the switch '51 of the means connected in parallel with the limit switch 21 is turned on as far as the rise is concerned.

It is also possible to keep the relay coil Ry energized and perform the polishing work by playback control.

Reference numeral 32 denotes a reaction force detection unit, which detects the magnitude and direction of the reaction force from the work 18 that is applied to the grinder 16 when the outer periphery of the work 18 is polished by the grinder 16 shown in FIG. It is detected by the change in resistance value (Fig. 3).

Reference numeral 33 denotes a pushing force/thrust force calculation unit, which calculates the pushing force and thrust (details will be described later) and inputted to the central processing unit 23 as an X-direction output and a Y-direction output.

Thereby, the central processing unit 23 causes the motors 6 and 10 to apply the pressing force and thrust (X direction and Y direction) calculated by the pressing force/thrust force calculation unit 33 to the grander 16.
control the drive current.

In other words, in the above-mentioned relaxed state, the required current command values Sa and Sb are output and Sa is inputted to the current control section 27 via the adder 34. At this time, the current from the speed control section 2 (command value is zero), motor 1 (sb not shown)
The current is also input to the current control section of the servo control circuit for 0 via an adder to control the drive current of each motor 6 and 10.

Next, details of the reaction force detection section 32 and the pressing force/thrust force calculation section 33 will be explained with reference to FIGS. 4 and 5.

9 on the sensor mounting plate 154 of the force sensor 15 shown in FIG.
Of the four sensor elements 15a to 15d attached at an angle of 0', 15a and 15b constitute the X-direction force sensor in FIG. 4, and 15c and 15d constitute the Y-direction force sensor. ing.

That is, the force sensor 1 is mounted so that the cross-shaped sensor mounting plate 154 faces the X direction and the Y direction, which are perpendicular to each other in the horizontal plane in FIG.
5 is attached, and when the grinder 16 is tilted in the X direction, the sensor element 15a.

Since one ISb expands and the other contracts, the resistance value of one increases and the resistance value of the other decreases. When the grinder 16 tilts in the Y direction, the sensor elements ISC, ISd
The resistance value of one side increases and the resistance value of the other side decreases. It usually appears as a combination of these.

The reaction force detection unit 32 in FIG. 4 includes a reaction force detection circuit 41 that detects the X direction component of the reaction force as a signal tQm from the resistance change of the sensor elements ISa and 15b as X direction force sensors;
It is constituted by a reaction force circuit 42 that detects the Y direction component of the reaction force as an electric signal from the resistance change of the sensor elements 15C and 15d as Y direction force sensors.

For example, as shown in FIG. 5, the reaction force detection circuit 41 includes a bridge circuit 41a, a DC amplifier 41b, and a low-pass filter 41C.

The bridge circuit 41a has two sides of a pair of sensor elements 15a and 15b as X-direction force sensors of the force sensor 15,
With resistors Ra and Rh as the other two sides, a power supply E is connected between a and b.
A voltage is applied between the sensor elements c and d, and a voltage corresponding to a change in the resistance value of the sensor elements ISa and ISb is output.

The DC amplifier 41b includes an operational amplifier OP1 and an input resistor Re.
, Rd, and a feedback volume VRf, and DC amplify the voltage output from the bridge circuit 41a. The degree of amplification is adjusted by the volume VRf.

The low-pass filter 41c is a resistor R constituting an integrating circuit.
e and capacitor Ca, and an operational amplifier oP2 constituting a buffer amplifier, remove the noise component of the detection signal amplified by the DC amplifier 41b, and respond to the X-direction component of the reaction force that the grinding 16 receives from the workpiece 18. outputs a voltage signal vx.

The reaction force detection circuit 42 for detecting the Y direction component is also similar to the reaction force detection circuit 41 described above, except that a pair of sensor elements 15e and 15d as Y direction force sensors of the force sensor 15 are connected to two sides of the bridge circuit. A voltage signal v! corresponding to the Y-direction component of the reaction force that the grinder 16 receives from the workpiece 18!
! Output.

The above-mentioned reaction force detection section 32 in FIG. 4 and beyond constitutes the pressing force/thrust force calculation section 33 in FIG. 1.

Here, first, voltage signals vc, v! are respectively output from the reaction force detection circuits 41 and 42. Absolute value comparator 4 for the magnitude of I
3, and based on the results, a pair of bi-inverting changeover switches 44 and 45 (actually analog switching circuits) are switched and controlled to apply a pressing force in the direction of the larger X and Y direction components of one reaction force. The circuit is switched so that the thrust is applied in the smaller direction.

Further, the comparator 46 outputs the voltage signal vx to the comparator 4
By 7 the voltage signal v! ! are compared with the O value (0 volts) from the zero setter 48 to determine whether the X-direction component and Y-direction component of one reaction force are positive or negative, respectively, and input them to the central processing unit 23 in FIG.

The pressing force calculation circuit 4 inputs the voltage signal vx or vg, whichever has a larger absolute value, and calculates the pressing force necessary to press the grinder 16, which is a tool, against the workpiece 18 according to its magnitude. calculate.

The thrust calculation circuit 50 outputs voltage signals Vz, V! The smaller absolute value of f is input, and the thrust required to move the grinder along the outer periphery of the workpiece 18 is calculated according to the magnitude.

Regarding the pressing force, it is necessary to set a lower limit value in order to constantly detect the reaction force, and an upper limit value in order to prevent slippage between the polishing disk 16a and the workpiece 18 during one day using the grinder.

Therefore, a lower limit value setter 51, an upper limit value setter 52, a comparator 53, 54, and a switching circuit 55 are provided. When it is smaller than the lower limit set by the upper limit setter 52, the comparator 53 determines it and switches the switching circuit 55 to output the lower limit, and when it is larger than the upper limit set by the upper limit setter 52, the comparator 54 determines this and switches the switching circuit 55 to output the upper limit value.

Further, regarding the thrust force, it is necessary to set a lower limit value so that the movement does not stop when the pressing direction and the thrust direction are switched.

Therefore, a lower limit value setter 56, a comparator 57, and a switching circuit 58 are provided, and when the thrust value calculated by the thrust calculation circuit 50 is smaller than the lower limit value set by the lower limit value setter 56, the comparator 57 determines this and switches the switching circuit 58 to output the lower limit value.

In this way, the signals indicating the pushing force and thrust values output from the switching circuits 55 and 56 are transmitted to the bi-inverting changeover switch 45.
Output interface 59 or 60 is selected by
Through these, it becomes the X direction output and the Y direction output, and the first
The data is input to the central processing unit 23 shown in the figure.

Note that the function of this pressing force/thrust force calculating section 33 is as follows.

It is also possible to perform software processing by a microcomputer in the central processing unit 23 shown in FIG.

Next, the operation of this embodiment will be explained with reference also to FIGS. 6 and 7.

The control device of this robot is taught the operation shown in FIG. 6 in advance and stored in the memory in the central processing unit 23 shown in FIG.

In the step, the arm 7.11 in FIG. 2 is driven by playback control to move the grinder 16 to its original position (retracted position).

In step (2), the air cylinder 12 is operated to lower the grinder 16 and move it to the approach point. At this time,
The limit switch 21 is turned off as long as it rises, cutting off the power to the relay coil Ry shown in Fig. 1, so the control switching circuit 30 switches all the movable contacts 30a, 3Qb, . . . to the ground side. , the motor 6.10 becomes free and the arm 7.11 becomes relaxed.

In step (2), the current command values Sa and S shown in FIG. 1 are input by the workpiece detection signal from the workpiece detector 20 shown in FIG.
b is output to move the grinder 16, for example, in the X direction and bring it into contact with the workpiece 18.

Using the contact point as the work start point, the grinder 16 is started in step (3), and the X-direction output and Y-direction output indicating the pressing force and thrust input from the pressing force/thrust force calculation unit 33 as described above, and the grinder 16 The grinder performs a polishing operation using the grinder while performing tracing control as will be described later, based on signals indicating the positive and negative values of the X-direction component and the Y-direction component of the reaction force received from the workpiece 18.

When the polishing work is completed in step ■, the air cylinder 12
to raise the grinder 16.

Playback control becomes possible by turning on the upper limit switch 21, and the process returns to step (2) to return to the original position.

Among these steps (2) to (2), the force is relaxed between steps (2) and (2), and the tracing control is further performed during the polishing operation of step (2).

An example of this two-dimensional tracing control will be explained with reference to FIG.

Grinder 1 attached to second arm 11 of robot 1
6 from the approach point a to the target workpiece 18.
Approach the work starting point on the outer circumference from the X direction in a relaxed state.

Then, when the tip of the grinder 1 contacts the work starting point, it receives a reaction force F from the workpiece 18.

The X-direction component FZ and the Y-direction component F! of this reaction force F! I,
As described above, it is detected by the force sensor 15 and the reaction force detection section 32, which are reaction force detection means.

Then, in response to the X-direction output and Y-direction output from the pressing force/thrust force calculation unit 33, the central processing unit 23 in FIG. Pressing force Pu is applied in the direction of the larger component among the direction components (at point b in Fig. 7, the direction is opposite to the direction of the X direction component F''C).
is applied in the smaller direction (also the Y direction component F!l
The thrust force Pr is not applied in the direction (direction of

The direction of the pressing force Pu and thrust Pr is switched when the reaction force in the pressing direction becomes zero. This allows the grinding disk 16 of the grinder 16 to be removed. The outer periphery of the workpiece 18 can be controlled so as to follow the outer periphery of the workpiece 18.

In FIG. 7, the reaction force F, its X-direction component and Y-direction component, as well as the pushing force Pu and the thrust force Pr at two points c and d, which have progressed from the work start point on the outer circumference of the workpiece 18, are indicated by arrows. It shows.

Above, we have described an example in which the control device according to the present invention controls a horizontally multi-jointed robot in which the posture of the movable parts does not collapse even when the robot is in a relaxed state. By providing a gravity balance compensation means that causes the motor driving the movable part to generate a torque that resists the rotational force due to the weight of the movable part, it is possible to perform tracing control in the same way as in the previous example. It is.

The tool used is not limited to the grinder, but various tools that perform work while in contact with the work can be used.

〔Effect of the invention〕

As explained above, according to the present invention.

While controlling the robot's movable part (arm or hand) to release force, it detects the reaction force from the workpiece that is applied to the tool attached to its tip, and applies pressing force and thrust to the tool according to the magnitude and direction of the reaction force. Since the tracing control is performed by controlling the drive current of the motor that drives the movable part, there is no need to teach the outer shape of the workpiece in advance.

In addition, the work can always be carried out faithfully following the shape of the workpiece, and any misalignment, deformation, or change in shape of the workpiece can be immediately dealt with without the need for any changes.

[Brief explanation of the drawing]

FIG. 1 is a block configuration diagram showing an embodiment of the present invention, and FIG. 2 is an external view of the robot tool and its surroundings to explain the structure of the robot and its work. FIG. 3 is a perspective view showing a detailed example of the capacitor 15 and the grinder. 4 is a block diagram showing an example of the reaction force detection section 32 and the pressing force/thrust force calculation section 33 in FIG. 1; FIG. 5 is a circuit diagram showing a specific example of the reaction force detection circuit 41 in FIG. 3; FIG. 6 is a flowchart showing the content of teaching in this embodiment, and FIG. 7 is an explanatory diagram of tracing control according to this embodiment. 1...Horizontal articulated robot 4.8...Tachometer generator 5.9...Pulse generator 6.10...DC servo motor 7.11...1st. Second arm (movable part) 12...
・Air cylinder 15...force sensor 16...
Grinder (tool) 17... Conveyor 18...
Workpiece (workpiece) 20... Workpiece detector 23.
...Central processing unit 30...Control switching circuit 32
...Reaction force detection section 33...Pushing force/thrust force calculation section Fig. 3 Prefecture 6 Fig. 7

Claims (1)

[Scope of Claims] 1. A robot that controls a drive current of a motor that drives a movable part of the robot according to a command value based on a deviation between a speed command value and a speed feedback value from a speed detection system of a movable part of the robot. In the control device, the control switching means sets the command value based on the deviation between the speed command value and the speed feedback value to zero regardless of the actual value, and puts the movable part into a relaxed state; A reaction force detection means for detecting a reaction force from a workpiece applied to an attached tool, and a necessary pressing force and thrust according to the magnitude and direction of the reaction force detected by the reaction force detection means. and a calculation means for calculating, and the motor is configured to apply the pressing force and thrust calculated by the calculation means to the tool with the command value based on the deviation set to zero by the control switching means. 1. A control device for a robot, characterized in that the control device controls a drive current of a robot so that the tool performs work while tracing the outer shape of the workpiece.