JP4883563B2 - Manipulator device - Google Patents

Description

  The present invention relates to a manipulator device, and is particularly suitable for a master-slave manipulator device having a multi-degree-of-freedom master manipulator and a slave manipulator.

  As a conventional manipulator device, there is one disclosed in Japanese Patent Laid-Open No. 9-98978 (Patent Document 1). The manipulator device includes a slave manipulator that drives a grasping forceps that is a surgical instrument, and a master manipulator that drives the slave manipulator. The manipulator device includes a strain gauge in the grip of the grasping forceps, and has a function of presenting detection information by the strain gauge to the operator when the biological tissue is gripped.

JP-A-9-98978

  Endoscopic surgery is widely recognized as a treatment technique that plays a central role in minimally invasive surgical treatment. This operation has many advantages such as excellent cosmetics and early return to society. On the other hand, it is a highly difficult operation for the surgeon, and a manipulator device that supports the operation in engineering is being developed. Also, in the surgical operation, the feel of the organ obtained through the surgical instrument is important. Similarly, in a manipulator device, it is desired to feed back high sensation sensitivity from a surgical instrument to an operator.

  In the manipulator device of Patent Document 1 described above, a strain gauge is used as a force sensor. However, since the strain gauge is easily affected by high-frequency noise or the like and has a frequency band as low as several tens of Hz, there is a problem that it is difficult to obtain high force sensitivity. Moreover, since electrical wiring is required with the attachment of the strain gauge to the surgical instrument, the wiring work becomes complicated and there is a problem in reliability such as durability. Furthermore, although the strain gauge can cope with low temperature gas sterilization, there is a problem that it is difficult to cope with simple autoclave sterilization of high pressure and high temperature steam.

  An object of the present invention is to provide a master / slave control manipulator device capable of feeding back a high-frequency force sense in a multi-degree-of-freedom manipulator while enabling sterilization of a surgical instrument by simple autoclave sterilization of high-pressure and high-temperature steam. .

In order to achieve the above object, the present invention provides a manipulator device including a slave manipulator that drives a surgical instrument and a master manipulator that drives the slave manipulator via a control device, wherein the slave manipulator includes a slave gimbal unit. A slave pitch axis and a slave yaw axis, a slave translation axis provided inside the slave gimbal part, a slave roll axis connected to the slave translation axis via a parallel link, and a tip of the slave roll axis. Surgical instrument drive mechanism provided, surgical instrument coupled to the surgical instrument drive mechanism and made of a material capable of autoclaving, and slave control with one end connected to the surgical instrument drive mechanism A cable that connects the cable and the other end of the slave control cable. And over Bed linear motion axis, said slave actuator provided in each slave axis is configured by a slave encoder the attached respectively to each slave actuator, the master manipulator is a master pitch shaft provided between Sutajinbaru portion And a master yaw axis, a master translation axis provided inside the master gimbal part,
A master roll shaft provided on the master translation shaft, a hand operating part provided at the tip of the master roll shaft, a master control cable having one end connected to the hand operating part, and other than the master control cable A master linear motion shaft having side ends connected thereto, a master actuator provided on each of the master shafts, and a master encoder attached to each of the master actuators, and the control device includes the slave encoder, broadband force generated based on the detection signal of the master encoder, from the surgical instrument of the slave manipulators over data that was configured to feedback control operation portion of the master manipulator.

A more preferable specific configuration example of the present invention is as follows.
(1) The actuator provided on the slave linear movement shaft is composed of a linear motor, the slave control cable has a slave wire and a slave tube containing the slave wire, and the slave wire has one end portion on the one side. The actuator is connected to the surgical instrument drive mechanism and the other side end is connected to the slave linear motion shaft. The actuator provided on the master linear motion shaft is composed of a linear motor. A master tube stored therein, the master wire having one side end connected to the hand operation unit and the other side end connected to the master linear movement shaft.
(2) A slave constant load spring that compensates for the load of the slave translation shaft and a master constant load spring that compensates for the load of the master translation shaft are provided.
(3) A slave balance weight for compensating for the load of the slave roll shaft is provided.

  According to the present invention, it is possible to provide a master / slave control manipulator device capable of feeding back a high-frequency force sense in a multi-degree-of-freedom manipulator while enabling sterilization of a surgical instrument by simple autoclave sterilization of high pressure and high temperature steam. .

  Hereinafter, a manipulator device according to an embodiment of the present invention will be described with reference to FIGS. 1 to 3.

  FIG. 1 is a perspective view of a slave manipulator 1 in a manipulator device according to an embodiment of the present invention. The manipulator device includes a slave manipulator 1 that drives a surgical instrument, and a master manipulator 2 that drives the slave manipulator 1 via a control device (not shown). The control device controls the slave manipulator 1 and the master manipulator 2 in an integrated manner.

  In FIG. 1, a slave caster 100 and a slave adjuster pad 101 are provided on the lower side of the slave base 10 of the slave manipulator 1, and an electric pillar 102 is provided on the upper side. The shape of the slave base 10 is a square having a width of 500 mm and a depth of 500 mm. The lift range of the electric pillar 102 is 0 to 300 mm. The slave caster 100 is rotated by manually pushing the slave base 10, and the electric pillar 102 is moved up and down by operating a pendant (not shown) connected via the controller 103.

  A surgical instrument drive unit 11 is provided on the electric pillar 102. The height from the floor surface to the surgical instrument drive unit 11 is 610 mm. The surgical instrument drive unit 11 is provided with three slave linear motors 110 constituting slave actuators and a slave linear encoder 111 attached to these slave linear motors 110. The rated thrust of the slave linear motor 110 is 20 N, and the movable range is ± 50 mm. The resolution of the slave linear encoder 111 is 0.1 μm after quadruple multiplication. The three axes of the surgical instrument driving unit 11 operate by master / slave control of force and position based on the reaction force observer and the acceleration signal.

  A slave control cable 112 is connected to each slave linear motor 110. The slave control cable 112 includes a slave wire 113 (see FIG. 2) as an inner and a slave tube 114 (see FIG. 2) as an outer. One end of the slave wire 113 is attached to the movable part of the slave linear motor 110, and the power of the front-rear operation is transmitted to the other end of the slave wire 113. The other ends of the slave wire 113 and the slave tube 114 are connected to a forceps attaching / detaching portion 16 described later. The slave wire 113 has a structure in which 19 stainless fine wires having an outer diameter of 1.8 mm and an element wire diameter of 0.36 mm are twisted. The slave wire 113 has a cutting strength of 3500N. The slave tube 114 has an inner diameter of 2.0 mm and an outer diameter of 5.0 mm, a flat wire is wound in a coil shape, the inner side is covered with a fluororesin having excellent slipperiness, and the outer side is covered with vinyl chloride. The gap as the difference between the outer diameter of the slave wire 113 and the inner diameter of the slave tube 114 is 0.2 mm. It is desirable that the gap interval be as small as possible because it affects transmission power and transmission time loss associated with wire buckling during driving force transmission.

  A slave gimbal portion 12 is provided on the upper surface of the surgical instrument driving portion 11 via a gate-shaped slave support 119. The height from the surgical instrument drive unit 11 to the slave gimbal unit 12 is 390 mm. The slave gimbal unit 12 is provided with a slave rotation motor 122 and a slave rotation encoder 123 for the slave pitch axis 120 and the slave yaw axis 121, and a slave yaw axis balance weight 124.

  The slave rotation motor 122 is constituted by a gearless direct drive motor and has a rated torque of 1.4 Nm. The resolution of the slave rotary encoder 123 is 324000ppr after multiplication by 4. The rotation range of the slave pitch axis 120 is ± 60 °, and the rotation range of the slave yaw axis 121 is ± 45 °. The slave pitch axis 120 and the slave yaw axis 121 operate by a master / slave control of force and position based on a reaction force observer and an acceleration signal. The slave yaw axis balance weight 124 compensates for the mass of the slave rotary motor 122 and the slave rotary encoder 123 of the opposing slave yaw axis 121, and its mass is 5 kg.

  A slave translation shaft 13 is provided at the tip of the slave yaw shaft 121 of the slave gimbal portion 12. The slave translation shaft 13 is provided with a slave linear motor and a slave linear encoder in the cover, and a slave constant load spring 132 is provided under the cover. The rated thrust of the slave linear motor is 10 N, and the movable range is ± 100 mm. The resolution of the slave linear encoder is 0.1 μm after quadruple multiplication. The slave translation axis 13 operates by a master / slave control of force and position based on a reaction force observer and an acceleration signal. The slave constant load spring 132 compensates for the mass of the parallel link 14 or the like applied as a load to the movable part of the slave linear motor, and its spring force is 40N.

  A parallel link 14 is provided above the slave translation shaft 13. The height from the slave gimbal part 12 to the parallel link 14 is 430 mm. Each link of the parallel link 14 is provided with a long link portion 140 and a short link portion 141. The length of the long link portion 140 is 580 mm, the length of the short link portion 141 is 145 mm, and the ratio of the length of the long link portion 140 to the length of the short link portion 141 is 4: 1.

  A parallel link balance weight 142 is provided at the tip of the short link portion 141. The parallel link balance weight 142 compensates for the tip mass of 0.7 kg of the long link portion 140, and its mass is 2.8 kg, which is four times the tip mass. The rod 143 having the parallel link balance weight 142 is attached to a free joint 144 that can slide and rotate the slave gimbal portion 12 so as to smoothly interlock with the rotation operation of the slave yaw shaft 121 and the linear operation of the slave translation shaft 13. Yes.

  A slave roll shaft 15 is provided at the distal end portion of the long link portion 140 of the parallel link 14. The slave roll shaft 15 is provided with a slave rotation motor 150 and a slave rotation encoder 151. The slave rotation motor 150 is constituted by a gearless direct drive motor and has a rated torque of 0.2 Nm. The resolution of the slave rotary encoder 151 is 324000ppr after multiplication by 4. The rotation range of the slave roll shaft 15 is ± 180 °. The slave roll shaft 15 operates by a master / slave control of force and position based on a reaction force observer and an acceleration signal.

  FIG. 2 is a perspective view of the forceps attaching / detaching portion 16 of the slave manipulator of FIG. A forceps attaching / detaching portion 16 is provided at the distal end portion of the slave roll shaft 15. The other ends of the three slave control cables 112 are connected to the forceps attaching / detaching portion 16. The slave wires 113 are attached to the slide portions 160 to 162, respectively. The power of the slave linear motor 110 provided in the surgical instrument drive unit 11 is transmitted to the slide units 160 to 162 via the slave control cable 112, and the slide units 160 to 162 are moved back and forth by moving the slave wires 113 back and forth. It is moved back and forth. The operation range of the slide portions 160 to 162 is ± 10 mm.

  An alignment pin fitting portion 163 and a safety mechanism magnet 164 are provided on the attachment / detachment surface of the forceps attachment / detachment portion 16. The pin fitting portion 163 is for fitting a knock pin of the forceps 17 that is a surgical instrument. The magnets 164 are provided at four locations on the attachment / detachment surface of the forceps attachment / detachment portion 16 and adsorb to the four magnets provided on the forceps 17. The magnet 164 is made of rare earth samarium cobalt having excellent heat resistance, and constitutes a safety mechanism in which the forceps 17 on the attachment / detachment surface is removed when an external force greater than the adsorption force is applied. The pin fitting portion 163 is fitted with a knock pin so that the forceps 17 does not fall into the body even when the safety mechanism is activated.

  The upper end portion of the forceps 17 is attached to the forceps attaching / detaching portion 16. The forceps 17 has an outer diameter of 10 mm and a length of 350 mm, and a virtual pivot point 170 is set on an extension line of the slave pitch shaft 120 of the slave gimbal portion 12.

  The drive transmission mechanism of the forceps 17 can be freely designed such as a rack and pinion mechanism or a rod mechanism as long as it is a mechanism that transmits the power of linear motion of the slide portions 160 to 162 provided in the forceps attaching / detaching portion 16. The operating range at the forceps tip 171 is ± 90 ° for all three axes of the bending 2 direction and the opening / closing 1 direction. As the material constituting the forceps 17, a member having excellent heat resistance such as metal is used so as to be compatible with autoclave sterilization. Similarly, a samarium cobalt magnet is provided on the connection surface between the forceps attaching / detaching portion 16 and the forceps 17 attaching / detaching. This magnet has excellent heat resistance and can be autoclaved. Cover all but the forceps 17 with a drape to ensure sterility.

  1 and 2, the initial positioning of the bedside of the slave manipulator 1, that is, the determination of the pivot point 170 just above the patient's abdominal cavity where the forceps 17 is inserted is performed on the floor surface, that is, the xy plane by the slave caster 100, and is lifted by the electric pillar 102. That is, the z plane is performed. The pivot point 170 is mechanically set by the gimbal portion 12 and the parallel link 14.

  The master / slave control with force feedback includes a total of seven axes including a slave translation axis 13, a slave pitch axis 120, a slave yaw axis 121, a slave roll axis 15, and two bending axes of forceps 17, and one opening / closing axis. Is the axis. The movable range is ± 100 mm for the slave translation axis 13, ± 60 ° for the slave pitch axis 120, ± 45 ° for the slave yaw axis 121, ± 180 ° for the slave roll axis 15, two bending axes of the forceps tip 171 and one opening / closing axis. All are ± 90 °. The rated force of each axis at the forceps tip 171 is 10N for the slave translation axis 13, 2.3N for the slave pitch axis 120 and slave yaw axis 121, 10N for the slave roll axis 15, 5N for the one bending axis, and one bending one axis. The opening / closing axis is 10N. The slave constant load spring 132 applies a pressure to the slave translation shaft 13 in the direction opposite to the gravity. The total height is 1330-1830 mm and the total mass is 72 kg.

  FIG. 3 is a perspective view of the master manipulator 2 in the manipulator device of the present embodiment. A master caster 200 and a master adjuster pad 201 are provided below the master base 20. The shape of the master base 20 is a square having a width of 500 mm and a depth of 500 mm. A hand operation drive unit 21 is provided on the upper side of the master base 20. The height from the floor surface to the hand operation drive unit 21 is 180 mm. The hand operation drive unit 21 is provided with three master linear motors 210 constituting a master actuator and a master linear encoder 211 serving as a master manipulator for these master linear motors 210. The master linear motor 210 has a rated thrust of 20 N and a movable range of ± 50 mm. The resolution of the master linear encoder 111 is 0.1 μm after quadruple multiplication. The three axes of the hand operation drive unit 21 operate by the master / slave control of the force and position based on the reaction force observer and the acceleration signal.

  A master control cable 212 is connected to each master linear motor 210. The master control cable 212 includes a master wire as an inner and a master tube as an outer. One end of the master wire is attached to the movable part of the master linear motor 210, and the power of the front-rear operation is transmitted to the other end of the master wire. The other ends of the master wire and the master tube are connected to a hand operating unit 27 described later. The master wire has a structure in which 19 stainless fine wires having an outer diameter of 1.8 mm and an element wire diameter of 0.36 mm are twisted. The master wire has a cutting strength of 3500N. The master tube has an inner diameter of 2.0 mm and an outer diameter of 5.0 mm, a flat wire is wound in a coil shape, the inner side is coated with a fluororesin having excellent slipperiness, and the outer side is covered with vinyl chloride. The gap as the difference between the outer diameter of the master wire and the inner diameter of the master tube is 0.2 mm. It is desirable that the gap interval be as small as possible because it affects transmission power and transmission time loss associated with wire buckling during driving force transmission.

  A master gimbal portion 22 is provided on the upper surface of the hand operation driving portion 21 via a gate-shaped master support 219. The height from the hand operation drive part 21 to the master gimbal part 22 is 280 mm. The master gimbal unit 22 is provided with a master rotation motor 222 and a master rotation encoder 223 for the master pitch shaft 220 and the master yaw shaft 221, and a master yaw axis balance weight 224.

  The master rotation motor 222 is a gearless direct drive motor, and its rated torque is 1.4 Nm. The resolution of the master rotary encoder 223 is 324000ppr after being multiplied by 4. The rotation range of the master pitch shaft 220 is ± 60 °, and the rotation range of the master yaw shaft 221 is ± 45 °. The master pitch axis 220 and the master yaw axis 221 operate by the master / slave control of the force and position based on the reaction force observer and the acceleration signal. The master yaw axis balance weight 224 compensates for the masses of the master rotary motor 222 and the master rotary encoder 223 of the opposing master yaw axis 221 and has a mass of 5 kg.

  A master translation shaft 23 is provided at the tip of the master yaw shaft 221 of the master gimbal portion 22. The master translation shaft 23 is provided with a master linear motor and a master linear encoder in the cover, and a master constant load spring 232 is provided under the cover. The master linear motor has a rated thrust of 10 N and a movable range of ± 100 mm. The resolution of the master linear encoder is 0.1 μm after quadruple multiplication. The master translation shaft 13 operates by a master / slave control of force and position based on a reaction force observer and an acceleration signal. The master constant load spring 232 compensates for the mass applied as a load to the movable part of the master linear motor, and its spring force is 40N.

  A master roll shaft 25 is provided above the master translation shaft 23. The height from the master gimbal part 22 to the master roll shaft 25 is 440 mm. The master roll shaft 25 is provided with a master rotation motor 250 and a master rotation encoder 251. The master rotation motor 250 is constituted by a gearless direct drive motor and has a rated torque of 0.2 Nm. The resolution of the master rotary encoder 251 is 324000ppr after quadruple multiplication. The rotation range of the master roll shaft 25 is ± 180 °. The master roll shaft 25 operates by a master / slave control of force and position based on a reaction force observer and an acceleration signal.

  A hand operating unit 27 is provided at the tip of the master roll shaft 25. The other end of the three control cables 212 is arranged in the hand operation unit 27. Each master wire as an inner part of the control cable 212 is attached to a slide portion (not shown). The power of the linear motor 210 arranged in the hand operation drive unit 21 is transmitted to the slide part of the hand operation unit 27 via the control cable 212. The operating range of the slide part is ± 5 mm. The transmission mechanism of the hand operating section 27 can be freely designed such as a rack and pinion mechanism or a rod mechanism as long as it is a mechanism that transmits the power of the linear motion of the slide section. Here, the shape is an extra-abdominal operation type, but an intra-abdominal operation type shape is also possible.

  In FIG. 3, initial positioning of the master manipulator 2, i.e., initial position determination according to the operator is performed only on the floor surface of the slave caster 200, that is, the xy plane. The z-axis is performed by a chair lifting / lowering function (not shown) on which the operator sits. When the master pitch shaft 220 is rotated by 45 °, the height to the master roll shaft 25 is 700 mm, which is the same as the height of a general office desk. The surgeon can operate by extending the sense of moving the pen on the desk. If the chair is equipped with an elbow rest, it can be used for a long time. The pivot point 270 is mechanically constituted only by the gimbal portion 22.

  The operation in the master / slave control is a multi-axis of a total of 7 axes including the master translation axis 23, the pitch axis 220, the master yaw axis 221, the master roll axis 25, the bending 2 axes of the hand operation section 27, and the opening and closing 1 axis. The movable range is ± 100 mm for the master translation axis 23, ± 60 ° for the pitch axis 220, ± 45 ° for the master yaw axis 221, ± 180 ° for the master roll axis 25, two bending axes and one opening / closing axis of the hand operating section 27. All are ± 22.5 °. The rated acting force of each axis in the hand operating section 27 is 10N for the master translation shaft 23, 2.5N for the pitch shaft 220 and the master yaw shaft 221, 4N for the master roll shaft 25, 5N for the bending one axis, and one bending one for the remaining bending. And the opening / closing axis is 7N. The master constant load spring 232 applies a pressure to the master translation shaft 23 in the direction opposite to the gravity. The total height is 900-1100 mm and the total mass is 45 kg. In addition, the mechanism can cope with a filtering function for preventing hand tremors in control and a scaling function capable of changing the relationship of the operation range with the slave manipulator 1.

  The control device generates a wide-range force sense generated based on the detection signals of the slave encoder of the slave manipulator 1 and the master encoder of the master manipulator 2 from the forceps 17 that is a surgical tool of the slave manipulator 2 to the hand operation unit 27 of the master manipulator 2. It is configured to provide feedback.

  According to the present embodiment, it is possible to provide a master / slave control manipulator device capable of feeding back a high-frequency force sense in a multi-degree-of-freedom manipulator while enabling sterilization of a surgical instrument by simple autoclave sterilization of high-pressure and high-temperature steam. it can. In other words, a multi-degree of freedom for master / slave control, in which a surgical instrument is constructed only with highly reliable mechanical parts, and a force sensitivity in the hundreds of Hz band can be obtained with a control system that uses the inner world sensor of the master manipulator as the actuator. A manipulator device can be provided. In addition, the surgical tool and the operation unit can be exchanged in various ways, so that the usability is improved and the backlash of the mechanism does not affect the force feedback control, so that the stability of the system is high.

It is a perspective view of a slave manipulator in a manipulator device of one embodiment of the present invention. It is a perspective view of the forceps attachment / detachment part of the slave manipulator of FIG. It is a perspective view of the master manipulator in the manipulator device of this embodiment.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Slave manipulator, 2 ... Master manipulator, 10 ... Slave base, 11 ... Surgical instrument drive part, 12 ... Slave gimbal part, 13 ... Slave translation axis, 14 ... Parallel link, 15 ... Slave roll axis, 16 ... Forceps attachment / detachment part , 17 ... forceps, 20 ... master base, 21 ... hand operation drive part, 22 ... master gimbal part, 23 ... master translation axis, 25 ... master roll axis, 27 ... hand operation part, 101 ... slave adjuster pad, 102 ... electric Pillar, 103 ... Controller, 110 ... Slave linear motor, 111 ... Slave linear encoder, 112 ... Slave control cable, 113 ... Slave wire, 114 ... Slave tube, 119 ... Slave gimbal support, 120 ... Slave pitch axis, 121 ... Slave yaw axis 122 ... Slave times Motor 123, slave rotary encoder 124, slave yaw axis balance weight 132 132 slave constant load spring 140 long link portion 141 short link portion 142 parallel link balance weight 143 rod 144 free joint DESCRIPTION OF SYMBOLS 150 ... Slave rotation motor, 151 ... Slave rotation encoder, 160-162 ... Slide part of forceps drive, 163 ... Pin fitting part, 164 ... Magnet, 170 ... Virtual pivot point, 171 ... Forceps tip, 200 ... Master caster, 201 ... Master adjuster pad, 210 ... Master linear motor, 211 ... Master linear encoder, 212 ... Master control cable, 219 ... Master gimbal support, 220 ... Master pitch axis, 221 ... Master yaw axis, 224 ... Master yaw axis balance weight, 32 ... master constant force spring.

Claims (4)

In a manipulator device comprising a slave manipulator that drives a surgical instrument, and a master manipulator that drives the slave manipulator via a control device,
The slave manipulator is
A slave pitch axis and a slave yaw axis provided in the slave gimbal part;
A slave translation shaft provided inside the slave gimbal part;
A slave roll axis coupled to the slave translation axis via a parallel link;
A surgical instrument drive mechanism provided at the tip of the slave roll shaft;
A surgical instrument formed of a material that is coupled to the surgical instrument drive mechanism and is compatible with autoclave sterilization;
A slave control cable having one end connected to the surgical instrument drive mechanism,
A slave linear motion shaft connected to the other end of the slave control cable;
A slave actuator provided for each slave axis;
A slave encoder attached to each of the slave actuators,
The master manipulator
The master pitch axis and Masutayo shaft provided between Sutajinbaru unit,
A master translation shaft provided inside the master gimbal portion;
A master roll shaft provided on the master translation shaft;
A hand operating part provided at the tip of the master roll shaft;
A master control cable having one end connected to the hand operation unit;
A master linear movement shaft connected to the other end of the master control cable;
A master actuator provided for each master axis;
A master encoder attached to each of the master actuators;
Manipulator and the control device, characterized in that said broadband force generated based on the slave encoder with the detection signal of the master encoder performs feedback control on the operation portion of the master manipulator from the surgical instrument of the slave manipulators over data apparatus.   2. The actuator according to claim 1, wherein the actuator provided on the slave linear movement shaft is configured by a linear motor, the slave control cable includes a slave wire and a slave tube that accommodates the slave wire, and the slave wire has an end portion on one side thereof. Is connected to the surgical instrument drive mechanism and the other side end is connected to the slave linear motion shaft. The actuator provided on the master linear motion shaft is composed of a linear motor. The master control cable is a master wire and the master motion cable. A manipulator device comprising: a master tube containing a wire, wherein one end of the master wire is connected to the hand operation unit, and the other end is connected to the master linear movement shaft.   2. The manipulator device according to claim 1, further comprising a slave constant load spring that compensates for the load of the slave translation shaft and a master constant load spring that compensates for the load of the master translation shaft.   2. The manipulator device according to claim 1, further comprising a slave balance weight that compensates for a load on the slave roll shaft.

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