Patent Description:
It is known to solve the misalignment problem of <FIG> by making the articulated section sprung. The misaligned configuration of <FIG> is energetically unfavourable compared to the aligned configuration of <FIG>. Thus, by making the articulated section sprung, the flexible section of the surgical instrument of <FIG> becomes more controllable. However, the size of the sprung force required to reliably control the articulated section depends on the magnitude and direction of the loads applied to the surgical instrument. A doubling or tripling of the force to actuate the joint compared to a non-sprung joint is typically required.

Document <CIT> discloses an articulate minimally invasive surgical instrument with a flexible wrist to facilitate the safe placement and provide visual verification of the ablation catheter or other devices in Cardiac Tissue Ablation (CTA) treatments. The instrument may be an endoscope which has an elongate shaft, a flexible wrist at the working end of the shaft, and a vision scope lens at the tip of the flexible wrist. The flexible wrist has at least one degree of freedom to provide the desired articulation. It is actuated and controlled by a drive mechanism located in the housing at the distal end of the shaft. The articulation of the endoscope allows images of hard-to-see places to be taken for use in assisting the placement of the ablation catheter on the desired cardiac tissue. The endoscope may further include couplings to releasably attach an ablation device/catheter or a catheter guide to the endoscope thereby further utilizing the endoscope articulation to facilitate placement of the ablation catheter on hard-to-reach cardiac tissues. The articulate instrument may also be a grasper or any other instrument with a flexible wrist and a built-in lumen to allow an endoscope to insert and be guided to the distal end of the instrument.

Document <CIT> discloses robotic instrument systems, apparatus, and methods for controllably rotating a tool or adapter coupled to a distal portion of a medical instrument such as a catheter. In document <CIT> an interface, which may be integral with the medical instrument or a component of a separate rotatable apparatus or adapter, is operably coupled, e.g. fixedly coupled, to the distal end of the instrument. A tool, such as a rotatable portion of a collar or tool base, or a working instrument operably coupled thereto, is rotatable relative to the interface. The interface and collar have guide channels. A control element extends through the medical instrument and respective guide channels such that the tool or collar is controllably rotatable about the instrument axis by axial movement of the control element relative to the instrument.

Document <CIT> discloses a bending section of an endoscope is constructed from non-round vertebrae. The vertebrae are D-shaped, having a planar portion and an arcuate portion. A first pair of protrusions extends from a first surface of the vertebra, defining a vertical bending axis. A second pair of protrusions extends from a second surface of the vertebra, defining a horizontal bending axis. Because the vertebra is D-shaped, the second pair of protrusions are farther from the longitudinal bending axis of the bending section than the first pair of protrusions. The first pair of protrusions are shorter than the second pair of protrusions. In addition, the first pair of protrusions extend at a different angle than the second pair and thus have a different shape, such that the first and second pair of protrusions are not symmetrically shaped with respect to each other. In addition, the apex of each protrusion is flat, providing a flat contact surface between adjacent vertebrae.

Document <CIT> discloses an articulating probe that comprises a first mechanism including a first link and a second link. The first link comprises a first longitudinal axis, a first articulation surface and a first motion-limiting element. The second link comprises a second longitudinal axis, a second articulation surface and a second motion-limiting element. Document <CIT> also discloses an articulation joint comprises the first articulation surface and the second articulation surface and constructed and arranged to allow two degree-of-freedom articulation of the second link relative to the first link. A motion resisting assembly comprises the first motion limiting element and the second motion limiting element, wherein the motion resisting assembly is constructed and arranged to resist rotation of the second link about the second longitudinal axis relative to the first longitudinal axis of the first link.

Document <CIT> discloses an articulating mechanism for use in a medical device, such as an endoscope or a catheter, includes a series of stacked links disposed adjacent to one another and movable with respect to each other. Each link includes a front face tapered to a pair of pivot points and a rear face defining a wedge shaped recess for receiving the pivot points of the adjacent link. Pull-wires provide tension and hold the staked links together while also allowing for controlled bending of the distal portion by movement of one or more of the pull-wires.

According to the invention, there is provided a robotic surgical instrument according to claim <NUM>.

The drive mechanism may constrain movement of the articulated section so as to permit the tip to rotate about axes in a plane transverse to the longitudinal axis of the shaft.

The flexible driving elements may extend through the shaft, engage with the articulated section and terminate in the tip.

The drive mechanism may be configured to always retain at least one flexible driving element in full tension.

Suitably, in a configuration in which the longitudinal axis of the tip is collinear with the longitudinal axis of the shaft, the drive mechanism is configured to retain all the flexible driving elements in full tension.

Suitably, in a configuration in which the longitudinal axis of the tip is not collinear with the longitudinal axis of the shaft, the drive mechanism is configured to retain only one flexible driving element in full tension. Suitably in this configuration, the drive mechanism is configured to retain at least one other flexible driving element in compression.

Suitably, the flexible driving elements resist compression and tension forces.

Suitably, the robotic surgical instrument comprises at least three flexible driving elements.

Suitably, the articulated section comprises a series of annular rings connected to each other by the flexible driving elements. The annular rings may be connected to the shaft and the tip by the flexible driving elements. Suitably, in a configuration in which the longitudinal axis of the tip is collinear with the longitudinal axis of the shaft, the annular rings are stacked such that their centres lie on an axis which is collinear with the longitudinal axes of the shaft and tip. In the said configuration, the facing surfaces of adjacent annular rings may be in full contact.

In a configuration in which the longitudinal axis of the tip is offset angularly from the longitudinal axis of the shaft, the facing surfaces of adjacent annular rings may contact each other at only one point.

The annular rings may be sprung apart from each other.

The articulated section may comprise a single-start helical cut spring. The articulated section may comprise a multi-start helical cut spring.

The robotic surgical instrument may further comprise strain gauges, each strain gauge configured to measure the tension on a respective flexible driving element.

The drive mechanism may be configured to displace a flexible driving element until that flexible driving element has a desired tension. The drive mechanism may be configured to receive the desired tension from a controller, the desired tension determined according to a model of the current and desired orientations of the tip and the tensions of the flexible driving elements.

The robotic surgical instrument may further comprise contact sensors for detecting contact between facing surfaces of adjacent annular rings.

Suitably, the drive mechanism is configured to displace a flexible driving element until contact is detected between facing surfaces of adjacent annular rings by the contact sensors.

<FIG> illustrates the distal end of a surgical instrument. The surgical instrument as a whole has the general form shown in <FIG>. In other words, the surgical instrument comprises a base <NUM> by which the surgical instrument connects to the surgical robot arm. The instrument base is designed cooperatively with the terminal end of the surgical robot arm, such that the instrument base is releasably attachable to the terminal end of the robot arm. A shaft <NUM> extends between the base <NUM> and an articulated section <NUM>. The articulated section <NUM> is connected at its proximal end to the shaft <NUM> and at its distal end to the instrument tip <NUM>. The instrument tip <NUM> has an attachment <NUM> suitable for attaching an end effector <NUM>. The shaft <NUM>, articulated section <NUM> and instrument tip <NUM> are all hollow. This allows passage of elements up these sections to actuate the end effector <NUM>. It also reduces the weight of the surgical instrument.

The end effector may take any suitable form. For example, the end effector may be smooth jaws, serrated jaws, a gripper, a pair of shears, a needle for suturing, a camera, a laser, a knife, a stapler, a cauteriser, a suctioner.

The articulated section <NUM> is flexible. Suitably, the articulated section <NUM> is not sprung. Alternatively, the articulated section <NUM> may be lightly sprung. The articulated section <NUM> of <FIG> comprises a set of annular rings <NUM>, <NUM>, <NUM> and driving elements <NUM>, <NUM> and <NUM>.

Three annular rings are depicted in <FIG>, however it will be understood that fewer or more annular rings may be used. The annular rings are not rigidly attached to each other. The annular rings are stacked such that when the instrument is in a straight configuration in which the tip is collinear with the shaft as shown in <FIG>, the centres of the annular rings lie on the longitudinal axis <NUM> of the instrument. Each annular ring comprises: a first surface <NUM> bounded by the inner and outer concentric rings of the annulus; a second surface <NUM> opposite the first surface and also bounded by the inner and outer concentric rings of the annulus; an inner surface <NUM> bounded by the inner concentric ring of the annulus and perpendicular to the first and second surfaces; and an outer surface <NUM> bounded by the outer concentric ring of the annulus and also perpendicular to the first and second surfaces. The outer surfaces of the annular rings are aligned with the exterior surfaces of the shaft and tip. The outer surfaces of the annular rings are flush with the exterior surfaces of the shaft and tip. For each annular ring, its first surface faces the second surface of the adjacent annular ring stacked on one side of it, and its second surface faces the first surface of the adjacent annular ring stacked on the other side of it. The exceptions to this are the annular rings at either end of the articulated section <NUM>, one of which faces an annular ring <NUM> on the terminal end of the shaft <NUM>, the other of which faces an annular ring <NUM> on the proximal end of the instrument tip <NUM>.

The inner and outer concentric rings of the annular rings shown in <FIG> are circular. The inner and outer rings may have a non-circular profile. For example, they may be oval or ellipse shaped. Suitably, the outer ring of the annular rings matches the profile of the outside of the shaft. Thus, if the shaft is circular in cross-section, the outer ring of the annular rings is a matching circular shape and size to that of the shaft. This provides a smooth exterior profile to the instrument which is less likely to get caught or snag in the surgical site.

The annular rings are connected to each other by the driving elements. Each driving element engages with each of the annular rings. In the arrangement shown in <FIG>, each driving element passes through an opening in each annular ring. That opening penetrates the annular ring through the first surface and second surface of the annular ring perpendicular to the first and second surfaces. The annular rings are not secured to the driving elements. The annular rings are free to slide along the driving elements. However, the motion of each annular ring is constrained by virtue of the driving elements which are passing through it. Thus, the driving elements prevent the annular rings from detaching from the surgical instrument. The annular rings are connected to the shaft and the tip by the driving elements. Each driving element passes through the annular ring <NUM> at the distal end of the shaft, through each of the annular rings in the flexible section, and through the annular ring <NUM> at the proximal end of the instrument tip <NUM>. The proximal ends of the driving elements are connected to a drive mechanism in the base of the surgical instrument. The driving elements extend through the shaft <NUM>, through the flexible section <NUM> and into the instrument tip <NUM>. The distal ends of the driving elements are secured to the instrument tip.

The driving elements are flexible. Each driving element is elongate. Each driving element is linear when at rest. In other words, each driving element is linear when in an unstrained state, when no external forces are being applied to it. Each driving element can be flexed laterally to its main extent. In other words, each driving element can be flexed transversely to its longitudinal axis. Each driving element is not flexible along its main extent. Each driving element resists compression and tension forces acting in the direction of its longitudinal axis.

Thus, the driving elements are able to transfer drive from the base of the instrument to the instrument tip. The driving elements may be rods. For example, the driving elements may be push/pull rods. The driving elements may be cables. The driving elements may be fabricated from a spring steel. Alternatively, the driving elements may be fabricated from a composite such as carbon fibre.

The driving elements are secured in the base of the instrument in such a way that they can be put under tension, and optionally also under compression. For example, a driving element may be secured to a plate. A screw is threaded through the plate. A motor drives rotation of the screw. By tightening the screw, the plate moves towards the proximal end of the instrument (i.e. towards the robot arm), thereby pulling the driving element. By loosening the screw, the plate moves towards the distal end of the instrument (i.e. towards the instrument tip), thereby pushing the driving element. As another example, a driving element may each be secured to a spool. A motor drives rotation of the spool. By rotating the spool in one direction, the driving element winds around the spool, thereby shortening the length of the driving element in the shaft and articulated portion. In other words, this action provides a tensioning or pulling force on the driving element. By rotating the spool in the other direction, the driving element unwinds around the spool, thereby increasing the length of the driving element in the shaft and articulated portion. In other words, this action provides a compressing or pushing force on the driving element.

When a driving element is pulled towards the instrument base, since the driving element is secured to the instrument tip, it pulls the instrument tip in the direction of the applied tension. In other words, it pulls the instrument tip towards the instrument base. This causes the articulated section <NUM> to compress in the region of that driving element. In the example of <FIG>, the shaft and instrument tip are rigid and fixed in length but the annular rings are slideable along the driving element. Thus, as a driving element is pulled, that driving element slides through the annular rings that it is engaged with, thereby pulling the annular rings that it passes through together. The stack of annular rings that the driving element passes through is thereby compressed.

When a driving element is pushed away from the instrument base, since the driving element is secured to the instrument tip, it pushes the instrument tip in the direction of the applied compression. In other words, it pushes the instrument tip away from the instrument base. This causes the articulated section <NUM> to extend in the region of that driving element. In the example of <FIG>, as a driving element is pushed, that driving element slides through the annular rings that it is engaged with, thereby pushing the annular rings that it passes through apart from each other. The stack of annular rings that the driving element passes through is thereby extended.

<FIG> illustrates a surgical instrument having three driving elements which engage with the articulated section <NUM> and the instrument tip <NUM> to orientate the instrument tip. Alternatively, four driving elements may be used. Further driving elements may also be used. At least three driving elements are used to enable the instrument tip to be orientated with two degrees of rotational freedom relative to the shaft <NUM>. <FIG>, <FIG> illustrate three arrangements of the driving elements which cause three different orientations of the instrument tip.

<FIG> illustrates a straight configuration of the surgical instrument. In this configuration the longitudinal axis <NUM> of the instrument tip is collinear with the longitudinal axis <NUM> of the shaft. In this configuration, the drive mechanism in the base of the instrument retains all the driving elements in full tension. Thus, in the example of <FIG>, all three driving elements <NUM>, <NUM> and <NUM> are pulled. This causes the articulated section <NUM> to fully compress. The annular rings stack on top of each other. The centres of the annular rings lie on an axis <NUM> which is collinear with the longitudinal axes of the instrument tip <NUM> and the shaft <NUM>. The facing surfaces of adjacent annular rings are in full contact. In other words, for each annular ring, its first surface contacts the second surface of the adjacent annular ring over its entire first surface. Similarly, for that annular ring, its second surface contacts the first surface of the adjacent annular ring over its entire second surface. For the annular ring at the shaft end of the articulated section, its surface facing the shaft surface <NUM> is in full contact with the shaft surface <NUM>. For the annular ring at the tip end of the articulated section, its surface facing the tip surface <NUM> is in full contact with the tip surface <NUM>.

<FIG> illustrates a first bent configuration of the surgical instrument. In this configuration the longitudinal axis <NUM> of the instrument tip is not collinear with the longitudinal axis <NUM> of the shaft. The longitudinal axis <NUM> of the instrument tip is offset angularly from the longitudinal axis <NUM> of the shaft. The drive mechanism in the base of the instrument retains only one driving element in full tension. In <FIG>, this is driving element <NUM>. Driving element <NUM> is pulled, which causes articulated section <NUM> to fully compress in the region of that driving element. The facing surfaces of adjacent annular rings contact only at one contact point <NUM>. This contact point is at the exterior edges of the facing surfaces of the adjacent annular rings closest to the driving element under tension. The facing surfaces of the annular rings are no longer equally spaced across their surfaces as in <FIG>. The facing surfaces of the annular rings are not parallel to each other as in <FIG>. The separation between the facing surfaces of adjacent annular rings increases from nothing at the contact point <NUM>, to a larger separation <NUM> at the opposite exterior edge. The instrument tip is thereby oriented into the first bent configuration shown. The centres of the annular rings lie on a uniform curve <NUM> which joins the longitudinal axis <NUM> of the instrument tip to the longitudinal axis <NUM> of the shaft.

The other driving elements may be put under no forces by the drive mechanism. Alternatively, one or more of the other driving elements may be pushed by the drive mechanism. By retaining the one or more other driving elements <NUM>, <NUM> in compression in addition to retaining the driving element <NUM> in tension, the configuration of the articulated section and instrument tip is more rigid. This provides extra stability to the position of the end effectors. Extra security and stability in the position of the end effectors is useful if they are to put the surgical instrument under stress, for example if a load is applied to the end effectors.

<FIG> illustrates a second bent configuration of the surgical instrument. In this configuration, the instrument tip is bent to the opposite side to that illustrated in <FIG>. The same principles apply as discussed above in relation to <FIG>. This time, only driving element <NUM> is in full tension. The facing surfaces of adjacent annular rings contact only at contact point <NUM>. Contact point <NUM> is at the exterior edges of the facing surfaces of the adjacent annular rings closest to the driving element <NUM>.

Facing surfaces of adjacent annular rings may be separated by light springs. For example, the light springs may have a spring constant between <NUM> N/mm and <NUM> N/mm. These light springs ensure that as the articulated section bends to a configuration such as that of <FIG>, the annular rings are evenly spaced out over the articulated section. The light springs are not strong enough to on their own prevent the configuration of <FIG> from developing.

In the configurations shown in <FIG>, <FIG>, the drive mechanism orients the instrument tip to a desired position by tensioning and (optionally) compressing the driving elements in a controlled manner. The drive mechanism always retains at least one driving element in full tension. This causes the articulated section <NUM> to always be fully compressed along at least one extent by which it connects the instrument tip and the shaft. This full compression is at the exterior edge of the articulated section along the portion which is closest to the driving element under full tension. Thus, for a given angular relationship between the instrument tip and the shaft, the length of the articulated section is minimised along at least one extent. The length of the articulated section is the separation of the head of the shaft <NUM> and the base of the instrument tip <NUM>. The length of the articulated section is minimised along the direction in which the annular rings are in contact. The articulated section always has this same minimum length in one extent whichever orientation the instrument tip is in. This is because the articulated section is always fully compressed, and hence at its shortest length along at least one extent. The articulation section is always fully compressed along the inside edge of the bend both when in a configuration such as those shown in <FIG>, <FIG>, and also when being moved from one configuration to another configuration.

The drive mechanism thus enables movement of the articulated section so as to permit the instrument tip to move with two degrees of rotational freedom relative to the shaft. Thus, the instrument tip is controllable by the drive mechanism via the articulated section to rotate about axes in a plane transverse to the longitudinal axis of the shaft. Three driving elements enable this rotation. The drive mechanism constrains the movement of the articulated section so as to not permit the instrument tip to move with translational freedom relative to the shaft. Thus, the drive mechanism constrains the movement of the articulated section such that there is never more than one curve in the profile of the articulated section. Thus, the misaligned configuration of <FIG> does not arise. By controlling the lengths of the driving elements <NUM>, <NUM>, <NUM>, the location and orientation of the instrument tip is controlled. If the driving elements are all the same length, then the articulated section takes the configuration shown in <FIG> in which the longitudinal axis <NUM> of the instrument tip <NUM> is collinear with the longitudinal axis <NUM> of the shaft <NUM>. This control of the instrument tip <NUM> is achieved without requiring the driving elements or the annular rings of the articulated section to be sprung. If the annular rings are lightly sprung apart, then this is only to maintain even separation of the annular rings when in a bent configuration such as that of <FIG>. The light springs do not provide a sufficient spring force to prevent the misaligned configuration of <FIG> from occurring.

A respective strain gauge may be attached to each driving element. Each strain gauge measures the tension on the driving element that it is attached to. Optionally, one or more strain gauge may also be attached to the instrument shaft. The strain gauges output their measured tensions to a controller. The controller maintains a model of the instrument system. The controller is a computer-based device which comprises a processor and non-transient computer-readable media such as a memory for storing computer executable instructions. The processor processes the computer executable instructions in order to control the operation of the drive mechanism of the instrument. The controller stores the current position and orientation of the instrument tip as well as the measured tensions of each of the driving elements, and optionally the measured tension of the instrument shaft. The controller receives a desired position of the instrument tip. This may be received, for example, from a user input. The controller determines the tensions to be applied to the driving elements in order to change the orientation of the instrument tip to the desired position. The controller makes this determination with reference to the model which maps tensions of the driving elements to positions of the instrument tip. The tensions determined by the controller to be applied to the driving elements are so as to maintain the instrument shaft in compression and so as to maintain at least one of the driving elements in full compression.

The desired tensions of the driving elements are signalled to the drive mechanism in the instrument base. The controller may signal the actual desired tensions of the driving elements to the drive mechanism. Alternatively, the controller may signal an indication of the desired tensions of the driving elements. For example, the controller may send a control signal which causes a motor to wind a spool by a certain amount. As another example, the controller may send a control signal which causes a motor to wind a screw by a certain amount. The drive mechanism receives the signalling, and implements the instructions. This causes the driving elements to be tensioned and compressed by the amounts determined by the controller.

The controller may signal the drive mechanism to tension a driving element, but not specify how much by. The drive mechanism receives this signal, and pulls the driving element. The strain gauge attached to that driving element measures the tension of that driving element and outputs it to the controller. On determining that the desired tension of the driving element has been reached, the controller may signal the drive mechanism to maintain the current tension on the driving element. In response, the drive mechanism stops further tension from being applied to the driving element, and maintains the current tension on the driving element.

By controlling the movement of the driving elements according to a stored model of the distal end of the instrument, full compression of the articulated section along at least one extent by which it connects the instrument tip and the shaft is ensured.

Full compression of the articulated section along at least one extent by which it connects the instrument tip and the shaft may be ensured by directly sensing the contact between facing surfaces of adjacent annular rings of the articulated section. Contact sensors located on the articulated section sense this contact, and output the sensed contact to the controller. The controller may signal the drive mechanism to displace the driving elements. The drive mechanism receives this signal, and displaces the driving elements as instructed. When the controller receives output from the contact sensors verifying that full compression of the articulated section is achieved, it signals the drive mechanism to maintain the current tension on the driving element. In response, the drive mechanism stops further tension from being applied to the driving element, and maintains the current tension on the driving element.

The attachment <NUM> may be rigidly attached to the instrument tip <NUM>. Alternatively, the attachment <NUM> may be connected to the instrument tip <NUM> by a roll joint. In this case, the controls for the roll joint (for example flexible rods or cables) pass up the inside of the shaft <NUM> and articulated section <NUM>. The controls for the end effector (for example flexible rods or cables) also pass up the inside of the shaft <NUM> and articulated section <NUM>.

The articulated section <NUM> may be implemented in a different way. For example, the articulated section <NUM> may comprise a cut spring. The cut spring may be single-start or multi-start. <FIG> illustrates an articulated section <NUM> which is a multi-start helical cut spring <NUM>. The spring is connected at one end to the end of the shaft <NUM>, and at the other end to the instrument tip <NUM>. The outer profile of the spring is aligned with the exterior surfaces of the shaft and tip. The outer profile of the spring is flush with the exterior surfaces of the shaft and tip. The spring is hollow on the inside to enable cables to be passed up through the shaft <NUM> to the instrument tip <NUM>. The shaft <NUM>, instrument tip <NUM>, attachment <NUM>, and driving elements <NUM>, <NUM> and <NUM> are arranged and operate as described with respect to the corresponding components of <FIG>, <FIG>. The spring is configured to compress and expand. The spring is able to compress more on one side than another. Thus, the spring enables the instrument tip <NUM> to be angularly displaced relative to the shaft <NUM> in a corresponding manner to that illustrated in <FIG>.

The instrument described with respect to <FIG>, <FIG> and <FIG> enables two degrees of freedom in the wrist which are controllable as a result of the manner in which the articulated section <NUM> is constrained to move. Only three driving elements are required to achieve this motion. The articulated flexible section comprises annular rings or a spring which are less complex, not as small and do not need to be as precisely made as the internal components of the flexible section in <FIG>. Thus, the external diameter of the instrument can be made to be <NUM>. No sprung forces acting on the articulated section are required to achieve the control described.

The instrument could be used for non-surgical purposes. For example it could be used in a cosmetic procedure.

Claim 1:
A robotic surgical instrument comprising:
a shaft (<NUM>);
an articulated section (<NUM>) extending from the shaft (<NUM>) and terminating at its distal end in a tip (<NUM>, <NUM>), the tip (<NUM>, <NUM>) having an attachment (<NUM>, <NUM>) for an end effector (<NUM>), where the attachment (<NUM>, <NUM>) is connected to the tip (<NUM>, <NUM>) by a roll joint; and
a drive mechanism configured to drive the articulated section (<NUM>) via flexible driving elements (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>) thereby altering the angular orientation of the tip (<NUM>, <NUM>) relative to the shaft (<NUM>), wherein the drive mechanism is configured to be controlled so as to always fully compress the articulated section (<NUM>) along at least one extent at an exterior edge of the articulated section (<NUM>) by which the articulated section (<NUM>) connects the tip (<NUM>, <NUM>) and the shaft (<NUM>) such that the articulated section (<NUM>) always has its shortest length along said at least one extent whilst driving the articulated section (<NUM>) from any one configuration to any other configuration, wherein the drive mechanism constrains movement of the articulated section (<NUM>) so as to permit the tip (<NUM>, <NUM>) to move with two degrees of rotational freedom and no degrees of translational freedom relative to the shaft (<NUM>).