Patent Publication Number: US-10779711-B2

Title: Center robotic arm with five-bar spherical linkage for endoscopic camera

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a division of application Ser. No. 13/915,564, filed Jun. 11, 2013, which is a continuation of application Ser. No. 11/623,311, filed Jan. 15, 2007, now U.S. Pat. No. 8,469,945, which claims the benefit pursuant to 35 U.S.C. 119(e) of U.S. Provisional Application No. 60/786,491, filed Mar. 28, 2006, and U.S. Provisional Application No. 60/762,233, filed Jan. 25, 2006, each of which is hereby incorporated by reference in its entirety. 
    
    
     FIELD OF INVENTION 
     The embodiments of the invention relate generally to robotic surgical systems. More particularly, the embodiments of the invention relate to linkage in robotic arms. 
     BACKGROUND 
     Minimally invasive surgery (MIS) provides surgical techniques for operating on a patient through small incisions using a camera and elongated surgical instruments introduced to an internal surgical site, often through trocar sleeves or cannulas. The surgical site often comprises a body cavity, such as the patient&#39;s abdomen. The body cavity may optionally be distended using a clear fluid such as an insufflation gas. In traditional minimally invasive surgery, the surgeon manipulates the tissues using end effectors of the elongated surgical instruments by actuating the instrument&#39;s handles while viewing the surgical site on a video monitor. 
     A common form of minimally invasive surgery is endoscopy. Laparoscopy is a type of endoscopy for performing minimally invasive inspection and surgery inside the abdominal cavity. In standard laparoscopic surgery, a patient&#39;s abdomen is insufflated with gas, and cannula sleeves are passed through small (generally ½ inch or less) incisions to provide entry ports for laparoscopic surgical instruments. The laparoscopic surgical instruments generally include a laparoscope (a type of endoscope adapted for viewing the surgical field in the abdominal cavity) and working tools. The working tools are similar to those used in conventional (open) surgery, except that the working end or end effector of each tool is separated from its handle by a tool shaft. As used herein, the term “end effector” means the actual working part of the surgical instrument and can include clamps, graspers, scissors, staplers, image capture lenses, and needle holders, for example. The end effector for the laparoscope may include lenses and light sources that may be optically couple to a camera and lamps through the tool shaft. To perform surgical procedures, the surgeon passes these working tools or instruments through the cannula sleeves to an internal surgical site and manipulates them from outside the abdomen. The surgeon monitors the procedure by means of a monitor that displays an image of the surgical site taken from the laparoscope. Similar endoscopic techniques are employed in other types of surgeries such as arthroscopy, retroperitoneoscopy, pelviscopy, nephroscopy, cystoscopy, cisternoscopy, sinoscopy, hysteroscopy, urethroscopy, and the like. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention may best be understood by referring to the following description and accompanying drawings that are used to illustrate embodiments of the invention by way of example and not limitation. In the drawings, in which like reference numerals indicate similar elements: 
         FIG. 1  is a plan view of a surgical suite in which embodiments of the invention are used. 
         FIG. 2  is a plan view of a portion of the operating suite of  FIG. 1 . 
         FIG. 3  is a side view of a portion of the operating suite of  FIG. 2 . 
         FIG. 4A  is a schematic view of a parallel five-bar linkage in a first pose. 
         FIG. 4B  is a schematic view of the parallel five-bar linkage of  FIG. 4A  in a second pose. 
         FIG. 5  is a schematic view of a parallel spherical five-bar linkage. 
         FIG. 6A  is a schematic view of another parallel spherical five-bar linkage in a first pose. 
         FIG. 6B  is a schematic view of the parallel five-bar linkage of  FIG. 6A  in a second pose. 
         FIG. 7A  is a pictorial view of an embodiment of the invention in a first pose. 
         FIG. 7B  is a pictorial view of the embodiment of  FIG. 7A  in a second pose. 
         FIG. 8  is a view of a first side of an embodiment of the invention. 
         FIG. 9  is a bottom view of the embodiment of the invention shown in  FIG. 8 . 
         FIG. 10  is view of a second side of the embodiment of the invention shown in  FIG. 8 . 
         FIG. 11  is a top view of the embodiment of the invention shown in  FIG. 8 . 
         FIG. 12  is an end view of the embodiment of the invention shown in  FIG. 8 . 
         FIG. 13  is a pictorial view of a portion of the embodiment as shown in  FIG. 12 . 
         FIG. 14  is a bottom view of the embodiment of the invention as shown in  FIG. 9  in a different operative position. 
         FIG. 15  is a bottom view of another embodiment of the invention. 
         FIG. 16  is an end view of another embodiment of the invention. 
         FIG. 17  is a schematic view of a parallel spherical five-bar linkage. 
         FIG. 18  is a schematic view of another parallel spherical five-bar linkage. 
         FIG. 19  is a pictorial view of another embodiment of the invention. 
         FIG. 20  is a schematic view of the parallel spherical five-bar linkage shown in  FIG. 19 . 
         FIG. 21  is a pictorial view of another embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The detailed description describes the invention as it may be used in a laparoscopic surgery. It is to be understood that this is merely one example of the types of surgeries in which the invention may be used. The invention is not limited to laparoscopy nor to the particular structural configurations shown which are merely examples to aid in the understanding of the invention. Traditional minimally invasive surgery requires a high degree of surgical skill because the surgeon&#39;s hand movements are controlling a surgical tool at a substantial distance from the surgeon&#39;s hands, often requiring unnatural and non-intuitive hand motions. In robotically assisted surgery, a surgeon may operate a master controller to control the motion of surgical instruments at the surgical site. Servo mechanisms may move and articulate the surgical instrument based on the surgeon&#39;s manipulation of the hand input devices. The robotic assistance may allow the surgeon to control the motion of surgical instruments more easily and with greater precision. 
       FIG. 1  shows a schematic plan view of a surgical suite in which the invention may be used. A patient  110  is shown on an operating table  112  undergoing robotically assisted laparoscopic surgery. A surgeon  120  may use a master controller  122  to view a video image of the internal surgical site provided by an endoscopic camera, a laparoscopic camera  104  in the case of abdominal surgery, and control one or more surgical instruments and the endoscopic camera by means of robotic servo mechanisms. The master controller  122  will typically include one or more hand input devices (such as joysticks, exoskeletal gloves, or the like) which are coupled by a servo mechanism to a surgical instrument. 
     A robotic arm  116  that embodies the invention may be used to support and move the laparoscopic camera  104  at the surgical site during robotically assisted surgery. It is desirable to support the laparoscopic camera  104  such that the tool shaft  118  of the instrument and the cannula  106  through which it passes pivot about a center of spherical rotation positioned in space along the length of the tool shaft and cannula. Additional robotic arms  100 ,  102  may support and move surgical instruments. The robotic arms  100 ,  102  for supporting the surgical instruments may be of a different form than the robotic arm  116  for supporting the laparoscopic camera. 
     Each robotic arm  100 ,  102 ,  116  may be supported by an articulated set-up arm  130 ,  132 ,  134 . The set-up arms may be attached to the operating table  112 . Each set-up arm may include a number of segments coupled by joints that provide one or more degrees of freedom that allow the robotic arm to be positioned within a defined range of motion. One or more locking mechanisms may be provided to fix the segments and joints of the set-up arm when the robotic arm is in the desired position. The set-up arms may allow the robotic arms  100 , 102 ,  116  to be fixed at an arbitrary position with respect to the operating table and the patient thereon. Joint angle sensors may be provided on the set-up arm to allow the pose of the set-up arm and the resulting position of the supported robotic arm to be determined. 
     Each robotic arm  100 ,  102 ,  116  may be fixed at a position where the center of spherical rotation is substantially at the access point to the internal surgical site (for example, with the incision that provides entry for the trocar or cannula  106  at the abdominal wall during laparoscopic surgery). An end effector of the surgical instrument  104  supported by the robotic arm  116  can be positioned safely by moving the proximal end of the tool shaft  118  with the robotic arm  116  without imposing dangerous forces against the abdominal wall. 
     Each robotic arm  100 ,  102 ,  116  will support one surgical instrument which may be detachable from the robotic arm. While a variety of surgical instruments  108  may replace the surgical instrument on the robotic arm  100 ,  102  during the course of a single surgery, the laparoscopic camera  104  is generally left in place throughout the course of a surgery. Each robotic arm  116  may support a cannula  106  that passes through an incision into the body of the patient  110 . The tool shaft  118  of the surgical instrument or laparoscopic camera  104  passes through the cannula  106  to the internal surgical site. 
     The robotic arm  116  may support the laparoscopic camera  104  such that the cannula  106  and the tool shaft  118  of the instrument pivot about a center of spherical rotation positioned in space along the length of the cannula  106 . The center of spherical rotation may also be called the remote center of spherical rotation because it is the spherical center of rotational motion for the robotic arm while being spaced apart from the structure of the robotic arm. Motion about the center of spherical rotation may be described as spherical motion because a point at a radial distance from the center of spherical rotation will move on a spherical surface having the radial distance as its radius. The cannula  106  defines an insertion axis that passes through an access point, such as an incision in the abdominal wall of the patient  110 , to the internal surgical site. The tool shaft  118  extends along the insertion axis. 
     Each robotic arm  100 ,  102 ,  116  may include one or more servo motors to move the arm to a desired position. Each robotic arm may include one or more additional servo motors to move the surgical instrument or laparoscopic camera  104  and/or an end effector on the surgical instrument or laparoscopic camera. One or more control cables  124  may provide signals between the computer  123  in the master controller  122  and the servo motors of the robotic arms  100 ,  102 ,  116 . The master controller  122  may include a computer  123  to provide signals that control the servo mechanisms of the robotic arms, the surgical instruments, and laparoscopic camera based on the surgeon&#39;s input and received feedback from the servo mechanisms. 
       FIG. 2  shows an enlarged view of a portion of  FIG. 1  including the patient  110  and the robotic arms  100 ,  102 ,  116 .  FIG. 3  shows an side view of the robotic arm  116  that supports and moves the laparoscopic camera looking from the patient&#39;s left hand side. A schematic crosssection of the patient  110  is shown in the area where the cannula  106  is inserted through an incision  314  in the abdominal wall. The tool shaft  118  of the laparoscopic camera  104  may be seen emerging from the end of the cannula  106  internal to the patient  110 . An end effector  300  at the distal end of the tool shaft  118  may provide lenses and light sources. The lenses and light sources may be optically coupled to a camera and lamps through the tool shaft. The camera and lamps may be supported by the robotic arm  116  at a proximal end of the tool shaft. 
     The robotic arm  116  includes a spherical linkage to support the laparoscopic camera, as will be discussed in greater detail below. The spherical linkage constrains the motion of the insertion axis to rotation about a remote center of spherical rotation  306  which may be located along the length of the cannula  106 . By locating the remote center of spherical rotation  306  at or near the incision  314 , the insertion axis may be moved without significant lateral motion at the incision. 
     The end effector  300  is passed through the cannula  106  to the internal surgical site along the insertion axis. The end effector  300  is supported by the tool shaft  118  and coupled to one or more of cameras, lamps, and servo mechanisms through the tool shaft. Translation of the end effector  300  may be accomplished by translation of the laparoscopic camera  104  with the tool shaft  118  and attached end effector. 
     The end effector  300  may be moved in two additional dimensions by moving the tool shaft  118  about its remote center of spherical rotation  306 . The robotic arm  116  will control these two dimensions of motion by moving the tool shaft  118  to change its angular position in space. The motion of the tool shaft  118  may be described in terms of the position of the insertion axis in a spherical coordinate system. A point in space may be specified in terms of two angles and a distance from a center of a spherical coordinate system. It will be appreciated that only the two angles are necessary to specify an insertion axis that passes through the center of the spherical coordinate system. 
     The robotic arm  116  of the present invention includes a parallel spherical five-bar linkage to move and support the laparoscopic camera  104  such that the tool shaft  118  of the instrument pivots about a remote center of spherical rotation  306  positioned in space along the insertion axis and generally along the length of the cannula  106 . 
       FIG. 4A  shows a simplified, 2-dimensional schematic diagram of a parallel five-bar linkage  400 . This example illustrates the linkage operating in essentially a flat plane. The inventive linkage operates similarly in 3-dimensional space and will be described subsequently. A parallel five-bar linkage is a system of four rigid bars or links  401 ,  402 ,  403 ,  404  pivoted to each other and to a fixed base link  405 . The fixed base link may be referred to as the ground link. It is to be understood that the ground link  405  is fixed only in the sense that it provides a fixed frame of reference for the remaining four links. The ground link  405  may be positioned in space to move the entire five-bar linkage  400 . 
     Each link includes two pivot axes. In the present invention, there is a substantial distance between the two pivot axes on each link. All of the pivot axes  411 ,  412 ,  413 ,  414 ,  415  are perpendicular to a common surface. The links are coupled at the pivot axes such that the links can rotate relative to each other about the pivot axis at which they are coupled. The rotatable coupling of the links at a pivot axis can take any of a variety of forms that limits the motion of the coupled links to rotation about the pivot axis. A number of axes are described for the parallel spherical five-bar linkage. The term “axis” may be used interchangeably to refer to a “joint” or a “pivot” except for the insertion axis. 
     The ground link  405  provides two inboard axes  412 ,  413 . An inboard link  401 ,  404  is pivotally coupled to each of the inboard axes  413 ,  412 . Each inboard link  401 ,  404  has an intermediate axis  414 ,  411  spaced apart from the inboard axis  413 ,  412 . Each inboard link  401 ,  404  is pivotally coupled to an outboard link  402 ,  403  at the intermediate axis  414 ,  411 . Each outboard link  402 ,  403  has an outboard axis  415  spaced apart from the intermediate axis  414 ,  411 . The two outboard links  402 ,  403  are pivotally coupled together at the outboard axis  415 . The outboard axis  415  can be positioned perpendicular to the common surface (in this 2-dimensional illustrative example) anywhere within its range of motion thus providing an endpoint motion at the outboard axis  415  with two degrees of freedom. If motors are provided to rotate each of the inboard links  401 ,  404  about their inboard axis  413 ,  412 , as suggested by the arrows, the outboard axis  415  may be positioned anywhere within its range of motion by rotating the two inboard links with the motors. Conversely, movement of the outboard axis  415  within its range of motion translates into rotation of the two inboard links  401 ,  404  about their inboard axis  413 ,  412 . 
     A linkage that couples rotation of two ground-referenced independent links with two dimensional movement of an axis is a parallel linkage. The rotary motion provided by the two motors to the two inboard links may be described as parallel rotary motion inputs. It should be noted that “parallel” is used here to indicate two inputs that are provided independently of one another and not in the geometric sense to indicate the direction of the inputs. In a parallel linkage, the two independent parallel inputs act upon the same body at some distal point where links coupled to the inputs join to drive the same object or link. 
     It will be appreciated that there are two possible positions for each of the inboard links  401 ,  404  in a five-bar linkage for most of the possible positions of the outboard axis. For example, the inboard links  401 ,  404  could also be positioned as indicated by the dashed lines  401 ′,  404 ′. These positions for the inboard links are generally considered undesirable because the distance between the intermediate axes  414 ′,  411 ′ is reduced and the angle between the outboard links  402 ′,  403 ′ is reduced. It is normally desirable to maximize the distance between the intermediate axes to provide a broad base of support for the outboard axis  415 . It is also normally desirable to have the outboard links  402 ′,  403 ′ as close to being at right angles to one another as possible to support the outboard axis  415 . While the conventional configuration of a five-bar linkage provides good structural support for the outboard axis  415 , the resulting structure requires a substantial amount of space in which to move. The alternative configuration as indicated by the links  401 ′,  402 ′,  403 ′,  404 ′ drawn with dashed lines occupies a smaller area (as projected onto the plane) and is therefore a more compact mechanical configuration. 
       FIG. 4B  shows the parallel five-bar linkage  400  after the inboard links  401 ,  404  have been rotated in a counter-clockwise direction. It may be seen that the outboard axis  415  has been moved generally to the left by the rotation of the inboard links  401 ,  404 . The same position of the outboard axis  415  may also be produced by a similar rotation of the inboard links  401 ′,  404 ′ when the parallel five-bar linkage  400  is in the compact mechanical configuration illustrated by the dashed lines. 
     A spherical linkage for the purposes of this description is a 3-dimensional version of the 2-dimensional mechanical linkage described above. In the 3-dimensional linkage, all pivot axes pass through a common remote center of spherical rotation. “Pass through” includes axes that may be slightly displaced (due to slight errors in manufacturing of the physical links, for example) from the remote center of spherical rotation to accommodate the structural limitations of the robotic arm where the displacement is small enough that the linkage has substantially the same kinematics (characteristic motions) as if the axes actually included the precise, theoretical remote center of spherical rotation. Note that axes that pass through a remote center of spherical rotation are also perpendicular to a spherical surface centered on the remote center of spherical rotation. 
       FIG. 5  shows a schematic diagram of a parallel spherical five-bar linkage  500 . As with the previously discussed planar five-bar linkage, the parallel spherical five-bar linkage  500  is a system of four rigid links  501 ,  502 ,  503 ,  504  pivoted to each other and to a fixed base or ground link  505 . When a parallel five-bar linkage is constructed in a spherical form, all of the pivot axes  511 ,  512 ,  513 ,  514 ,  515  are perpendicular to a common spherical surface and therefore pass through a remote center of spherical rotation  520  of the common spherical surface. In particular, the outboard axis  515  will always pass through the remote center of spherical rotation  520  within its range of motion. Thus, a parallel spherical five-bar linkage  500  provides the desired constrained motion for a surgical instrument such that the tool shaft of the instrument pivots about a remote center of spherical rotation when supported and moved by the outboard axis  515  of the linkage  500 . The motors to move the surgical instrument are placed at the inboard axes  513 ,  512  of the ground link  505 . This avoids the need to move one motor with the other motor as might be required if a serial arm mechanism were used. 
     As shown schematically in  FIG. 6A , it has been discovered that a parallel spherical five-bar linkage  600  can be constrained so that the intermediate axes  614 ,  611  do not assume the conventional configuration where the intermediate axes are at their maximum possible separation and, surprisingly, provide good structural support for the outboard axis  615 . This results in a more compact configuration that is better suited for use as a robotic arm to support an endoscopic camera where it is often necessary to have other robotic arms in close proximity within a limited amount of space as shown by the exemplary system in  FIGS. 1 and 2 . 
     The parallel spherical five-bar linkage  600  shown schematically includes a ground link  605 , two inboard links  601 ,  604  pivotally coupled to the ground link, and two outboard links  602 ,  603  pivotally coupled to each other at one end and to the two inboard links  601 , 604  respectively at an opposite end. The first inboard link  601  is pivotally coupled to the ground link  605  at a first axis of rotation  613 . The first inboard link  601  further includes a first intermediate axis  614  at a first distance from the first axis of rotation  613 . A first outboard link  602  is pivotally coupled to the first inboard link  601  at the first intermediate axis  614 . The first outboard link  602  has an outboard axis  615  at a second distance from the first intermediate axis  614 . 
     The second inboard link  604  is pivotally coupled to the ground link at a second axis of rotation  612 . The second inboard link  604  has a second axis of rotation  612  that is separated from the first axis of rotation  613  by a fourth distance. The second inboard link  604  further includes a second intermediate axis  611  at a fifth distance from the second axis of rotation  612 . A second outboard link  603  is pivotally coupled to the second inboard link  604  at the second intermediate axis  611  and to the first outboard link  602  at the outboard axis  615 . The outboard axis  615  is at a sixth distance from the second intermediate axis  611 . 
     A mechanical stop may limit the rotation of the outboard links  602 ,  603  about the outboard axis  615  such that a minimum angle is maintained between the outboard links, perhaps a minimum angle in the range of 15 to 30 degrees. The links are assembled and constrained such that when the outboard axis  615  lies in a plane  622  that is the perpendicular bisector of the line segment from the first axis of rotation  613  to the second axis of rotation  612 , each of the inboard links  601 ,  604  intersects  624  the bisecting plane  622 . (The double dashed lines are intended to suggest an edge of the portion of the imaginary bisecting plane  622  in the vicinity of the linkage  600 . The dashed circle indicates the point of intersection between each of the inboard links  601 ,  604  and the bisecting plane  622 , which is at the same place for the configuration and pose shown.) When an inboard link intersects the bisecting plane, the axis of rotation and the intermediate axis will lie on opposite sides of the plane. It will be appreciated that this requires the inboard links  601 ,  604  to be able to cross over one another. 
     A specific position assumed by a robotic arm may be referred to as a pose. Placing a robotic arm in a specific position may be referred to as posing the robotic arm. The parallel spherical five-bar linkage may be limited in its motion such that the two intermediate axes  614 ,  611  are relatively close together compared to the maximum separation possible for any given pose of the robotic arm  600 . In particular, each inboard link  601 ,  604  may be in one of two positions for a given position of the outboard axis  615 , except for the singularities where the axis of rotation  612 ,  613 , the intermediate axis  611 ,  614 , and the outboard axis  615  are coplanar. One of the two positions for each of the two inboard links  601 ,  604  will provide the maximum distance between the intermediate axes  611 ,  614 . The pose where each of the two inboard links  601 ,  604  is in the other of the two positions will be described as the compact pose. It will be appreciated that this always results in less than the maximum distance between the intermediate axes  611 ,  614  although it may not result in the minimum possible distance. If the outboard links are constrained to maintain at least a minimum angle between the outboard links and the parallel five-bar spherical linkage is assembled in a compact pose, then the linkage will be limited to a range of compact poses. 
       FIG. 6B  shows the parallel spherical five-bar linkage  600  after one of the inboard links  601  has been rotated in a counter-clockwise direction. It may be seen that the outboard axis  615  has been moved generally to the left by the rotation of the inboard link  601 . It may also been seen that points on the outboard axis  615  are constrained to move on a spherical surface. In the pose shown in  FIG. 6B  neither of the two inboard links  601 ,  604  intersect the bisecting plane  622 . It will be observed that the linkage  600  retains the compact configuration even though it has moved away from the pose where the outboard axis  615  lies in a plane  622  that is the perpendicular bisector of the line segment from the first axis of rotation  613  to the second axis of rotation  612 . 
     Referring now to  FIG. 7A , the inboard links  701 ,  704  and the outboard links  702 ,  703  are illustrated for the embodiment shown in  FIGS. 1-3 . The ground link, which is provided by a motor assembly, is not shown in  FIG. 7  to allow the relationship between the four moving links to be better seen. The two inboard links  701 ,  704  each can rotate about one of the axes of rotation  713 ,  712 . Each inboard link  701 ,  704  is pivotally coupled to an outboard link  702 ,  703  at an intermediate axis  711 ,  714 . The two outboard links  702 ,  703  are pivotally coupled together at an outboard axis  715 . The outboard axis  715  may also be the insertion axis on which the cannula (not shown) is centered. 
     In some embodiments, the first axis  713  and second axis  712  of rotation are driven by motors connected to a controller that provides signals to the motors. A first motor may rotate the first inboard link  701  and a second motor may rotate the second inboard link  704 . The controller may limit the motion of the links so that the parallel five-bar spherical linkage is limited to a range of compact poses. The controller may limit the motion of the inboard links  701 ,  704  such that each of the inboard links  701 ,  704  intersects a perpendicular bisecting plane of the line segment from the first axis of rotation  713  to the second axis of rotation  712  when the outboard axis  715  lies in the bisecting plane. When an inboard link intersects the bisecting plane, the axis of rotation and the intermediate axis will lie on opposite sides of the bisecting plane. The controller may also limit the rotation of the inboard links  701 ,  704  such that a minimum angular distance is maintained between the intermediate axes  711 ,  714 , perhaps a minimum angular distance in the range of 15 to 30 degrees. The controller can provide the same constraint on the range of motion of the links  701 - 704  as a mechanical stop that limits the angle between the outboard links  702 ,  703  at the outboard axis  715 . 
     The parallel spherical five bar linkage may be used to move the outboard axis  715  to a desired position by controllably rotating the inboard links  701 ,  704 , such as by use of a servo motor or stepper motor.  FIG. 7B  illustrates the parallel spherical five bar linkage after one of the inboard links  701  has been rotated in a counter-clockwise direction. The poses of the parallel spherical five bar linkage shown in  FIGS. 7A and 7B  are generally similar to the poses of the parallel spherical five bar linkage shown schematically in  FIGS. 6A and 6B  respectively. 
     In another embodiment, the parallel spherical five bar linkage may be used to sense a position of the outboard axis by determining the bearings of the two inboard axes that result from manipulation of the outboard axis. For example, rotary encoders, or other sensors, may be placed at the first  713  and second  712  axis of rotation of the parallel spherical five bar linkage illustrated by  FIG. 7 . The controller may be replaced by a computer coupled to the two rotary encoders to receive the bearing of each of the inboard links  701 ,  704 . The computer may then compute the position of the outboard axis, which may be manipulated by an operator to provide a position input. It will be appreciated that the outboard axis is constrained to rotate about the remote center of spherical rotation  720  of the spherical linkage. Thus, the parallel spherical five bar linkage may also be used in the control console  122  of  FIG. 1  to receive position input for the outboard axis  715  from the surgeon  120 . The position input will have the same constrained motion as the outboard axis of the robotic arm  116 . 
     Referring now to  FIGS. 8, 9, 10, 11, and 12 , orthogonal views are shown for four sides and an end of the robotic arm  116  used to support the laparoscopic camera in the same pose as shown in  FIGS. 1-3 .  FIG. 8  is a first side view.  FIG. 9  is a bottom view.  FIG. 10  is a second side view of the side opposite the first side.  FIG. 11  is a top view.  FIG. 12  is a view of the end that is to the right in  FIGS. 8-11 . 
       FIGS. 8-12  show a robotic arm  116  that embodies the invention. The robotic arm includes a motor assembly  800  that serves as a ground link and four movable links  701 ,  702 ,  703 ,  704  to provide a parallel spherical five bar linkage. The relationship of the four movable links was discussed above in connection with  FIG. 7 . The motor assembly  800  provides two rotatable shafts  802 ,  804 . Each of the rotatable shafts is coupled to one of the two inboard links  701 ,  704  at one of the axes of rotation  713 ,  712  (shown in  FIG. 7 ). A cannula  106  is supported by the two outboard links  702 ,  703  in a position that is coaxial with the outboard axis  715  (shown in  FIG. 7 ). In this embodiment, the outboard axis  715  is coincident with the insertion axis for the tool shaft of an endoscopic camera. 
       FIG. 13  shows the robotic arm  116  of  FIG. 12  with the two outboard links  702 ,  703  removed so that the relationship between the motor assembly  800  and the two inboard links  701 ,  704  can be seen. The motor assembly  800  and the two inboard links  701 ,  704  are shaped and coupled in a configuration that allows the two inboard links to pass over one another and the motor assembly. It may be seen that the two rotatable shafts  802 ,  804  emerge from the motor assembly  800  in substantially opposite directions in this embodiment. The two rotatable shafts  802 ,  804  may be driven by motors coupled to the shafts through right angle drives, such as a worm and helix drive. 
     One inboard link  701  moves within a spherical “shell” that is closer to the center of spherical motion than the motor assembly. The other inboard link  704  moves within a spherical “shell” that is further from the center of spherical motion than the motor assembly. The motor assembly  800  lies between these two spherical “shells.” Thus one pair of links passes the motor assembly to the inside and the other pair of links passes to the outside. 
       FIG. 14  shows the robotic arm  116 ′ of  FIG. 9  in a pose with the outboard axis  806  close to the motor assembly  800 . (The motor assembly  800  is drawn as though transparent as suggested by the dashed lines to allow the configuration of the movable links  701 ′,  702 ′,  703 ′,  704 ′ to be seen.) One inboard link  701 ′, which is coupled to a first rotatable shaft  802  that extends toward the remote spherical center, and the coupled outboard link  702 ′ have passed to the inside of the motor assembly  800 . These links lie between the motor assembly  800  and the remote spherical center. The other inboard link  704 ′, which is coupled to a second rotatable shaft  804  that extends away from the remote spherical center, and the coupled outboard link  703 ′ have passed to the outside of the motor assembly  800 . The motor assembly  800  lies between these links and the remote spherical center. 
       FIG. 15  shows another robotic arm  1500  that embodies the invention. The motor assembly includes two motors  1502 ,  1504  that are coupled by a support  1506  at a substantial distance from the two axes of rotation  1508 ,  1510 . The motor assembly provides the ground link for the parallel spherical five bar linkage. This configuration of the support  1506  may permit the outboard axis  1512 , which may also be the axis for the cannula  1514 , to pass between the two axes of rotation  1508 ,  1510  and the two motors  1502 ,  1504  to provide a greater range of motion. 
       FIG. 16  shows still another robotic arm  1600  that embodies the invention. The motor assembly includes two motors  1602 ,  1604  that are coupled by a support  1606  to provide the ground link for the parallel spherical five bar linkage. The two axes of rotation  1608 ,  1610  may coincide with axes of the two motors  1602 ,  1604  such that a right angle drive is not required. At least one of the inboard links  1614  has an angular length that is substantially less than the angular distance between the two axes of rotation  1608 ,  1610 . This permits the inboard link  1614  to the motor  1604  that is coupled to the other inboard link  1616 . The other inboard link  1616  may or may not have an angular length that is substantially less than the angular distance between the two axes of rotation  1608 ,  1610  as it may be configured to pass to the inside of the motor  1602 , between the motor and the remote spherical center, that is coupled to the shortened inboard link  1614 . 
       FIG. 17  shows a schematic representation of a robotic arm  1700  that is similar to the robotic arm  1600  shown in  FIG. 16 . A first pair of inboard and outboard links  1701 ,  1702  are pivotally coupled at a first intermediate axis  1714 . A second pair of inboard and outboard links  1704 ,  1703  are pivotally coupled at a second intermediate axis  1711 . The two outboard links  1702 ,  1703  are pivotally coupled at an outboard axis  1715 . One of two motors  1733 ,  1734  is coupled to each of the inboard links  1701 ,  1704  to rotate the inboard link about an axis of rotation  1713 ,  1712 . The two motors are coupled by a ground link  1705  to complete the parallel spherical five-bar linkage. 
     It may be observed that the first pair of inboard and outboard links  1701 ,  1702  may be constructed so that they move within a first spherical shell  1736 . The second pair of inboard and outboard links  1704 ,  1703  move within a second spherical shell  1738  that is not shared with the first spherical shell  1736  except in the vicinity of the outboard axis  1715 . This arrangement permits the inboard links  1701 ,  1704  to cross over one another. The inboard links  1701 ,  1704  in this arrangement may also pass to the inside, closer to the remote center of spherical rotation  1720 , of the ground link  1705  that couples the two motors  1733 ,  1734  if the ground link lies outside the second spherical shell  1738 . 
     The arrangement of the linkage  1700  has the further characteristic that when the first inboard link  1701  lies in the same plane as the ground link  1705  as shown, a first directional vector  1721  from the first axis of rotation  1713  to the first intermediate axis  1714  has the same direction as a second directional vector  1722  from the first axis of rotation  1713  to the second axis of rotation  1712 . Likewise, when the second inboard link  1704  lies in the same plane as the ground link  1705 , a third directional vector  1723  from the second axis of rotation  1712  to the second intermediate axis  1711  has the same direction as a fourth directional vector  1724  from the second axis of rotation  1712  to the first axis of rotation  1713 . 
       FIG. 18  shows a schematic representation of a robotic arm  1800  that is similar to the robotic arm  116  as shown in  FIG. 11 . A first pair of inboard and outboard links  1801 ,  1802  are pivotally coupled at a first intermediate axis  1814 . A second pair of inboard and outboard links  1804 ,  1803  are pivotally coupled at a second intermediate axis  1811 . The two outboard links  1802 ,  1803  are pivotally coupled at an outboard axis  1815 . One of two motors  1833 ,  1834  is coupled to each of the inboard links  1801 ,  1804  to rotate the inboard link about an axis of rotation  1813 ,  1812 . The two motors are coupled by a ground link  1805  to complete the parallel spherical five-bar linkage. 
     In the arrangement shown in  FIG. 18 , the ground link  1805  is between the two inboard links  1801 ,  1804  when all three links are in the same plane. The first pair of inboard and outboard links  1801 ,  1802  may move within a first spherical shell  1836 . The second pair of inboard and outboard links  1804 ,  1803  may move within a second spherical shell  1838  that is not shared with the first spherical shell  1836  except in the vicinity of the outboard axis  1815 . If the ground link is within a third spherical shell  1837  that lies between the first and second spherical shells, then the inboard links  1801 ,  1804  may cross over one another and also cross over the ground link. The arrangement of the linkage  1800  has the same directionality characteristic when the inboard links  1801 ,  1804  lie in the same plane as the ground link  1805  as discussed above for the linkage  1700  shown in  FIG. 17 . 
     In the arrangement shown in  FIG. 18 , the axes of the motors  1833 ,  1834  may be perpendicular to the axes of rotation  1813 ,  1812 . This may be done to allow all or part of the motors to be within the third spherical shell  1837  over which the inboard links  1801 ,  1804  may pass. A drive shaft  1840 ,  1842  may couple the motors  1833 ,  1834  to inboard links  1801 ,  1804  by means of a right angle drive  1844 ,  1846 . In other embodiments, the drive shaft may be coupled to the motors in other arrangements or be a coaxial extension of the motor shaft. The end of the drive shaft  1840 ,  1842  coupled to the motors  1833 ,  1834  may be described as the driven end. In the arrangement shown, it may be observed that a first drive shaft  1840  extends from the driven end toward the remote center of spherical rotation  1820  and a second drive shaft  1842  extends from the driven end away from the remote center of spherical rotation  1820 . 
       FIG. 19  shows a parallel spherical five-bar linkage  1900  that embodies the invention with a structure similar to the robotic arm  116  shown in  FIGS. 7-12 .  FIG. 20  shows a schematic view of the parallel spherical five-bar linkage  1900  of  FIG. 19 . Five pivot axes  1911 - 1915 , about which the four movable links  1901 - 1904  rotate, all pass through a common remote center of spherical rotation  1920 . The first inboard link  1901  and the second inboard link  1904  may be coupled to motors that can rotate the inboard links about the first  1913  and second  1912  axes of rotation. The two motors may be coupled together to form the fifth link (not shown), which is the ground link. 
     The movable links  1901 ,  1902 ,  1903 ,  1904  are shown as having a generally arcuate form. It will be appreciated that the links may have any desired form without affecting the function of the invention. The linkage will function as a spherical linkage as long as the axes of the pivoted connections  1921 ,  1922 ,  1923 ,  1924 ,  1925  all pass substantially through a common remote center of spherical rotation  1920 . Any of the links may have an irregular shape, which may include arcuate segments, to accommodate placement of the pivoted connections such that the links and pivots can pass one another. It will be appreciated that the form of the links is unimportant as long as they support the pivot axes such that they pass substantially through the remote center of spherical rotation  1920 . 
     In the compact configuration of the inventive parallel spherical five bar linkage, it may be desirable to configure the linkage such that the first pair of links  1901 ,  1902  coupling the first axis of rotation  1913  to the outboard axis  1915  can freely pass the second pair of links  1904 ,  1903  coupling the second axis of rotation  1912  to the outboard axis  1915 . Since the only requirement of the parallel spherical five-bar linkage is that all the pivot axes pass substantially through the common remote center of spherical rotation  1920 , the first pair of links  1901 ,  1902  and the first intermediate pivot  1914  may be configured so that a first volume swept out by the first pair does not intersect a second volume swept out by the second pair of links  1904 ,  1903  and the second intermediate pivot  1911 . The only connections between the first and second volumes are in the vicinity of the outboard axis  1915  and the ground link  1905 . The form of the links in the embodiment illustrated by  FIGS. 19 and 20  are an example of a configuration that permits the first pair of links  1901 ,  1902  to pass the second pair of links  1904 ,  1903 . 
       FIG. 21  shows another embodiment of a parallel spherical five-bar linkage  2100  for a robotic arm including two inboard links  2101 ,  2104 , two outboard links, and a ground link provided by the motor assembly  2105 . In comparison with the linkage  1900  of  FIG. 19 , the parallel spherical five-bar linkage  2100  includes an outboard link  2103  having an insertion axis  2119  that is spaced apart from the outboard axis  2115  by an offset distance. Ideally the insertion axis  2119  is coincident with the outboard axis  2115 . Mechanical packaging advantages can be obtained, however, by separating the insertion axis  2119  from the outboard axis  2115 . 
     Preferably the insertion axis  2119  will be placed on the outboard link  2103  further from the intermediate axis  2111  than the outboard axis  2115 . As long as the insertion axis  2119  is perpendicular to the surface of the sphere centered on the remote center of spherical rotation  2120  and therefore passes through the remote center of spherical rotation  2120 , then the insertion axis will have the same kinematic characteristics as the pivot axes  2111 - 2115  of the parallel spherical five-bar linkage  2100 . That is, the insertion axis  2119  will move relative to the remote center of spherical rotation  2120 . The insertion axis  2119  may or may not lie in the plane defined by the intermediate axis  2114  and the outboard axis  2115 . 
     The placement of the insertion axis  2119  outboard from the pivot axes of the parallel spherical five-bar linkage may allow the endoscopic camera (not shown) to be supported and manipulated without interfering with the motion of the linkage  2100 . It may also simplify the construction, installation, removal, and sterile boundary construction of the cannula  2106  and its associated mechanical attachment means. 
     In some embodiments having a spaced apart insertion axis, such as the one illustrated in  FIG. 21 , the insertion axis  2119 , the outboard axis  2115 , and the intermediate axis  2111  may be coplanar. This arrangement may simplify the relationship between the positions of the two inboard links  2101 ,  2104  and the position of the outboard axis  2115 . Note that the insertion axis  2119  can be placed on either of the two outboard links  2102 ,  2103 . 
     The parallel spherical five-bar linkage of the invention may be described using spherical geometry, which is a plane geometry on the surface of a sphere. While the links of the inventive linkage need not lie of the same spherical surface, or any spherical surface, they can be projected onto a common spherical surface for the purpose of describing the linkage. In spherical geometry, distances may be measured as angles because the geometric relationships on the spherical surface are unaffected by changing the radius of the sphere. Angular distance remains the same regardless of the radius of the sphere. 
     Navigation on the surface of the Earth is a common example of spherical geometry. Latitude and longitude as used in global navigation are a familiar system for describing locations and directions in a spherical system. The equator defines the points at 0° latitude. The north pole defines 90° latitude and the south pole defines −90° latitude. Longitude is the angular distance on a circle of constant latitude from an arbitrarily defined line of 0° longitude. Longitude is conventionally expressed as being in the range 180° west to 180° east of the 0° longitude line. Bearings are lines of direction from a point expressed as the angle between the bearing and a line of direction to the north pole. Westerly bearings can be expressed as positive angles and easterly bearings can be expressed as negative angles. The following is a description of an embodiment of the invention expressed in terms of a spherical geometry. 
     Referring again to  FIG. 6 , the first axis of rotation  613  of the first inboard link  601  will be considered as being at 0° latitude and 0° longitude. The second axis of rotation  612  of the second inboard link  604  is shown as being at the same latitude and at a positive (easterly) longitude. The second axis of rotation  612  may be at a fixed position of 55° longitude and 0° latitude, for example. Thus, in this example the ground link has an angular length of 55°. It should be remembered that a fixed position means fixed within the frame of reference of the spherical geometry of the linkage and that the entire linkage with its frame of reference may be freely positioned in space. 
     All of the movable links  601 - 604  may have the same angular length as the ground link. For example, the first intermediate axis  614  may be spaced apart from the first axis of rotation  613  by 55°. The first outboard axis  615  may be spaced apart from the first intermediate axis  614  by 55°. The insertion axis  619  may be spaced apart from the outboard axis  615  by 30°. The second intermediate axis  611  may be spaced apart from the second axis of rotation  612  by 55°. The second intermediate axis  611  may be spaced apart from the outboard axis  615  by 55°. 
     The range of rotation of the inboard links  601 ,  604  about the axes of rotation  613 ,  612  may constrained such that a minimum angle of 15° is maintained between the outboard links  602 ,  603 , for example. The range of rotation of the inboard links  601 ,  604  may further constrained such that when the outboard axis  615  has a longitude of 27.5°, for example, the first inboard link  601  has a negative (easterly) bearing and the second inboard link  604  has a positive (westerly) bearing. The line segment that most directly connects the axis of rotation  613 ,  612  to the intermediate axis  614 ,  611  on the common spherical surface will cross the longitude line of the outboard axis  615  for both of the inboard links. Thus, the inboard links will cross one another when the outboard axis is at or near the center of its east-west range of motion. The constraints on the rotation of the inboard links prevents them from uncrossing when the outboard axis is in the central portion of its east-west range of motion. 
     These dimension are merely by way of example. The invention may be practiced with linkages having substantially different dimensions and substantially different ranges of motion. The invention is only limited by the claims. It may be desirable to use different dimensions and different ranges of motion to adapt the invention for needs of particular types of surgeries which have particular requirements for the range of motion of the insertion axis and for the space occupied by the device through its range of motion. 
     It is to be understood that the inventive parallel spherical five-bar linkage may be embodied in both powered and unpowered configurations. In powered embodiments, devices such as servo motors rotate the inboard links. The parallel spherical five-bar linkage translates those rotations into two dimensional movement of the outboard axis. In unpowered embodiments, two dimensional movement of the outboard axis is translated by the parallel spherical five-bar linkage into rotations of the inboard links. Devices such as rotary encoders may sense the bearings of the inboard links and that information may be used to compute the position of the outboard axis. Constraining the rotation of an intermediate axis as previously described is advantageous in unpowered embodiments because the constraint limits the position of the outboard axis to one of the two possible positions that correspond to the bearings of the inboard links. 
     While certain exemplary embodiments have been described and shown in the accompanying drawings, it is to be understood that such embodiments are merely illustrative of and not restrictive on the broad invention, and that this invention not be limited to the specific constructions and arrangements shown and described, since various other modifications may occur to those ordinarily skilled in the art. Instead, the embodiments of the invention should be construed according to the claims that follow below.