Patent Publication Number: US-2023149109-A1

Title: Curved gimbal link geometry

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to and the benefit of U.S. Provisional Patent Application No. 63/000,247, entitled “Curved Gimbal Link Geometry,” filed Mar. 26, 2020, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     The embodiments described herein relate to control input devices, and more specifically to a master controller which may be used by a user to direct movements of a robot and in particular to direct movements of robotic surgical instruments or tools. 
     Controller mechanisms, e.g., control input devices, allow a user to control functions of various types of mechanisms, instruments, and tools. Teleoperated surgical devices that operate with at least partial computer assistance (“telesurgical systems”), for example, can use various types of medical instruments to perform minimally invasive surgical procedures that reduce damage to healthy tissue of patients. The medical instruments can be connected to slave devices such as slave arms that can be manipulated to perform the surgical procedures. Control of the medical instruments attached to a slave device can be provided to an operator at one or more master control devices, e.g., at a remote operator terminal or station, and/or using a hand control device. Actuators of the slave device can be controlled by the master control device to cause motion or initiate another function of a medical instrument, camera, or other end effector at the slave device that interacts with the patient operating site. In some examples, the master control device at the operator station can be physically manipulated by the operator in one or more degrees of freedom to control the end effector to be moved in coordination with the manipulation of the control device, e.g., to move in corresponding degrees of freedom at the operating site. 
     One of the degrees of freedom of a master control device can include a rotational degree of freedom of a handle of the master control device. For example, in some telesurgical systems, a master control device can include a handle attached to one or more gimbal links that are rotated by the operator via the handle to control a corresponding motion of an end effector in a three-dimensional space. Known systems use a gimbal assembly with multiple links to provide the desired degrees of freedom (DOFs) associated with the associated instrument and instrument end effector. For example, as the handle is moved by the operator, actuators within the one or more gimbal links detect a change in rotational (or translation) position, which can then be translated to initiate a corresponding change in position in the end effector. The actuators can also apply a torque or force to provide resistance feedback to the user consistent with the behavior at the end effector. 
     Because movement of the handle at the master control device is used to produce corresponding movement at the end effector, it is desirable that the movement of the handle via the gimbal assembly be smooth (i.e., not be subject to perceptibly high friction, perceptible irregularities in motion, or undesirable detents or other unpredicted haptic sensations). In addition, for effective control it is desirable that operation of the master control device handle appear weightless (i.e., gravity-free) to the operator. This apparent weightlessness keeps the handle stationary in space to prevent unwanted movement or unwanted haptic feedback to the operator. Therefore, as the operator moves each individual gimbal link in space, and as gravity exerts a changing force on each moving link, an associated changing torque must be applied to each gimbal link to compensate for the torque from gravity. But in addition, since the operator&#39;s gimbal link movement is dynamic and rapid, large gravity-compensating moments of inertia must be applied to maintain the handle&#39;s weightless sensation as the operator moves the gimbal links. 
     Techniques in the related art to counteract inertia associated with one or more gimbal links include employing actuators or other counterbalance mechanism to counteract mass observed and felt by the operator. Additionally, enhanced surgical devices (e.g., with heavier or larger end effectors) may require more powerful actuators in the master control device to ensure that the desired feedback force and torque produced in the master device accurately mimics the force torque which is present at the end effector. But, addition of more powerful motors in the gimbal assembly adds more mass to the gimbal links, which in turn increases each link&#39;s inertia that must be counteracted. Because of the dynamic nature of the master control device operation, and because of the increased weight and inertia of each gimbal link, the operator may struggle with fluidly moving the handle from one position to the next while also contending with the variable output of the actuators and/or counterbalance systems. 
     Thus, a need exists for an improved gimbal assembly of a master control input device to provide less restrictive and more fluid input control and haptic feedback output to the operator, and more specifically a need exists to effectively incorporate more powerful actuators for each gimbal link into a gimbal assembly of a master control input device for a telesurgical system. 
     SUMMARY 
     This summary introduces certain aspects of the embodiments described herein to provide a basic understanding. This summary is not an extensive overview of the inventive subject matter, and it is not intended to identify key or critical elements or to delineate the scope of the inventive subject matter. 
     In some embodiments, a control assembly includes an input handle, a first link, a second link, and an actuator. The input handle is rotatable about a first rotational axis and includes a handle input shaft. The first link includes a first link first end portion, a first link second end portion opposite the first link first end portion, and a joint shaft rotatable about a second rotational axis perpendicular to the first rotational axis and coupled to the first link second end portion. The first link first end portion is coupled to the input handle such that the handle input shaft extends within the first link. The second link includes a second link first end portion, a second link second end portion, and a second link housing. The second link housing extends from the second link first end portion to the second link second end portion. The actuator is mounted within the second link housing and is configured to exert a torque on the joint shaft of the first link about an actuator axis such that the actuator axis and the second rotational axis define an offset angle larger than 0 degrees and less than 90 degrees. 
     In some embodiments, the offset angle is between about 30 degrees and 60 degrees. In some embodiments, a gimbal center point is defined at an intersection of the first rotational axis and the second rotational axis. A gimbal radius is defined by a distance between the gimbal center point and the first end portion of the second link, and at least a portion of the second link housing is curved. A portion of the second link housing has a radius of curvature between about 0.5 to 1.5 times the gimbal radius. In some embodiments, a gimbal center point is defined at an intersection of the first rotational axis and the second rotational axis. A gimbal radius is defined by a distance between the gimbal center point and the first end portion of the second link. A gimbal envelope is defined as a spherical volume surrounding the gimbal center point and characterized by the gimbal radius, and the second link housing includes a curved portion within the gimbal envelope. In some embodiments, a gimbal center point is defined at an intersection of the first rotational axis and the second rotational axis. A gimbal radius is defined by a distance between the gimbal center point and the first end portion of the second link. The second link housing defines an offset gimbal surface extending at least partially along the actuator axis, and the offset gimbal surface intersects an arc defined by the gimbal radius. 
     In some embodiments, the actuator is a motor, and the motor includes a motor shaft extending along the actuator axis and operatively coupled the joint shaft. In some embodiments, the control input assembly includes an actuator transmission mounted within the second link housing. The actuator transmission includes one or more gears and the motor shaft is operatively coupled to the joint shaft via the one or more gears of the actuator transmission. In some embodiments, the one or more gears of the actuator transmission include a bevel gear and a spur gear, and the bevel gear and the spur gear are mounted to a gear shaft. 
     In some embodiments, a gimbal center point is defined at an intersection of the first rotational axis and the second rotational axis. A gimbal radius is defined by a distance between the gimbal center point and the first end portion of the second link. The actuator is a first actuator, the actuator axis is a first actuator axis, the joint shaft is a first joint shaft, and the offset angle is a first offset angle. The second link includes a second joint shaft rotatable about a third rotational axis and is coupled to the second link second end portion of the second link. The control input assembly further includes a third link and a second actuator. The third link includes a third link first end portion coupled to the second link second end portion via the second joint shaft of the second link, a third link second end portion opposite the third link first end portion, and a third link housing extending from the third link first end portion to the third link second end portion. The second actuator is mounted within the third link housing and coupled to exert a torque on the second joint shaft of the second link about a second actuator axis such that the second actuator axis and the third rotational axis of the second joint shaft define a second offset angle larger than 0 degrees and less than 90 degrees. 
     In some embodiments, the gimbal radius is a first gimbal radius and a second gimbal radius is defined by a distance between the gimbal center point and the third link first end portion. The second link housing includes a curved portion having a radius of curvature between about 0.5 to 1.5 times the first gimbal radius. The second link includes a curved portion having a radius of curvature between about 0.5 to 1.5 times the second gimbal radius. 
     In some embodiments, a control input assembly includes an input handle, a first link, a second link, and an actuator. The input handle includes a handle input shaft rotatable about a first rotational axis. The first link includes a first link first end portion, a first link second end portion opposite the first link first end portion, and a joint shaft. The first link first end portion is coupled to the input handle such that the handle input shaft extends within the first link. The first link second end portion is coupled to the joint shaft. The joint shaft defines a second rotational axis and the second rotational axis is perpendicular to the first rotational axis. An intersection of the first rotational axis and the second rotational axis defines a gimbal center point. The second link includes a first end portion, a second end portion, and a middle portion between the first end portion and second end portion. The second link first end portion is coupled to the first link second end portion via the joint shaft. A gimbal radius is defined between the gimbal center point and the second link first end portion. A gimbal envelop is defined as a spherical volume surrounding the gimbal center point characterized by the gimbal radius and the middle portion being curvilinear and entirely within the gimbal envelop. The actuator is mounted within the second link and operatively coupled to exert a torque on the joint shaft of the first link. 
     In some embodiments, the actuator is an electric motor, and the electric motor includes a motor shaft operatively coupled to the joint shaft of the first link. In some embodiments, the control input assembly further includes an actuator transmission mounted within the second link housing. The actuator transmission includes one or more gears, and the motor shaft is operatively coupled to the joint shaft of the first link via the one or more gears of the actuator transmission. In some embodiments, the one or more gears includes a driving gear and a driven gear. The driving gear includes a first number of gear teeth. The driven gear includes a second number of gear teeth and the second number of gear teeth is larger than the first number of gear teeth. In some embodiments, a gear ratio of the driven gear to the driving gear is between about 5:1 to 7:1. In some embodiments, the actuator transmission includes a transmission shaft. The one or more gears includes a first bevel gear, a second bevel gear, a spur gear, and an output gear. The motor shaft includes an end portion, and the first bevel gear is mounted to the end portion of the motor shaft. The first bevel gear is coupled to drive the second bevel gear. The second bevel gear and the spur gear are coupled to the transmission shaft such that the second bevel gear, the spur gear, and the transmission shaft rotate at a common rotational speed. The spur gear is coupled to drive the output gear, the output gear is coupled to the joint shaft such that the spur gear drives rotation of the join shaft. 
     In some embodiments, the actuator transmission includes a transmission shaft. The motor shaft of the electric motor is rotatable about an actuator axis. The transmission shaft is rotatable about a transmission axis. The transmission axis and the actuator axis define an offset angle between about 30 degrees and 60 degrees. In some embodiments, a radius of curvature of the second link middle portion is about 0.75 to 1.25 times the gimbal radius. 
     In some embodiments, a control input assembly includes an input handle, a first link, a second link, a third link, a first actuator, and a second actuator. The input handle includes a handle input shaft rotatable about a first rotational axis. The first link includes a first link first end portion, a first link second end portion, and a first joint shaft rotatable about a second rotational axis perpendicular to the first rotational axis. The first link first end portion is coupled to the input handle such that the handle input shaft extends within the first link. The first link second end portion is coupled to the first joint shaft. The second link includes a second link first end portion, a second link second end portion opposite the second link first end portion, and a second joint shaft, and a second link middle portion extending between the second link first end portion and the second link send end portion. The second link first end portion is coupled to the first link second end portion of via the first joint shaft. The second link middle portion extends in a first direction. The first direction including a component parallel to the first rotational axis and a component parallel to the second rotational axis. The first actuator is coupled to the second link and operably coupled to exert a torque on the first joint shaft of the first link. At least a portion of the first actuator extends within the second link middle portion. The third link includes a third link first end portion, a third link middle portion, a third link second end portion. The third link middle portion extends between the third link first end portion and third link second end portion. The third link first end portion is coupled to the second link second end portion via the second joint shaft. The third link middle portion extends in a second direction. The second direction includes a component parallel to the second rotational axis and a component parallel to the third rotational axis. The second actuator is coupled to the third link and operably coupled to exert a torque on the second link second joint shaft. At least a portion of the second actuator extends within the third link middle portion. 
     In some embodiments, the first actuator drives rotation about a first actuator axis, and the second actuator drives rotation about a second actuator axis. The first actuator axis and the second rotational axis define a first offset angle larger than 0 degrees and less than 90 degrees. The second actuator axis and the third rotational axis define a second offset angle larger than 0 degrees and less than 90 degrees. In some embodiments, the first offset angle is between about 25 degrees and 65 degrees, and the second offset angle is between about 15 degrees and 75 degrees. 
     In some embodiments, a control input assembly includes a gimbal link, a transmission housing, a gear shaft, an output gear, an actuator, an input gear, and a joint shaft. The gimbal link includes a first end portion and a second end portion, the transmission housing being mounted to the first end portion of the gimbal link. The joint shaft is rotatably supported by the first end portion of the gimbal link. The transmission housing includes a gear shaft support portion and an actuator support portion. The gear shaft is rotatably supported by the gear shaft support portion of the transmission housing to rotate about a gear axis. The output gear is mounted on the gear shaft. The actuator includes a motor, a motor body, and a motor shaft rotatable about an actuator axis. At least a portion of the motor body is mounted to the actuator support portion of the transmission housing. The input gear is mounted on the motor shaft and meshed with the output gear to transfer torque to the joint shaft. The gear axis and the actuator axis define an offset angle larger than 0 degrees and less than 90 degrees. 
     In some embodiments, the offset angle is between about 45 degrees and 85 degrees. In some embodiments, the input gear comprises a first number of gear teeth, the output gear comprises a second number of gear teeth, and the second number of gear teeth is larger than the first number of gear teeth. In some embodiments, a gear ratio of the output gear to the input gear is between about 5:1 to 7:1. In some embodiments, a gear ratio of the output gear to the input gear is about 6.9:1. 
     In some embodiments, a control input assembly includes a first gimbal link, a second gimbal link and a motor. The first gimbal link includes a distal end portion. The second gimbal link includes a proximal end portion coupled to the distal end portion of the first gimbal link to rotate about a gimbal link axis of rotation with reference to the first gimbal link. The motor is mounted to one of the first gimbal link or the second gimbal link. The motor includes a motor shaft coupled to drive the second gimbal link about the gimbal link axis of rotation. The motor shaft rotates about a motor shaft axis of rotation, the motor shaft axis being at an acute angle relative to the gimbal link axis of rotation. In some embodiments, the first gimbal link comprises a curved portion and the motor is mounted within the curved portion of the first gimbal link. The first gimbal link includes a proximal end portion and the curved portion of the first gimbal link extends between the proximal and distal end portions of the first gimbal link. 
     In some embodiments, the second gimbal link includes a curved portion and the motor is mounted within the curved portion of the second gimbal link. The second gimbal link includes a distal end portion and the curved portion of the second gimbal link extends between the proximal and distal end portions of the second gimbal link. In some embodiments, the control input assembly includes an operator handle coupled to the second gimbal link. In some embodiments the control input assembly is embodied in a control unit of a telesurgical system. 
     Other control input devices, related components, medical device systems, and/or methods according to embodiments will be or become apparent to one with skill in the art upon review of the following drawings and detailed description. It is intended that all such additional control input devices, related components, medical device systems, and/or methods included within this description be within the scope of this disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a plan view of a minimally invasive teleoperated medical system according to an embodiment being used to perform a medical procedure such as surgery. 
         FIG.  2    is a perspective view of a user control console of the minimally invasive teleoperated surgery system shown in  FIG.  1   . 
         FIG.  3    is a perspective view of an auxiliary unit of the minimally invasive teleoperated surgery system shown in  FIG.  1   . 
         FIG.  4    is a front view of a manipulator unit, including a plurality of instruments, of the minimally invasive teleoperated surgery system shown in  FIG.  1   . 
         FIG.  5    is a diagrammatic illustration of an input control device according to an embodiment. 
         FIG.  6    is a diagrammatic illustration of an input control device according to an embodiment. 
         FIG.  7    is a front perspective view of an input control device according to an embodiment. 
         FIG.  8    is a front view of the input control device of  FIG.  7   . 
         FIG.  9    is a front view of the input control device of  FIG.  7    with the handle and first link hidden. 
         FIG.  10    is a rear perspective view of the input control device of  FIG.  7    in a first orientation. 
         FIG.  11    is a rear perspective view of the input control device of  FIG.  7    in a second orientation. 
         FIG.  12    is a rear perspective view of the input control device of  FIG.  11    with housing covers hidden. 
         FIG.  13    is a side view of a gimbal link of the input control device of  FIG.  7   . 
         FIG.  14    is an exploded view of the gimbal link shown in  FIG.  13   . 
         FIG.  15    is a top view of a portion of the gimbal link shown in  FIG.  13   . 
         FIG.  16    is a top view of a transmission housing of the gimbal link shown in  FIG.  14   . 
         FIG.  17    is a perspective view of an actuator and transmission arrangement of the gimbal link shown in  FIG.  13   . 
     
    
    
     DETAILED DESCRIPTION 
     The embodiments described herein can advantageously be used in a wide variety of teleoperated surgical systems and allow a user to control functions of various types of mechanisms, instruments, and tools. 
     As used herein, the term “about” when used in connection with a referenced numeric indication means the referenced numeric indication plus or minus up to 10 percent of that referenced numeric indication. For example, the language “about 50” covers the range of 45 to 55. Similarly, the language “about 5” covers the range of 4.5 to 5.5. 
     As used in this specification and the appended claims, the word “distal” refers to direction towards a work site, and the word “proximal” refers to a direction away from the work site. Thus, for example, the end of a tool that is closest to the target tissue would be the distal end of the tool, and the end opposite the distal end (i.e., the end manipulated by the user or coupled to the actuation shaft) would be the proximal end of the tool. 
     Further, specific words chosen to describe one or more embodiments and optional elements or features are not intended to limit the invention. For example, spatially relative terms—such as “beneath”, “below”, “lower”, “above”, “upper”, “proximal”, “distal”, and the like—may be used to describe the relationship of one element or feature to another element or feature as illustrated in the figures. These spatially relative terms are intended to encompass different positions (i.e., translational placements) and orientations (i.e., rotational placements) of a device in use or operation in addition to the position and orientation shown in the figures. For example, if a device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be “above” or “over” the other elements or features. Thus, the term “below” can encompass both positions and orientations of above and below. A device may be otherwise oriented (e.g., rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. Likewise, descriptions of movement along (translation) and around (rotation) various axes includes various spatial device positions and orientations. The combination of a body&#39;s position and orientation define the body&#39;s pose. 
     Similarly, geometric terms, such as “parallel”, “perpendicular”, “round”, or “square”, are not intended to require absolute mathematical precision, unless the context indicates otherwise. Instead, such geometric terms allow for variations due to manufacturing or equivalent functions. For example, if an element is described as “round” or “generally round,” a component that is not precisely circular (e.g., one that is slightly oblong or is a many-sided polygon) is still encompassed by this description. 
     In addition, the singular forms “a”, “an”, and “the” are intended to include the plural forms as well, unless the context indicates otherwise. The terms “comprises”, “includes”, “has”, and the like specify the presence of stated features, steps, operations, elements, components, etc. but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, or groups. 
     Unless indicated otherwise, the terms apparatus, medical device, instrument, and variants thereof, can be interchangeably used. 
     Aspects of the invention are described primarily in terms of an implementation using a da Vinci® Surgical System, commercialized by Intuitive Surgical, Inc. of Sunnyvale, Calif. Examples of such surgical systems are the da Vinci Xi® Surgical System (Model IS4000), da Vinci X® Surgical System (Model IS4200), and the da Vinci Si® Surgical System (Model IS3000). Knowledgeable persons will understand, however, that inventive aspects disclosed herein may be embodied and implemented in various ways, including computer-assisted, non-computer-assisted, and hybrid combinations of manual and computer-assisted embodiments and implementations. Implementations on da Vinci® Surgical Systems (e.g., the Model IS4000, the Model IS3000, the Model IS2000, the Model IS1200) are merely presented as examples, and they are not to be considered as limiting the scope of the inventive aspects disclosed herein. As applicable, inventive aspects may be embodied and implemented in both relatively smaller, hand-held, hand-operated devices and relatively larger systems that have additional mechanical support. 
       FIG.  1    is a plan view illustration of a computer-assisted teleoperation system. Shown is a medical device, which is a Minimally Invasive Robotic Surgical (MIRS) system  500  (also referred to herein as a minimally invasive teleoperated surgery system), used for performing a minimally invasive diagnostic or surgical procedure on a patient P who is lying on an operating table  505 . The system can have any number of components, such as a user control unit  900  for use by a surgeon or other skilled clinician S during the procedure. The MIRS system  500  can further include a manipulator unit  530  (which may be referred to as a surgical robot), and an optional auxiliary equipment unit  520 . The manipulator unit  530  can include an arm assembly  540  and a tool assembly removably coupled to the arm assembly  540 . The manipulator unit  530  can manipulate at least one removably coupled instruments  550  (also referred to herein as a “tool”) through a minimally invasive incision in the body or natural orifice of the patient P while the surgeon S views the surgical site and controls movement of the instrument  550  through the user control unit  900 . An image of the surgical site is obtained by an endoscope (not shown), such as a stereoscopic endoscope, which can be manipulated by the manipulator unit  530  to orient the endoscope. The auxiliary equipment unit  520  can be used to process the images of the surgical site for subsequent display to the Surgeon S through the user control unit  900 . The number of instruments  550  used at one time will generally depend on the diagnostic or surgical procedure and the space constraints within the operating room, among other factors. If it is necessary to change one or more of the instruments  550  being used during a procedure, an assistant removes the instrument  550  from the manipulator unit  530  and replaces it with another instrument  550  from a tray  510  in the operating room. Although shown as being used with the instruments  550 , any of the instruments described herein can be used with the MIRS  500 . For example, the instruments  550  can be, but are not limited to, clamps, graspers, scissors, scalpel, blade, staplers, hooks, suction irrigation tools, clip appliers, needle holders, electrocautery devices, and the like. 
       FIG.  2    is a perspective view of the user control unit  900 . The user control unit  900  includes a viewer with a left eye display  912  and a right eye display  914  for presenting the surgeon S with a coordinated stereo view of the surgical site that enables depth perception. The user control unit  900  further includes one or more input control devices  1000  (also referred to as master controllers), which in turn cause the manipulator unit  530  (shown in  FIG.  1   ) to manipulate one or more tools. The input control devices  1000  provide at least the same degrees of freedom as instruments  550  with which they are associated to provide the surgeon S with telepresence, or the perception that the input control devices  1000  are integral with (or are directly connected to) the instruments  550 . For example, each input control device  1000  includes a handle  1120  that can be gripped and repositioned by the surgeon S. The handle  1120  is attached to a first gimbal link  1040 , a second gimbal link  1060 , and a third gimbal link  1080 . The handle  1120  is rotatably mounted to the first gimbal link  1040  about axis A 1 , the first gimbal link  1040  is rotatably mounted to the second gimbal link  1060  about axis A 2 , and the third gimbal link  1080  is rotatably mounted to a base  1130  of the user control unit  900 . In this manner, the user control unit  900  provides the surgeon S with a strong sense of directly controlling the instruments  550 . The handle  1120  and/or one or more of the gimbal links  1040 ,  1060 ,  1080  includes sensors and/or actuators (not shown) to detect a change in position and orientation of the handle  1120  in three-dimensional space, which is, in turn, used to move an instrument  550  in use in a corresponding manner. 
     In some embodiments, the handles  1120  further include one or more buttons (not shown) used to control a function of the instrument  550 , such as a grasping or cutting function, for example. To this end, position, force, and tactile feedback sensors (not shown) may be employed to transmit position, force, and tactile sensations from the instruments  550  back to the surgeon&#39;s hands through the input control devices  1000 . In some embodiments, the user control unit  900  includes one or more foot controls  920  positioned below the input control devices  1000 . The foot controls  920  can be depressed, slid, and/or otherwise manipulated by a user&#39;s feet to input various commands to the teleoperated system while the surgeon S is sitting behind the user control unit  900 . 
     The user control unit  900  is shown in  FIG.  1    as being in the same room as the patient P so that the surgeon S can directly monitor the procedure, be physically present if necessary, and speak to an assistant directly rather than over the telephone or other communication medium. In some embodiments, the user control unit  900  and the surgeon S can be in a different room, a completely different building, or other remote location from the patient allowing for remote surgical procedures. 
       FIG.  3    is a perspective view of the auxiliary equipment unit  520 . The auxiliary equipment unit  520  can be coupled with the endoscope (not shown) and can include one or more processors to process captured images for subsequent display, such as via the user control unit  900 , or on another suitable display located locally and/or remotely. For example, where a stereoscopic endoscope is used, the auxiliary equipment unit  520  can process the captured images to present the surgeon S with coordinated stereo images of the surgical site via the left eye display  912  and the right eye display  914 . Such coordination can include alignment between the opposing images and can include adjusting the stereo working distance of the stereoscopic endoscope. As another example, image processing can include the use of previously determined camera calibration parameters to compensate for imaging errors of the image capture device, such as optical aberrations. 
       FIG.  4    shows a front perspective view of the manipulator unit  530 . The manipulator unit  530  includes the components (e.g., arms, linkages, motors, sensors, and the like) to provide for the manipulation of the instruments  550  and an imaging device (not shown). For example, the imaging device is a stereoscopic endoscope, used for the capture of images of the site of the procedure. Specifically, the instruments  550  and the imaging device can be manipulated by teleoperated mechanisms having a number of joints. Moreover, the instruments  550  and the imaging device are positioned and manipulated through incisions or natural orifices in the patient P in a manner such that a software and/or kinematic remote center of motion is maintained at the incision or orifice. In this manner, the incision size can be minimized. 
       FIG.  5    is a schematic illustration of an input control device  2000  according to an embodiment. The input control device  2000  includes an input handle  2120 , a first link  2040  (which functions as a first gimbal link), a second link  2060  (which functions as a second gimbal link), and a base portion  2130 . The input handle  2120  includes a handle portion  2121 , a first handle input  2122 , a second handle input  2123 , and a handle input shaft  2124 . The handle input shaft  2124  defines a first rotational axis A 1  (which may function as a roll axis; the term roll is arbitrary) and is rotatably coupled to the first link  2040 . The handle portion  2121  is supported on the handle input shaft  2124  and is configured to be rotated relative to the first link  2040  about the first rotational axis A 1 . In some embodiments, the input shaft  2124  extends at least partially within the first link  2040 . The first handle input  2122  and the second handle input  2123  can be manipulated to produce a desired action at the end effector (not shown). For example, in some embodiments, the first handle input  2122  and the second handle input  2123  can be squeezed together to produce a gripping movement at the end effector. In other embodiments, however, the input handle  2120  need not include the handle inputs. 
     The first link  2040  includes a first end portion  2041 , a second end portion  2042 , and a first joint shaft  2045 . The second link  2060  includes a first end portion  2061 , a second end portion  2062 , and a second joint shaft  2065 . The second end portion  2042  of the first link  2040  is rotatably coupled to the first end portion  2061  of the second link  2060  via the first joint shaft  2045 . Similarly stated, the second end portion  2042  of the first link  2040  is coupled to the first end portion  2061  of the second link  2060  such that the first joint shaft  2045  extends within the second link  2060 . The first joint shaft  2045  defines a second rotational axis A 2  (which may function as a yaw axis; the term yaw is arbitrary). In some embodiments, the second rotational axis A 2  is perpendicular to the first rotational axis A 1 . An intersection of the first rotational axis A 1  and the second rotational axis A 2  defines a gimbal center GC. In some embodiments, the distance from the gimbal center GC to the first end portion  2061  of the second link  2060  defines a gimbal radius R G . 
     The second link  2060  further includes a link housing  2063  extending between the first end portion  2061  and the second end portion  2062 . The second link  2060  is rotatably coupled to the base portion  2130  via the second joint shaft  2065 . Similarly stated, the second link  2060  is coupled to the base portion  2130  such that the second joint shaft  2065  extends within the base portion  2130 . The second joint shaft  2065  defines a third rotational axis A 3  (which may function as a pitch axis; the term pitch is arbitrary). In some embodiments, the third rotational axis A 3  is perpendicular to the second rotational axis A 2 . In some embodiments, as shown in  FIG.  5   , the first rotational axis A 1  and the third rotational axis A 3  are oriented co-linearly, however, it will be appreciated by one skilled in the art that the first rotational axis A 1  and the third rotational axis A 3  can be positioned to intersect one another when the first link  2040  is rotated about the second rotational axis A 2  from the initial position (which may also be referred to as an initial pose) shown in  FIG.  5   . 
     In some embodiments, the input control device  2000  includes an actuator  2150  mounted in the second link  2060  within the link housing  2063 . The actuator  2150  defines an actuator axis A M . The actuator  2150  is configured to exert a torque on or receive torque from the first joint shaft  2045 . In some embodiments, the actuator  2150  is a motor  2151  that includes a motor shaft  2152 . As shown, the motor shaft  2152  is operatively coupled to the first joint shaft  2045  by a driving gear  2154  and a driven gear  2155 . The driving gear  2154  is fixed to the motor shaft  2152  and is configured to rotate together with the motor shaft  2152 . The driven gear  2155  is configured to mesh with and be driven by the driving gear  2154 . In some embodiments, the driving gear  2154  includes a first number of teeth, the driven gear  2155  includes a second number of teeth, and the second number of teeth is greater than the first number of teeth. In some embodiments, a gear ratio of the driven gear  2155  to the driving gear  2154  is about 5:1 to about 7:1. In some embodiments, the driving gear  2154  is a straight spur gear or a bevel gear. In some embodiments, the driven gear  2155  is a bevel gear. Although directly driven gears are shown, it will be appreciated that a pulley and belt system, gear and chain system, or other transmission systems can be employed. 
     In some embodiments, the motor shaft  2152  extends along the actuator axis A M . In some embodiments, one or more encoders or sensors are provided to detect a rotational position of the motor shaft  2152  and/or the first joint shaft  2045 . As shown, the actuator axis A M  and the second rotational axis A 2  define an offset angle θ that is less than 90 degrees. In some embodiments, the offset angle θ is less than about 60 degrees. In some embodiments, the offset angle θ is between about 20 degrees and 70 degrees. In some embodiments, the offset angle θ is between about 25 degrees and 65 degrees. In some embodiment the offset angle θ is between about 30 degrees and 60 degrees. 
     In use, the input control device  2000  can be manipulated by a user, such as the surgeon S, to control a surgical instrument (such as the instruments  550  described herein). As the surgeon S grips and repositions the handle portion  2121  about one or more of the first rotational axis A 1 , the second rotational axis A 2 , and/or the third rotational axis A 3 , a corresponding instrument or tool connected to a user control unit (such as the user control unit  900  described herein) and controlled by the input control device  2000  can be repositioned in a corresponding manner. For example, if the tool selected is a grasper that includes a vertically oriented tool shaft and an end effector, clockwise rotation of the handle portion  2121  about the second rotational axis A 2  may cause the end effector to rotate clockwise about a longitudinal axis of the tool shaft. 
     As shown in  FIG.  5   , the gravitation force F g  acts in a downward direction in the diagram. It will be appreciated that when the second link  2060  is rotated relative to the third rotational axis A 3 , the gravitational force F g  will act on the handle portion  2121  and cause the first link  2040  to rotate about the second rotational axis A 2 , for example. In other words, as the second link  2060  is moved out of the initial position (e.g., resting position) shown in  FIG.  5   , the gravitation force F g  will act on one or more of the input handle  2120 , the first link  2040 , and the second link  2060 . In some embodiments, the actuator  2150  can be operated to output a torque to the first joint shaft  2045  to counteract the torque applied by the gravitational force F g  on the handle portion  2121 . As such, once the surgeon S has moved the handle portion  2121  to a particular position and orientation, the actuator  2150  can be operated to hold the input control device  2000  at that last position and orientation placed by the surgeon S. The tool or instrument at the patient operating site (such as instrument  500  described herein) can also be held at a corresponding position and orientation until the surgeon S provides a new input. By offsetting the gravitational forces acting on the input control device  2000 , the surgeon S is provided with a more natural and less restrictive way of controlling the instrument  500 . As a result the input control devices described herein are operable to provide the surgeon S with a more fluid and weightless experience by isolating forces acting on the input control device  2000  if left unassisted. In doing so, the input control devices described herein may be able to provide improved fine motor control of the instrument  500  and/or reduce fatigue experienced by the surgeon S during operation. In some embodiments, the actuator  2150  can be operated to output a torque to resist movement input by the surgeon S to simulate a condition observed at the tool. For example, if the tool at the patient operating site is controlled by the surgeon S to move from open space to contacting a target tissue, the actuator  2150  can produce a torque to simulate the contact and resistance observed by the tool when the tool contacts the target tissue and/or when the tool is pressed into the target tissue. In other words, the actuator  2150  is configured to provide feedback to the surgeon S through the input control device  2000  based on inputs or conditions observed by the tool. 
     To further improve the dynamics of master controllers, reduction in mass and moment of inertia (I=m·r 2 ) at the input control devices minimizes the external forces that would need to be offset, thereby reducing the strain or output requirements on the actuator  2150 . Additionally or alternatively, the reduction in mass and moment of inertia can enable smaller actuators to be employed thereby further reducing the total mass of the input control devices. For example, in conventional input control devices with gimbal links, the gimbal links typically include L-shaped enclosures such that components housed therein (e.g., actuators) are spaced substantially away from a gimbal center. As contemplated in the present disclosure, reduction in mass and moment of inertia can be achieved by moving a center of mass of the gimbal links and components housed therein (e.g., the actuator  2150 ) towards a gimbal center GC. As shown, the second link  2060  includes a single diagonal leg (e.g., hypotenuse) to reduce the total length and mass associated with the gimbal link. The location of the diagonal link further improves moment of inertia by moving a center of gravity closer to the gimbal center and the axes about which the second link  2060  rotates. Furthermore, components that would otherwise be housed in one leg of the L-shaped leg can be housed within the diagonal leg, further improving the moment of inertia. 
     In some embodiments, the link housing  2063  of the second link  2060  extends at an angle relative to the second rotational axis A 2  and the rotational axis A 3 . In some embodiments, the link housing  2063  extends parallel along the actuator axis A M . In some embodiments, the link housing  2063  extends at an angle of between about 20 degrees and 70 degrees relative to the second rotational axis A 2 . In some embodiments, at least a portion of the link housing  2063  is spaced a distance away from the gimbal center GC, the distance being between 0.75 to 1.25 times the gimbal radius R G . For example, as shown in  FIG.  5   , a distance D is about 1.25 times the gimbal radius R G . At least a portion of the link housing  2063  is spaced within a distance of between 0.75 to 1.25 times the gimbal radius R G . In some embodiments, the link housing  2063  includes an offset gimbal surface extending along the actuator axis A M , and the offset gimbal surface intersects an arc defined by the gimbal radius R G . 
     In some embodiments, a link of an input control device can include a curved portion. For example,  FIG.  6    is a schematic illustration of an input control device  3000  according to an embodiment. The input control device  3000  includes an input handle  3120 , a first link  3040 , a second link  3060 , a third link  3080 , and a base portion  3130 . The input handle  3120  includes a handle portion  3121 , a first handle input  3122 , a second handle input  3123 , and a handle input shaft  3124 . The handle input shaft  3124  defines a first rotational axis A 1  (which may function as a roll axis; the term roll is arbitrary) and is rotatably coupled to the first link  3040 . The handle portion  3121  is supported on the handle input shaft  3124  and is configured to be rotated relative to the first link  3040  about the first rotational axis A 1  In some embodiments, the input shaft  3124  extends at least partially within the first link  3040 . The first handle input  3122  and the second handle input  3123  can be manipulated to produce a desired action at the end effector (not shown). For example, in some embodiments, the first handle input  3122  and the second handle input  3123  can be squeezed together to produce a gripping movement at the end effector. In other embodiments, however, the input handle  3120  need not include the handle inputs. 
     The first link  3040  includes a first end portion  3041 , a second end portion  3042 , and a first joint shaft  3045 . The second link  3060  includes a first end portion  3061 , a second end portion  3062 , and a second joint shaft  3065 . The third link  3080  includes a first end portion  3081 , a second end portion  3082 , and a third joint shaft  3085 . The second end portion  3042  of the first link  3040  is rotatably coupled to the first end portion  3061  of the second link  3060  via the first joint shaft  3045 . Similarly stated, the second end portion  3042  of the first link  3040  is coupled to the first end portion  3061  of the second link  3060  such that the first joint shaft extends within the second link  3060 . The first joint shaft  3045  defines a second rotational axis A 2  (which may function as a yaw axis; the term yaw is arbitrary). The second rotational axis A 2  is perpendicular to the first rotational axis A 1 . An intersection of the first rotational axis A 1  and the second rotational axis A 2  defines a gimbal center GC. In some embodiments, the distance from the gimbal center GC to the first end portion  3061  of the second link  3060  defines a first gimbal radius R G1 . 
     The second link  3060  further includes a second link housing  3063  extending between the first end portion  3061  and the second end portion  3062 . The second end portion  3062  of the second link  3060  is rotatably coupled to the first end portion  3081  of the third link  3080  via the second joint shaft  3065 . Similarly stated, the second link  3060  is coupled to the third link  3080  such that the second joint shaft  3065  extends within the third link  3080 . The second joint shaft  3065  defines a third rotational axis A 3  (which may function as a pitch axis; the term pitch is arbitrary) and the third rotational axis A 3  is perpendicular to the second rotational axis A 2 . In some embodiments, as shown in  FIG.  6   , the first rotational axis A 1  and the third rotational axis A 3  are oriented co-linearly. However, it will be appreciated by one skilled in the art that the first rotational axis A 1  and the third rotational axis A 3  can be positioned to intersect one another when the first link  3040  is rotated about the second rotational axis A 2  from the initial position shown in  FIG.  6   , for example. 
     The third link  3080  further includes a third link housing  3083  extending between the first end portion  3081  and the second end portion  3082 . The second end portion  3082  of the third link  3080  is rotatably coupled to the base portion  3130  via the third joint shaft  3085 . Similarly stated, the third link  3080  is coupled to the base portion  3130  such that the third joint shaft  3085  extends within the base portion  3130 . The third joint shaft  3085  defines a fourth rotational axis A 4 . The fourth rotational axis A 4  is perpendicular to the third rotational axis A 3 . In some embodiments, the distance from the gimbal center GC to the first end portion  3081  of the third link  3080  defines a second gimbal radius R G2 . 
     In some embodiments, as shown in  FIG.  6   , the second rotational axis A 2  and the fourth rotational axis A 4  are oriented co-linearly, however, it will be appreciated by one skilled in the art that the second rotational axis A 2  and the fourth rotational axis A 4  can be positioned to intersect one another when the second link  3060  is rotated about the third rotational axis A 3  from the initial position shown in  FIG.  6   , for example. 
     In some embodiments, the input control device  3000  includes a first actuator  3150  mounted in the second link  3060  within the second link housing  3063 . The first actuator  3150  is configured to exert a torque on or receive torque from the first joint shaft  3045 . In some embodiments, the first actuator  3150  is a motor  3151  (e.g., electric motor) that includes a motor shaft  3152 . The motor shaft  3152  is operatively coupled to the first joint shaft  3045 . The input control device  3000  includes a first actuator transmission  3153  mounted within the second link  3060 . As shown, the first actuator transmission  3153  is coupled to the first end portion  3061  of the second link  3060 . In some embodiments, the first actuator transmission  3153  includes a driving member and a driven member (not shown). In some embodiments, the driving member is fixed to the motor shaft  3152  and configured to rotate together with the motor shaft  3152 . The driven member can be configured to engage and be driven by the driving member, which in turn drives the first joint shaft  3045 . 
     In some embodiments, the input control device  3000  includes a second actuator  3160 . The second actuator  3160  is mounted in the third link  3080  within the third link housing  3083 . The second actuator  3160  is configured to exert a torque on or receive torque from the second joint shaft  3065 . In some embodiments, the second actuator  3160  is a motor  3161  that includes a motor shaft  3162 . The motor shaft  3162  is operatively coupled to the second joint shaft  3065 . The input control device  3000  includes a second actuator transmission  3163  mounted within the third link  3080 . As shown, the second actuator transmission  3163  is coupled to the first end portion  3081  of the third link  3080 . In some embodiments, the second actuator transmission  3163  includes a driving member and a driven member (not shown). In some embodiments, the driving member is fixed to the motor shaft  3162  and configured to rotate together with the motor shaft  3162 . The driven member can be configured to engage and be driven by the driving member, which in turn drives the second joint shaft  3065 . 
     As shown in  FIG.  6   , if the gravitation force F g  acts downwardly in the diagram, it will be appreciated that as the second link  3060  is rotated relative to the third rotational axis A 3 , the gravitational force F g  will act on the handle portion  3121  and cause the first link  3040  to rotate about the second rotational axis A 2 , for example. In other words, as the second link  3060  is moved out of the initial position (e.g., resting position) shown in  FIG.  6   , the gravitation force F g  will act on one or more of the input handle  3120 , the first link  3040 , the second link  3060 , and the third link  3080 . Similar to the actuator  2150  described above, the first actuator  3150  and/or the second actuator  3160  can be operated to output torque to counteract the gravitational force F g  applied on one or more of the first link  3040 , the second link  3060 , and the input handle  3120 . For example, if the second link  3060  is rotated away from the resting position, the actuator  3160  can be operated to output a torque to the second joint shaft  3065  to counteract the torque applied by the gravitational force F g  on the first link  3040 , the second link  3060 , and the input handle  3120 . As such, once the surgeon S has moved the handle portion  3121  to a particular position and orientation, the actuator  3150  can be operated to hold the input control device  3000  at that last position and orientation placed by the surgeon S. The tool or instrument at the patient operating site (such as instrument  500  described herein) can also be held at a corresponding position and orientation until the surgeon S provides a new input. By offsetting the gravitational forces acting on the input control device  3000 , the surgeon S is provided with a more natural and less restrictive way of controlling the instrument  500 . As a result the input control devices described herein are operable to provide the surgeon S with a more fluid and weightless experience by isolating forces acting on the input control device  3000  if left unassisted. In doing so, the input control devices described herein may be able to provide improved fine motor control of the instrument  500  and/or reduce fatigue experienced by the surgeon S during operation. In some embodiments, the first actuator  3150  and/or the second actuator  3160  can be operated to output a torque to resist movement input by the surgeon S to simulate a condition observed at the tool and provide feedback to the surgeon S. 
     As described herein, the dynamics of master controllers can be improved by reducing the overall weight and moment of inertia at the input control devices. As shown in  FIG.  6   , the second link housing  3063  is curved and extends between the first end portion  3061  of the second end portion  3062 . In some embodiments, the second link housing  3063  has a radius of curvature that is between about 0.5 to 1.5 times the first gimbal radius R G1 . In some embodiments, the second link housing  3063  has a radius of curvature that is between about 0.75 to 1.25 times the first gimbal radius R G1 . For example, as shown in  FIG.  6   , a distance D 1  is about 1.25 times the first gimbal radius R G1 . Similarly stated, a curvature of the second link housing  3063  need not follow a circular curvature. Instead, the curved portion can include a blended curve defined by a variable or multiple radii of curvature. In some embodiments, a first gimbal envelope is defined as a spherical volume centered about the gimbal center GC and characterized by a first envelope radius. In some embodiments, the first envelope radius is between about 0.75 to 1.25 times the first gimbal radius R G1 . A middle portion of the second link housing  3063  extends into or within the first gimbal envelope. 
     As shown, the third link housing  3083  is curved and extends between the first end portion  3081  of the second end portion  3082 . In some embodiments, the third link housing  3083  has a radius of curvature that is between about 0.5 to 1.5 times the second gimbal radius R G2 . In some embodiments, the third link housing  3083  has a radius of curvature that is between about 0.75 to 1.25 times the second gimbal radius R G2 . For example, as shown in  FIG.  6   , a distance D 2  is about 1.25 times the gimbal radius R G2 . Similarly stated, a curvature of the third link housing  3083  need not follow a circular curvature. Instead, the curved portion can include a blended curve defined by a variable or multiple radii of curvature. In some embodiments, a second gimbal envelope is defined as a spherical volume centered about the gimbal center GC and characterized by a second envelope radius. In some embodiments, the second envelope radius is between about 0.75 to 1.25 times the second gimbal radius R G2 . A middle portion of the third link housing  3083  extends into or within the second gimbal envelope. 
       FIGS.  7 - 13    show views of an input control device  4000  according to an embodiment. The input control device  4000  includes a first link  4040  (which functions as a first gimbal link), a second link  4060  (which functions as a second gimbal link), a third link  4080  (which functions as a third gimbal link), and an input handle  4120 . The input control device  4000  is mounted to a base portion  4130 , which may be a part of a user control unit, such as the user control unit  900  described herein. The input handle  4120  includes a handle portion  4121 , a first handle input  4122 , a second handle input  4123 , and a handle input shaft  4124 . As shown generally in  FIGS.  10  and  11   , the handle input shaft  4124  defines a first rotational axis A 1  (which may function as a roll axis; the term roll is arbitrary) and is rotatably coupled to the first link  4040 . The handle portion  4121  is supported on the handle input shaft  4124  and is configured to be rotated relative to the first link  4040  about the first rotational axis A 1 . The input shaft  4124  extends at least partially within the first link  4040 . The first handle input  4122  and the second handle input  4123  can be manipulated to produce a desired action at the end effector (not shown). For example, in some embodiments, the first handle input  4122  and the second handle input  4123  can be squeezed together to produce a gripping movement at the end effector. The first and second handle inputs  4122 ,  4123  can be similar to the grip members shown and described in in U.S. Patent Application Pub. No. US 2020/0015917 A1 (filed Jun. 14, 2019), entitled “Actuated Grips for Controller,” which is incorporated herein by reference in its entirety. For example, In other embodiments, however, the input handle  4120  need not include the handle inputs. 
     As shown in  FIGS.  10 - 12   , the first link  4040  includes a first end portion  4041 , a second end portion  4042 , and a first joint shaft  4045 . The second link  4060  includes a first end portion  4061 , a second end portion  4062 , and a second joint shaft  4065 . The third link  4080  includes a first end portion  4081 , a second end portion  4082 , and a third joint shaft  4085 . The second end portion  4042  of the first link  4040  is rotatably coupled to the first end portion  4061  of the second link  4060  via the first joint shaft  4045 . Similarly stated, the second end portion  4042  of the first link  4040  is coupled to the first end portion  4061  of the second link  4060  such that the first joint shaft extends within the second link  4060 . The first joint shaft  4045  defines a second rotational axis A 2  (which may function as a yaw axis; the term yaw is arbitrary). The second rotational axis A 2  is perpendicular to the first rotational axis A 1 . An intersection of the first rotational axis A 1  and the second rotational axis A 2  defines a gimbal center GC. In some embodiments, the distance from the gimbal center GC to the first end portion  4061  of the second link  4060  defines a first gimbal radius R G1 . 
     The second link  4060  further includes a second link housing  4063  extending between the first end portion  4061  and the second end portion  4062 . The second end portion  4062  of the second link  4060  is rotatably coupled to the first end portion  4081  of the third link  4080  via the second joint shaft  4065 . Similarly stated, the second link  4060  is coupled to the third link  4080  such that the second joint shaft  4065  extends within the third link  4080 . The second joint shaft  4065  defines a third rotational axis A 3  (which may function as a pitch axis; the term pitch is arbitrary) and the third rotational axis A 3  is perpendicular to the second rotational axis A 2 . 
     The third link  4080  further includes a third link housing  4083  extending between the first end portion  4081  and the second end portion  4082 . The second end portion  4082  of the third link  4080  is rotatably coupled to the base portion  4130  via the third joint shaft  4085 . Similarly stated, the third link  4080  is coupled to the base portion  4130  such that the third joint shaft  4085  extends within the base portion  4130  (see, e.g.,  FIGS.  7  and  12   ). The third joint shaft  4085  defines a fourth rotational axis A 4 . The fourth rotational axis A 4  is perpendicular to the third rotational axis A 3 . In some embodiments, the distance from the gimbal center GC to the first end portion  4081  of the third link  4080  defines a second gimbal radius R G2 . 
     In some embodiments and in certain orientations, as shown in  FIGS.  8 - 10   , the second rotational axis A 2  and the fourth rotational axis A 4  are oriented co-linearly, however, it will be appreciated by one skilled in the art that the second rotational axis A 2  and the fourth rotational axis A 4  can be positioned to intersect one another when the second link  4060  is rotated about the third rotational axis A 3 . For example, as shown in  FIGS.  11  and  12   , when the second link  4060  is rotated from an initial pose, the second rotational axis A 2  and the fourth rotational axis A 4  are no longer co-linear. 
     As shown in  FIGS.  12 - 14   , the input control device  4000  includes a first actuator  4150 . The first actuator  4150  is mounted in the second link  4060  within the second link housing  4063 . The first actuator  4150  defines a first actuator axis A M1 . The first actuator  4150  is configured to exert a torque on or receive torque from the first joint shaft  4045 . In this embodiment, the first actuator  4150  is a motor  4151  that includes a motor shaft  4152 . The motor shaft  4152  is operatively coupled to the first joint shaft  4045 . Additionally, the input control device  4000  includes a first actuator transmission  4153  mounted to the first end portion  4061  within the second link  4060 . The first actuator transmission  4153  includes a driving gear  4154  and a driven gear  4155 . The driving gear  4154  is fixed to the motor shaft  4152  and is configured to rotate together with the motor shaft  4152 . The driven gear  4155  is configured to mesh with and be driven by the driving gear  4154 , which in turn drives the first joint shaft  4045 . 
     As shown in  FIG.  12   , the input control device  4000  includes a second actuator  4160 . The second actuator  4160  is mounted in the third link  4080  within the third link housing  4083 . The second actuator  4160  defines a second actuator axis (not shown). The second actuator  4160  is configured to exert a torque on or receive torque from the second joint shaft  4065 . In this embodiment, the second actuator  4160  is a motor  4161  that includes a motor shaft  4162 . The motor shaft  4162  is operatively coupled to the second joint shaft  4065 . In some embodiments, the input control device  4000  includes a second actuator transmission  4163  mounted within the third link  4080 . The second actuator transmission  4163  is mounted to the first end portion  4081  of the third link  4080 . In some embodiments, as generally shown in  FIG.  12   , the second actuator transmission  4163  includes a driving gear and a driven gear, which can be arranged in a similar fashion as the first actuator transmission  4153 . In some embodiments, the driving gear of the second actuator transmission  4163  can fixed to the motor shaft  4162  and configured to rotate together with the motor shaft  4162 . The driven gear can be configured to mesh with and be driven by the driving gear, which in turn drives the second joint shaft  4065 . 
     As shown for example in  FIGS.  10  and  11   , if the gravitation force F g  acts downwardly in the diagram, it will be appreciated that as the second link  4060  is rotated relative to the third rotational axis A 3 , the gravitational force F g  will act on the handle portion  4121  and cause the first link  4040  to rotate about the second rotational axis A 2 , for example. In other words, as the second link  4060  is moved out of the initial position (e.g., resting position) shown in  FIG.  10   , the gravitation force F g  will act on one or more of the input handle  4120 , the first link  4040 , the second link  4060 , and the third link  4080 . Similar to the actuator  2150  described above, the first actuator  4150  and/or the second actuator  4160  can be operated to output torque to counteract the gravitational force F g  applied on one or more of the first link  4040 , the second link  4060 , and the input handle  4120 . For example, if the second link  4060  is rotated away from the resting position, the second actuator  4160  can be operated to output a torque to the second joint shaft  4065  to counteract the torque applied by the gravitational force F g  on the first link  4040 , the second link  4060 , and the input handle  4120 . As such, once the surgeon S has moved the handle portion  4121  to a particular position and orientation, the first actuator  4150  and/or the second actuator  4160  can be operated to hold the input control device  4000  at that last position and orientation placed by the surgeon S. The tool or instrument at the patient operating site (such as instrument  500  described herein) can also be held at a corresponding position and orientation until the surgeon S provides a new input. By offsetting the gravitational forces acting on the input control device  4000 , the surgeon S is provided with a more natural and less restrictive way of controlling the instrument  500 . As a result the input control devices described herein are operable to provide the surgeon S with a more fluid and weightless experience by isolating forces acting on the input control device  4000  if left unassisted. In doing so, the input control devices described herein may be able to provide improved fine motor control of the instrument  500  and/or reduce fatigue experienced by the surgeon S during operation. In some embodiments, the first actuator  4150  and/or the second actuator  4160  can be operated to output a torque to resist movement input by the surgeon S to simulate a condition observed at the tool and provide feedback to the surgeon S, as described herein. 
     As discussed above, the dynamics of master controllers can be improved by reducing the overall weight and moment of inertia at the input control devices. As shown in  FIGS.  8 - 11   , the link housing  4063  is curved and extends between the first end portion  4061  of the second end portion  4062 . In some embodiments, the second link housing  4063  has a radius of curvature that is between about 0.5 to 1.5 times the first gimbal radius R G1 . In some embodiments, the second link housing  4063  has a radius of curvature that is between about 0.75 to 1.25 times the first gimbal radius R G1 . Similarly stated, a curvature of the second link housing  4063  need not follow a circular curvature. Instead, the curved portion can include a blended curve defined by a variable or multiple radii of curvature. In some embodiments, a first gimbal envelope is defined as a spherical volume centered about the gimbal center GC and characterized by a first envelope radius. In some embodiments, the first envelope radius is between about 0.75 to 1.25 times the first gimbal radius R G1 . For example, as shown in  FIG.  9   , a distance D 1  is about 1.25 times the first gimbal radius R G1 . A middle portion of the second link housing  4063  extends into or within the first gimbal envelope. 
     As shown, the third link housing  4083  is curved and extends between the first end portion  4081  of the second end portion  4082 . In some embodiments, the third link housing  4083  has a radius of curvature that is between about 0.5 to 1.5 times the second gimbal radius R G2 . In some embodiments, the third link housing  4083  has a radius of curvature that is between about 0.75 to 1.25 times the second gimbal radius R G2 . Similarly stated, a curvature of the third link housing  4083  need not follow a circular curvature. Instead, the curved portion can include a blended curve defined by a variable or multiple radii of curvature. In some embodiments, a second gimbal envelope is defined as a spherical volume centered about the gimbal center GC and characterized by a second envelope radius. In some embodiments, the second envelope radius is between about 0.75 to 1.25 times the second gimbal radius R G2 . For example, as shown in  FIG.  9   , a distance D 2  is about 1.25 times the second gimbal radius R G2 . A middle portion of the third link housing  4083  extends into or within the second gimbal envelope. 
     As shown in  FIGS.  12  and  13   , the motor  4151  is mounted in the second link housing  4063 . The first actuator axis A M1  of motor  4151  and the second rotational axis A 2  define a first offset angle θ 1 . In some embodiments, the first offset angle θ 1  is less than 90 degrees. In some embodiments, the first offset angle θ 1  is less than 90 degrees. In some embodiments, the first offset angle θ 1  is between about 20 degrees and 70 degrees. In some embodiment the first offset angle θ 1  is between about 30 degrees and 60 degrees. Similarly, the motor  4161  is mounted in the third link housing  4083 . Similar to the first actuator  4150 , the second actuator  4160  and the third rotational axis A 3  define a second offset angle (not shown). In some embodiments, the second offset angle is less than 90 degrees. In some embodiments, the second offset angle is between about 20 degrees and 70 degrees. In some embodiment the second offset angle is between about 25 degrees and 65 degrees. In some embodiment the second offset angle is between about 30 degrees and 60 degrees. 
     As shown in  FIGS.  14 - 16   , the first actuator transmission  4153  includes a transmission housing  4170  to facilitate mounting of the first actuator transmission  4153  within the second link  4060  in a manner to provide the desired interface of the gears. The transmission housing  4170  includes a base portion  4171 , a gear support portion  4172 , and an actuator support portion  4173 . The gear support portion  4172  is removably secured to the base portion  4171  via one or more fasteners (not shown). The base portion  4171  includes a shaft support (not shown) and the gear support portion  4172  includes a shaft support aperture  4178 . The shaft support aperture  4178  is an aperture configured to rotatably support a gear shaft  4181 . In other embodiments, the shaft support of the base portion  4171  and/or the gear support portion  4172  are configured to support a bearing or bushing member through which the gear shaft  4181  is supported on. The transmission housing  4170  includes a plurality of mounting holes  4174  and the gear support portion includes a plurality of mounting holes  4177  for securing the gear support portion to the transmission housing  4170  via one or more fasteners (not shown). For example, the fasteners can include but are not limited to screws, bolts, rivets, welds, and adhesives. 
     The base portion  4171  includes a first mounting element  4175 , and a second mounting element  4176 . The first mounting element  4175  and the second mounting element  4176  are through holes configured to receive a fastener to secure the transmission housing  4170  to the first end portion  4061  of the second link  4060 . In some embodiments, the first mounting element  4175  is a circular through-hole and the second mounting element  4176  is an elongated through-hole. As shown in  FIG.  15   , the first end portion  4061  of the second link  4060  includes a mounting portion  4066 . In some embodiments, the mounting portion  4066  has a first mounting surface  4066   a  and a second mounting surface  4066   b . The first mounting surface  4066   a  includes a first fastener receiver  4067   a  and a second fastener receiver  4068   a . The second mounting surface  4066   b  includes a first fastener receiver  4067   b  and a second fastener receiver  4068   b.    
     In some embodiments, the first fastener receivers  4067   a ,  4067   b  are threaded screw holes. In some embodiments, the second fastener receivers  4068   a ,  4068   b  are elliptical through-holes. As shown generally in  FIGS.  14  and  15   , the base portion  4171  of the transmission housing  4170  is mounted onto the mounting portion  4066  by first aligning the first mounting element  4175 , and a second mounting element  4176  over the first fastener receivers  4067   a ,  4067   b . The transmission housing  4170  is secured to the mounting portion  4066  by inserting and securing a first fastener, such as a screw, downward through the first mounting element  4175  and into the first fastener receiver  4067   a . A second fastener can be inserted and secured downward through the second mounting element  4176  and into the first fastener receiver  4067   b . Because of the elongated shape of the elliptical through-hole in the second mounting element  4175 , the transmission housing  4170  may be rotated about the first fastener receiver  4067   a  to adjust a position of the transmission housing  4170  relative to the first end portion  4061  of the second link  4060 . By facilitating an adjustment to the position of the transmission housing  4170  and the gear shaft  4181  supported by the transmission housing  4170 , a lash of the gears can be set and adjusted during manufacture or during servicing. Maintaining a desired lash between the gears of the transmission allows for improved efficiency and smooth operation. 
     As shown in  FIGS.  13 ,  14 , and  16   , the motor  4151  is mounted to the actuator support portion  4173 . The motor  4151  is axially and rotatably fixed to the actuator support portion  4173 . In some embodiments, the motor  4151  is secured to the actuator support portion  4173  by adhesive. In some embodiments, the motor  4151  is secured to the actuator support portion  4173  using one or more fasteners. 
     As shown in  FIGS.  13  and  14   , the gear shaft  4181  defines a transmission axis A T  and the motor  4151  defines a motor axis A MM . The transmission axis A T  and the motor axis A MM  define a transmission offset angle θ T . In some embodiments, the transmission offset angle θ T  is less than 90 degrees. In some embodiments, the transmission offset angle θ T  is between about 20 degrees and 70 degrees. In some embodiment the transmission offset angle θ T  is between about 25 degrees and 65 degrees. In some embodiment the transmission offset angle θ T  is between about 30 degrees and 60 degrees. As shown in  FIG.  13   , the transmission axis A T  and the second rotational axis A 2  are parallel, and the transmission offset angle θ T  is equal to the first offset angle θ 1 . In some embodiments, the gear shaft  4181  is configured to be adjusted along the transmission axis A T  to adjust a lash between the driving gear  4154  and the driven gear  4155 . Once the lash between the driving gear  4154  and the driven gear  4155  has been adjusted, a position of the gear shaft  4181  can be set relative to the base portion  4171  and a gear support portion using a combination of shims, spacers, clips, and/or fasteners. In some embodiments, the position of the gear shaft  4181  is set using a combination of shims and E-clips. 
     In some embodiments, as shown in  FIG.  17   , the first actuator transmission  4153  includes a reduction gear system with an input gear  4182  and an output gear  4183 . The input gear  4182  is mounted to the gear shaft  4181  and configured to rotate at a same angular velocity as the driven gear  4155 . The output gear  4183  is mounted to the first joint shaft  4045  and configured to mesh with and be driven by the input gear  4182 . The reduction gear system is configured to decrease the load applied on the motor  4151  and increase the torque transferred to the first joint shaft  4045  via the output gear  4183 . 
     In some embodiments, the input gear  4182  includes a first number of teeth, the output gear  4183  includes a second number of teeth, and the second number of teeth is greater than the first number of teeth. In some embodiments, a gear ratio of the output gear  4183  to the input gear  4182  is about 5:1 to about 7:1. In some embodiments, the gear ratio of the output gear  4183  to the input gear  4182  is set at about 6.9:1. As shown, the input gear  4182  and the output gear  4183  are spur gears. Although directly driven gears are shown, it will be appreciated that a pulley and belt system, gear and chain system, or other transmission systems can be employed. 
     As shown, the driving gear  4154  is configured to engage the driven gear  4155 . In some embodiments, a gear ratio of the driven gear  4155  to the driving gear  4154  is about 5:1 to about 7:1. Thus, the effective gear ratio between the output gear  4183  and the driving gear  4154  is about 25:1 to 49:1. In some embodiments, the effective gear ratio between the output gear  4183  and the driving gear  4154  is set at about 48.2:1. The combination of directly driven gears provides an efficient transfer of power while maintaining a compact design compared with a planetary gear system or other related gear systems. The compact and lightweight gear system described herein reduces the overall mass of the input control device  4000  and enables the use of smaller actuators due to the torque conversion provided by the reduction gear system. 
     As described above, the transmission housing  4170  is operable to rotate about the first fastener receiver  4067   a . In some embodiments, the transmission housing  4170  may be rotated and adjusted to set a gear lash between the input gear  4182  and the output gear  4183 . 
     Although the transmission housing  4170  and associated components shown in  FIGS.  14 - 17    are discussed in association with the first actuator  4150  and the second link  4060 , a similar arrangement can also be employed for the second actuator  4160  and the third link  4080 . In other embodiments, the transmission housing  4170  may be formed integrally with the second link  4060  or the third link  4080 . For example, the housing  4170  may be monolithically formed on the first end portion  4061  of the second link  4060 . 
     While various embodiments have been described above, it should be understood that they have been presented by way of example only, and not limitation. Where methods and/or schematics described above indicate certain events and/or flow patterns occurring in certain order, the ordering of certain events and/or operations may be modified. While the embodiments have been particularly shown and described, it will be understood that various changes in form and details may be made. 
     For example, any of the instruments described herein (and the components therein) are optionally parts of a surgical assembly that performs minimally invasive surgical procedures, and which can include a manipulator unit, a series of kinematic linkages, a series of cannulas, or the like. Thus, any of the instruments described herein can be used in any suitable surgical system, such as the MIRS system  1000  shown and described above. 
     Although various embodiments have been described as having particular features and/or combinations of components, other embodiments are possible having a combination of any features and/or components from any of embodiments as discussed above. For example, in some embodiments, the second actuator transmission  4163  may include the same components as the first actuator transmission  4153 . In some embodiments, the input control device  4000  includes only one actuator and transmission (e.g., only the first actuator  4150  and the first actuator transmission  4153 , or only the second actuator  4160  and the second actuator transmission  4163 ). Aspects have been described in the general context of medical devices, and more specifically surgical instruments, but inventive aspects are not necessarily limited to use in medical devices.