Abstract:
A mechanical tracking system comprises a first set of linkage arms, a second set of linkage arms, a pair of shafts connected at a first end to one arm of the first set of linkage antis and at a second end to one arm of said second set of the linkage arms, wherein each arm of the second set of linkage arms is oriented out of phase with a respective arm of the first set of linkage arms, an attachment shaft positioned adjacent to the first set of linkage arms to accommodate a tool, and a sensor arrangement configured to sense the orientation and position of the attachment shaft.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 61/671,701 to Jeffrey Bax et al. filed on Jul. 14, 2012, the entire content of which is incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to tracking systems and in particular to a mechanical tracking system to assist in medical imaging. 
       BACKGROUND OF THE INVENTION 
       [0003]    Hepatocellular carcinoma (HCC) is one of the most common diagnosed malignancies and one of the most frequent causes of cancer related deaths worldwide. Incidence is particularly high in Asia and Sub-Saharan Africa due to the large incidence of hepatitis B and C, both of which are complicated by hepatic cirrhosis, the greatest risk factor for HCC. Increasing trends in HCC have been reported in Western countries. Further, the liver is one of the most common sites of metastatic cancer arising in other organs. 
         [0004]    When feasible, surgical resection or liver transplant is the accepted standard therapeutic approach, and has the highest success rate of available treatment methods for primary and metastatic liver cancer. Unfortunately, only approximately 15% of patients are candidates the surgery. Patients who do not qualify for surgery are offered other therapeutic solutions such as for example chemotherapy and radiotherapy, however these other solutions have variable success rates. 
         [0005]    Minimally invasive percutaneous techniques, such as for example radio-frequency (RF) and microwave (MW) ablation of malignant tissue in the liver is a rapidly expanding research field and treatment tool for patients who are not candidates for surgical resection or liver transplant. In some cases, these minimally invasive percutaneous techniques act as a bridge to liver transplantation. Due to low complication rates and short recovery times, the indications for these minimally invasive techniques are increasing. These techniques, however, have a higher local recurrence rate than surgical resection mainly due to insufficient or inaccurate local ablation of cancerous cells. 
         [0006]    MW energy-induced tissue heating by near field probes is a common thermal treatment of liver tumours. Application of MW for tumour ablation has multiple advantages over other techniques, including higher treatment temperatures and the ability to create larger uniformly shaped ablation zones in shorter time periods. However, the accurate placement of the ablation probe is critical in achieving the predicted treatment goal. The current standard uses computed tomography (CT) images for planning and two-dimensional ultrasound image guidance for intra-operative guidance of the ablation probe(s) into the target lesion. This approach suffers from several disadvantages such as: (1) 2D ultrasound imaging requires users (physicians) to mentally integrate a sequence of 2D images to form an impression of the anatomy and pathology, leading to variability in guidance during interventional procedures; (2) 2D ultrasound imaging does not permit the viewing of planes parallel to the skin; (3) liver deformation and motion artifact due to breathing reduces targeting accuracy; (4) the use of 2D ultrasound imaging for measurement of tumour volume needed for the treatment plan is variable and at times inaccurate and (5) the use of 2D ultrasound imaging makes it difficult to detect and track the needle delivering the thermal energy to the liver, which is crucial for accurate placement of the needle relative to the tumour. 
         [0007]    The use a three-dimensional (3D) ultrasound imaging helps to overcome the above-noted disadvantages resulting in improved accuracy of ablation probe placement and improved ablation of the lesion. 3D ultrasound imaging also helps to show the features of liver masses and the hepatic vasculature more clearly, allowing guidance of the ablation probe to the target to be carried out more accurately and allowing more accurate monitoring of the ablation zone during the procedure and during follow up. As a result, 3D ultrasound imaging helps to increase the overall success rate and reliability of minimally invasive liver interventions. Thus, 3D ultrasound in combination with follow up CT images can help physicians to decide whether a repeat ablation is required. 
         [0008]    The ability to increase the overall success rate of minimally invasive techniques for the treatment of liver cancer provides better treatment options for non-surgical candidates. It is them fore an object of the present invention at least to provide a novel mechanical tracking system to assist in medical imaging. 
       SUMMARY OF THE INVENTION 
       [0009]    Accordingly, in one aspect there is provided a mechanical tracking system comprising a first set of linkage arms, a second set of linkage arms, a pair of shafts connected at a first end to one arm of said first set of linkage arms and at a second end to one arm of said second set of said linkage arms, wherein each arm of the second set of linkage arras is oriented out of phase with a respective arm of the first set of linkage arms, an attachment shall positioned adjacent to the first set of linkage arms to accommodate a tool, and a sensor arrangement configured to sense the orientation and position of the attachment shaft. 
         [0010]    In one embodiment, the first and second sets of linkage arms are 180° out of phase with respect to one another and form spherical packages. The spherical linkages are coupled to opposite ends of a parallelogram linkage. The first set of linkage anus and parallelogram linkage are coupled to a linear slide assembly. 
         [0011]    In one embodiment, the sensor arrangement comprises at least one encoder. The in least one encoder may be a magnetic encoder and an optical encoder. In another embodiment, the sensor arrangement comprises a plurality of sensors at different locations about the mechanical tracking system. 
         [0012]    In one embodiment, the mechanical tracking system further comprises a counterbalance mechanism for maintaining balance between the first and second set of linkage arms. The counterbalance mechanism may comprise counterweights mounted on the first set of linkage arms. 
         [0013]    According to another aspect there is provided an assembly comprising a parallelogram linkage; a first spherical linkage coupled to one end of the parallelogram linkage and being configured to connect to a tool; a second spherical linkage coupled to an opposite end of the parallelogram linkage; and a counterbalance mechanism separated from said first spherical linkage. 
         [0014]    In one embodiment, the first and second spherical linkages are mirrored at opposite ends of the parallelogram linkage and the counterbalance mechanism is associated with the second spherical linkage. The counterbalance mechanism may comprise counterweights mounted on linkage aims of said second spherical linkage. In one embodiment, the assembly further comprises a shaft and U-joint arrangement extending between the first and second spherical linkages and the parallelogram linkage and second spherical linkage are coupled to a linear slide assembly. 
         [0015]    The mechanical tracking assembly is advantageous in that it allows for both spherical and vertical counterbalanced motion and reduced inertia. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0016]    Embodiments will now be described more fully with reference to the accompanying drawings in which: 
           [0017]      FIG. 1  is an isometric view of a mechanical tracking system; 
           [0018]      FIG. 2  is a bottom view of the mechanical tracking system of  FIG. 1 ; 
           [0019]      FIG. 3  is a cross-sectional view of the mechanical tracking system of  FIG. 1 ; 
           [0020]      FIGS. 4   a  to - 4   c  are front perspective, rear perspective, and top views, respectively, of the mechanical tracking system of  FIG. 1 ; 
           [0021]      FIG. 5  is an isometric view of the mechanical tracking system of  FIG. 1  showing axes of movement thereof; 
           [0022]      FIG. 6  is an isometric view of the mechanical tracking system of  FIG. 1  showing a sensor assembly thereof; 
           [0023]      FIG. 7  is a bottom view of the mechanical tracking system of  FIG. 1  showing the sensor assembly thereof; 
           [0024]      FIG. 8  is a schematic diagram showing the relationship between the coordinate system of the mechanical tracking system and a reference frame; 
           [0025]      FIG. 9   a  and  9   b  are isometric and side views, respectively, of another embodiment of a mechanical tracking system; 
           [0026]      FIG. 10  is an isometric view of yet another embodiment of a mechanical tracking system; 
           [0027]      FIG. 11  is an isometric view of yet another embodiment of a mechanical tracking system holding an ultrasound imaging system; and 
           [0028]      FIG. 12  is an isometric view of still yet another embodiment of a mechanical tracking system coupled to a magnetic resonance imaging machine. 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0029]    Tuning to  FIGS. 1 and 2 , a mechanical tracking system is shown and is generally identified by reference numeral  100 . The mechanical tracking system  100  comprises a linear sliding assembly  150 , a rearward spherical linkage  200 , an arm assembly  250 , a spring counterbalance assembly  260  and a forward spherical linkage  300 . The forward spherical linkage  300  comprises an attachment shaft  310  for connecting to a tool such as for example a medical imaging device (e.g. an ultrasound probe CT scanner, MR scanner etc.). The mechanical tracking system  100  also comprises a sensor arrangement  400  for monitoring the motion thereof. 
         [0030]    The linear sliding assembly  150  comprises a first base bracket  152  having one end configured to be secured or otherwise mounted on supporting structure. A horizontally extending linear carriage  154  is mounted adjacent the other end of the first base bracket. A bottom portion of a second base bracket  156  is slidably connected to the linear carriage  154  via a linear slide  158 . A brake  166  is provided to selectively inhibit or permit movement of the linear slide  158  along the linear carriage  154 . A top portion of the second base bracket  156  is connected to a yaw bearing block  160 . The yaw bearing block  160  supports a rear base plate  162 . A first pitch bearing block  164  is connected to the rear base plate  162 . Although not visible in  FIG. 1 , a second pitch bearing block is connected to the rear base plate  162  below the first pitch bearing block  164 . 
         [0031]    The rearward spherical linkage  200  extends rearwardly from the rear base plate  162  and comprises four (4) spherical linkage arms  202  to  208 , which in this embodiment are made of aluminum or other suitable material. The spherical linkage arms  202  to  208  are arranged in a generally rectangular shape and are connected to one another via a pair of stainless steel bearings that are seethed by a threaded screw and a bolt (not shown). Specifically, a first end of each of spherical linkage arms  202  and  206  is connected to opposing ends of spherical linkage arm  204 . A second end of spherical linkage arm  206  is connected to a first end of spherical linkage arm  208  and a second end of spherical linkage arm  202  is connected to an approximate midpoint of spherical linkage arm  208 . The second end of spherical linkage arm  208  extends generally outward from the connection point of the second end of spherical linkage arm  202 . Counterweights  210  formed of tungsten or other suitable material are positioned approximately at the midpoints of spherical linkage arms  202 ,  204  and  206 , at the connection point between the first end of spherical linkage arm  202  and spherical linkage arm  204 , and at the second end of spherical linkage arm  208 . As will be further described below, the rearward spherical linkage  200  is used to counterbalance the mass of the forward spherical linkage  300  and tool connected thereto via attachment shaft  310 . 
         [0032]    The arm assembly  250  extends forwardly from the rear base plate  162  and is in the form of a parallelogram linkage that comprises an upper parallelogram linkage arm  252  and a lower parallelogram linkage arm  254 , respectively. In this embodiment, each of the upper and lower parallelogram linkage arms  252  and  254  is U-shaped and is connected at a first end to the rear base plate  162  via is pair of stainless steel bearings associated with the first pitch bearing block  164  and second pitch bearing block (not shown), and at a second end to a forward base plate  256  via a pair of stainless steel bearings associated with a third pitch bearing block  258  and a fourth pitch bearing block (not shown). Positioned within a space intermediate the upper parallelogram linkage arm  252  and the lower parallelogram linkage arm  254  is the spring counterbalance assembly  260 . The spring counterbalance assembly  260  is similar to that described in International PCT Application Publication No. WO 2009/039659 to Bax et al., the relevant portions of the disclosure of which are incorporated herein by reference. 
         [0033]      FIG. 3  shows a cross-sectional view of the mechanical tracking system  100 . Generally, the spring counterbalance assembly  260  is used to support the mass of the arm assembly  250 , forward spherical linkage  300  and tool connected to the attachment shaft  310  and comprises an upper counterbalance spring  262  connected at a first end to the rear base plate  162 , identified as point A in  FIG. 3 , and at a second end to a first end of an upper crank BE via a pinned connection E, which itself is connected to the forward base plate  256 . The spring counterbalance assembly  260  comprises a lower counterbalance spring  264  connected at a first end to the rear base plate  162 , identified as point C in  FIG. 3 , and at a second end to a first end of a lower crank CF via a pinned connection F. The second end of the lower crank CF is connected to the forward base plate  256  at point D. As will be appreciated from this arrangement, the force generated by the upper counterbalance spring  262  is 90 degrees out of phase with respect to the lower counterbalance spring  264  and upper crank BE is at a right angle with respect to lower crank CF. In this embodiment the upper and lower counterbalance springs  262  and  264  are steel alloy springs. 
         [0034]    Referring back to  FIGS. 1 and 2 , the forward spherical linkage  300  extends forwardly from the forward base plate  256  and comprises four (4) spherical linkage arms  302  to  308 , which in this embodiment are made from aluminum or other suitable materials. The spherical linkage arms  302  to  308  are arranged in a generally rectangular shape and are connected to one another via a pair of stainless steel bearings that are secured by a threaded screw and a bolt (not shown). Specifically, a first end of each of spherical linkage arms  302  and  306  is connected to opposing ends of spherical linkage arm  304 . A second end of spherical linkage arm  306  is connected to a first end of spherical linkage arm  308  and a second end of spherical linkage arm  302  is connected to an approximate midpoint of spherical linkage arm  308 . The second end of spherical linkage arm  308  extends generally outward from the connection point of the second end of spherical linkage arm  302 . The second end of spherical linkage arm  308  houses the attachment shaft  310 . The attachment shaft  310  extends generally inwards and is moveable with the spherical linkage arms  302  to  308 , as will be described. 
         [0035]    As can be seen, spherical linkage arms  202 ,  204 ,  206  and  208  correspond to spherical linkage arms  302 ,  304 ,  306  and  308 , respectively and thus, the rear and forward spherical linkages  200  and  300  are mirrored at opposite ends of the parallelogram linkage. The rearward spherical linkage  200  and forward spherical linkage  300  are coupled to one another via shaft and U-joint arrangements. The shafts  350   a  and  350   b  of the arrangements in this embodiment are parallel and are made of stainless steel or other suitable material. The rearward spherical linkage  200  is connected to a first end of each of the shafts  350   a  and  350   b  via a pair of U-joints  352 . Each pair of U-joints  352  is connected to one another such that they are 90° out of phase with respect to one another. The forward spherical linkage  300  is connected to a second end of each of the shafts  350   a  and  350   b  via a pair of U-joints  354 . Each pair of U-joints  354  is connected to one another such that they at 90° out of phase with respect to one another. As a result, the rearward spherical linkage  200  and forward spherical linkage  300  are positioned 180° out of phase with respect to one another, that is, spherical linkage arms  202 ,  204 ,  206  and  208  are 180° out of phase with respect to spherical linkage arms  302 ,  304 ,  306  and  308 , respectively. 
         [0036]      FIGS. 4   a  to  4   c  are respective front perspective, rear perspective, and top views of the mechanical tracking system  100  showing, the relationship between the U-joints  352  and  354  and the pivot axes of the upper parallelogram linkage arm  252 , lower parallelogram linkage arm  254 , forward spherical linkage  300  and rearward spherical linkage  200 . As can be seen, the center of rotation of each pair of U-joints  352  and  354  is aligned with the pivots adjacent to the respective forward spherical linkage  300  (points G and l which are coplanar with respect to the plane defined by parallel axes A and C) or rearward spherical linkage  200  (points H and J which are coplanar with respect to the plane defined by parallel axes B and D) such that all four pairs of U-joints are parallel to the pinned axis supporting the forward spherical linkage  300  (axis L) and rearward spherical linkage  200  (axis K). 
         [0037]    As best shown in  FIG. 1 , the rearward spherical linkage  200  is rotatable about a rear center of motion RCOM and the forward spherical linkage  300  is rotatable about a forward center of motion ECOM. The forward spherical linkage  300  permits a user to pivot a tool attached to attachment shaft  310  about the forward center of motion FCOM with three degrees of rotation; namely yaw, pitch and roll. The arm assembly  250  which is pinned to the second base bracket  156  that is attached to the linear sliding assembly  150  permits three degrees of translation to adjust the position (X, Y, Z) of the forward center of motion FCOM and the tool attached to the attachment shaft  310 . As will be appreciated, the three degrees of translation is provided through a combination of the up/down movement of the parallelogram linkage about axes ABCD shown in  FIG. 5 , the pivoting of the parallelogram linkage about axis M, and the translation along the linear sliding assembly  150  according to direction N. A pair of brakes  356  (shown in  FIG. 1 ) is provided to selectively inhibit or permit rotation of the forward spherical linkage  300  and rearward spherical linkage  200 . 
         [0038]    The position of the tool attached to attachment shaft  310  is tracked by the sensor arrangement  400  relative to a fixed coordinate frame. The sensor arrangement  400  is identified in  FIGS. 6 and 7 . As can be seen, the sensor arrangement  400  comprises six (6) encoders S 1  to S 6 . In this embodiment, each of the six encoders S 1  to S 6  is a magnetic rotary encoder, such as the RM Series Rotary Encoder manufactured by Renishaw, and is used to measure the angle between the encoder body (identified as S 1  to S 6 ) and an associated encoder magnet (not shown). Each of the encoders S 1  to S 6  is connected to a general purpose computing deice via a wired or wireless connection (not shown). Encoder S 1  is positioned on the second base bracket  156 . Encoder S 2  is positioned atop rear base plate  162 . Encoder  53  is positioned on an exterior side of upper parallelogram linkage arm  252 . Encoder  54  is positioned behind the forward base plate  256 . Encoder S 5  is positioned behind the connection point of spherical linkage arms  302  and  304 . Encoder S 6  is positioned behind attachment shaft  310  on spherical linkage arm  308 . 
         [0039]    Referring to  FIG. 8 , the position of the tool is determined by calculating the forward center of motion FCOM position, having coordinates (X, Y, Z) relative to a known starting point using data obtained by encoders S 1 , S 2  and S 3  and the following transformation matrix: 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     
                       
                         
                           cos 
                            
                           
                               
                           
                            
                           A 
                         
                       
                       
                         
                           sin 
                            
                           
                               
                           
                            
                           A 
                         
                       
                       
                         0 
                       
                       
                         
                           
                             
                               x 
                               4 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             A 
                           
                           + 
                           
                             
                               x 
                               3 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             A 
                              
                             
                                 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             B 
                           
                           + 
                           
                             
                               x 
                               2 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             A 
                           
                           + 
                           
                             x 
                             1 
                           
                         
                       
                     
                     
                       
                         
                           
                             - 
                             sin 
                           
                            
                           
                               
                           
                            
                           A 
                         
                       
                       
                         
                           cos 
                            
                           
                               
                           
                            
                           A 
                         
                       
                       
                         0 
                       
                       
                         
                           
                             
                               - 
                               
                                 x 
                                 4 
                               
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             A 
                           
                           - 
                           
                             
                               x 
                               3 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             A 
                              
                             
                                 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             B 
                           
                           - 
                           
                             
                               x 
                               2 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             A 
                           
                         
                       
                     
                     
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         
                           
                             
                               - 
                               
                                 x 
                                 3 
                               
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             B 
                           
                           + 
                           
                             z 
                             1 
                           
                         
                       
                     
                     
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                     
                   
                   ] 
                 
               
               
                 
                   [ 
                   1 
                   ] 
                 
               
             
           
         
       
     
         [0040]    where x 1 , x 2 , x 3  and x 4  are constants determined from the geometry of the forward spherical linkage  300 , z 1  is the displacement along the linear carriage  154  measured by encoder S 1 , angle A is the yaw angle measured by encoders S 2  and S 3 , and angle B is the pitch angle measured by encoders S 2  and S 3 . 
         [0041]    The orientation of the tool is determined by calculating the orientation of point C using data obtained by encoders S 4 , S 5  and S 6 . The orientation of the tool about the axis from the forward center of motion ECOM to point C, referred to as axis FCOM-C, is measured by encoder S 6 . The location of point C with respect to the forward center of motion FCOM is measured by encoders S 4  and S 5 . The orientation of the tool is specified in spherical coordinates by the angle φ, the angle axis FCOM-C makes with respect to the z axis, and the angle θ representing the orientation of the tool in the x-y plane. 
         [0042]    The relationship between the coordinate system of the mechanical tracking system  100  and the reference frame defined by the encoders S 1  to S 6  is shown in  FIG. 8 . The attachment shaft  310  orientation measured by the encoders S 4  to S 6  is defined by the spherical triangle ABC, and is linked to the forward center of motion FCOM by the spherical triangle ADC. The angle between joints A and B in link AB is π/4. Similarly, the angle between joints B and C in link BC is π/4. 
         [0043]    The kinematics equations of motion for the forward spherical linkage  300  derived by applying the Napier analogies to spherical triangle ADC shown in  FIG. 8  are: 
         [0000]    
       
         
           
             
               
                 
                   
                     tan 
                      
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         θ 
                         + 
                         α 
                       
                       ) 
                     
                   
                   = 
                   
                     cos 
                      
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         ψ 
                         - 
                         
                           π 
                           2 
                         
                       
                       ) 
                     
                      
                     sec 
                      
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         ψ 
                         + 
                         
                           π 
                           2 
                         
                       
                       ) 
                     
                      
                     cot 
                      
                     
                       1 
                       2 
                     
                      
                     ζ 
                   
                 
               
               
                 
                   [ 
                   
                     2 
                      
                     a 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     tan 
                      
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         θ 
                         - 
                         α 
                       
                       ) 
                     
                   
                   = 
                   
                     sin 
                      
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         ψ 
                         - 
                         
                           π 
                           2 
                         
                       
                       ) 
                     
                      
                     csc 
                      
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         ψ 
                         + 
                         
                           π 
                           2 
                         
                       
                       ) 
                     
                      
                     cot 
                      
                     
                       1 
                       2 
                     
                      
                     ζ 
                   
                 
               
               
                 
                   [ 
                   
                     2 
                      
                     b 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     tan 
                      
                     
                       1 
                       2 
                     
                      
                     ϕ 
                   
                   = 
                   
                     tan 
                      
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         ψ 
                         - 
                         
                           π 
                           2 
                         
                       
                       ) 
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           θ 
                           + 
                           α 
                         
                         ) 
                       
                     
                      
                     
                       cos 
                        
                       
                         ( 
                         
                           θ 
                           - 
                           α 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     2 
                      
                     c 
                   
                   ] 
                 
               
             
           
         
       
     
         [0044]    As will be appreciated, Equations 2a to 2c are used to define the spherical coordinates of axis FCOM-C in terms of the geometric configuration of the linkage angles ψ and ζ. 
         [0045]    The configuration of the forward spherical linkage  300  in terms of the angles measured by encoders S 4  and S 5  is defined according to Equations  3   a  and  3   b  below. It will be appreciated that Equations  3   a  and  3   b  are derived by solving the right spherical triangle ABE in  FIG. 8 : 
         [0000]    
       
         
           
             
               
                 
                   
                     tan 
                      
                     
                       1 
                       2 
                     
                      
                     ψ 
                   
                   = 
                   
                     cos 
                      
                     
                         
                     
                      
                     ξ 
                   
                 
               
               
                 
                   [ 
                   
                     3 
                      
                     a 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     cot 
                      
                     
                       1 
                       2 
                     
                      
                     ψ 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                      
                     tan 
                      
                     
                         
                     
                      
                     γ 
                   
                 
               
               
                 
                   [ 
                   
                     3 
                      
                     b 
                   
                   ] 
                 
               
             
           
         
       
     
         [0046]    The positions of spherical linkage aims  306  and  308  of forward spherical linkage  300  correspond to arms AB and BC, respectively. Accordingly, the position of each spherical linkage arm  306  and  308  is determined by measuring the spherical angles at each of the pinned couplings A and B, respectively. Encoder S 4  measures the angle (ξ+ζ) between arm AB and the x-Z plane, and encoder S 5  measures the angle γ between arm AB and arm BC. As will be appreciated, Equations  3   a  and  3   b  are used to decouple the values for angles ξ and γ, which in turn are used to solve Equations  2   a  to  2   e , above. 
         [0047]    During operation, the general purpose computing, device (not shown) polls the encoders S 1  to S 6  to obtain coordinates therefrom in this embodiment, the general purpose computing device polls each encoder S 1  to S 6  at a one of 10 polls per second. The general purpose computing, novice processes the coordinates and displays the coordinates of the tool attached to the attachment shaft  310 . In embodiments where the tool is a medical imaging device, the general purpose computing device may superimpose the coordinates or tool path of the medical imaging device on a display screen atop a reconstructed image such as for example an ultrasound image, a computed tomography (CT) image, or a magnetic resonance (MR) image. Further, if the tool is a CT or MR imaging scanner, the mechanical tracking system may automatically register the tool to the reconstructed CT or MR image providing information about the tool location relative to the scanned anatomy. 
         [0048]    Turning now to  FIGS. 9   a  and  9   b , another embodiment of a mechanical tracking system  100 ′ is shown. In this embodiment, like reference numerals are used to indicate like components. As can be seen, mechanical tracking system  100 ′ is similar to that of mechanical tracking system  100  shown in  FIG. 1 , with the addition of a motor arrangement  500 . In this embodiment, motor arrangement  500  comprises six (6) motors M 1  to M 6 . Motor M 1  controls, the movement of the arm assembly  250 , rearward spherical linkage  200  and forward spherical linkage  300  along the linear carriage  154 . Motor M 2  controls the pivotal movement of the arm assembly  250 , rearward spherical linkage  200  and forward spherical linkage  300  with respect to axis M. Motor MS controls the up/down movement of the arm assembly  250  and forward spherical linkage  300 . Motors M 4  and M 5  control the yaw and pitch of the tool connected to the attachment shaft  310  and are directly connected to spherical linkage arms  306  and  304 , respectively. Motor M 6  controls the roll orientation of the tool connected to attachment shaft  310  about the longitudinal axis thereof. 
         [0049]    As will be appreciated, motor arrangement  500  is used as a power assist device for lifting and manipulating large payloads and/or a master-slave robotic assistant when coupled to a general purpose computing device (not shown). When used as a master-slave robotic assistant, the sensor data obtained by encoders S 1  and S 6  is communicated to the general purpose computing device for processing to control motors M 1  to M 6  and thus, adjust the position and orientation of the tool. As will be appreciated, the orientation and position of the mechanical tracking system (and thus the tool) may be adjusted through any input device such as for example a mouse, a keyboard, a tracking ball, etc. 
         [0050]    Turning now to  FIG. 10 , another embodiment of a mechanical tracking system  100 ″ is shown. In this embodiment, like reference numerals are again used to indicate like components. As can be seen, mechanical tracking system  100 ″ is similar to that of mechanical tracking system  100 ′described above with reference to  FIGS. 9   a  and  9   b , with the exception that motor M 3  of the motor arrangement  500  is replaced with a proportional gain solenoid  600 . In this embodiment, the proportional gain solenoid  600  is integrated within the spring counterbalance assembly  260  to generate a force vector that is independent of the orientation of the arm assembly  250 , rearward spherical linkage  200  and forward spherical linkage  300 . The value of the force vector generated is communicated to the general purpose computing device, through the spring counterbalance assembly  260  using the proportional gain solenoid  600  to provide force feedback along the vertical axis. As will be appreciated, six degrees of force feedback may be achieved by adding a solenoid assembly in place of each motor or by integrating the solenoid into the spring counterbalance assembly  260  as shown in  FIG. 10 . Alternatively, a solenoid can be integrated into the lower counter/balance spring  264 . If integrated into the lower counterbalance spring  264 , the force exerted by the solenoid on the forward spherical linkage  300  would be equivalent to exerting the same force through the center of mass of the payload, which is independent of the forward spherical linkage  300  configuration. As will be appreciated, the proportional gain solenoid  600  may be replaced with a pneumatic or hydraulic cylinder. 
         [0051]    Although in the above embodiments, components are described as being formed of specific materials such as aluminum and stainless steel, it will be appreciated that other suitable materials may be used such as for example plastic, brass, ceramic, etc. 
         [0052]    Although in the embodiments described above, magnetic rotary encoders are used, those skilled in the art will appreciate that non-magnetic optical encoders or other suitable sensors may be used. 
         [0053]    Although the counterbalance springs are described above as being made of a steel ally those skilled in the an will appreciate plastic left springs or other suitable spring-like devices may be used. 
         [0054]    As mentioned previously, the attachment shaft  310  may be used to connect to a medical tool. An example of the attachment shaft  310  connected to an ultrasound imaging device  800  is shown in  FIG. 11 . In this example, the mechanical tracking system  100 ″′ is similar to that of mechanical tracking system  100 ′ ,shown  FIGS. 9   a  and  9   b , with the exception that the tungsten counterweights  210  are replaced with a spring balance assembly  700 . The spring balance assembly  700  is similar to that described in above-incorporated International PCT Application Publication No. WO 2009/039659 to Bax et al. In this example, the ultrasound imaging device  800  is similar to that described in International PCT Application No. PCT/CA2013/000302 to Barker et. al., the relevant portions of the disclosure of which are incorporated herein by reference. 
         [0055]      FIG. 12  shows the attachment shaft  310  of mechanical tracking system  100 ″″ connected to an ultrasound imaging device  800  with the mechanical tracking system being mounted adjacent an MR imaging system  900 . In this embodiment, it will be appreciated that all components of the mechanical tracking system  100  are formed of non-metallic materials so as to not interfere with the MR imaging. Specifically, the counterbalance springs are plastic leaf springs, the encoders are non-magnetic optical encoders, and all other components are made of non-metallic; materials such as for example plastic, or ceramic. 
         [0056]    Although in above embodiments, the spring counterbalance assembly comprises upper and lower cranks, in another embodiment the upper and lower cranks may be replaced with two eccentric cams positioned 90 degrees out of phase with respect to another. 
         [0057]    Although it is described above that the position and orientation of the mechanical tracking system (and thus the tool) may be adjusted through any input device such as for example a mouse, a keyboard, a tracking ball, etc., those skilled in the art will appreciate that the position and orientation of the mechanical tracking system may be adjusted using any type of input device. For example, a scaled down model of the mechanical tracking system may be provided to a user and coupled to the general purpose computing device. In this example, the user may manipulate the sealed down model and in response, the mechanical tracking system is automatically conditioned to mirror the resultant movement of the scaled down model. As another example, a graphical user interface (GU) maY be displayed On a display screen associated with the general purpose computing device providing a number of control buttons to the user. Further, the control buttons may be associated with a predefined movement and orientation pattern preset by the user. 
         [0058]    Although embodiments are described above with reference to the accompanying drawings, those skilled in the art will appreciate that variations and modifications may be made without departing from the scope thereof as defined by the appended claims.