Abstract:
There is provided a mechanical arm assembly comprising: an arm rotatable about a pivot, a first force generating device for maintaining the arm at a datum, a second force generating device for compensating for the first generating device to maintain the arm in positions other than the datum.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates generally to counterbalances and, more particularly, to a counterbalance for a joint of a mechanical arm. 
       BACKGROUND OF THE INVENTION 
       [0002]    Apparatus comprising a mechanical arm that can hold and guide a payload have been shown to be of valuable assistance in various industrial procedures or medical procedures, for example, manipulation of tools, manipulation of cameras or sensors, etc. 
         [0003]    These apparatus typically have one or more degrees of freedom and may be manually driven in that the one or more degrees of freedom may be equipped with a brake with motive force being provided by a human user, or may be automated in that at least one degree of freedom is driven by a computer controlled actuator. 
         [0004]    A balancing mechanism may be used to counteract the force of gravity for hinged and/or articulated arm. Elimination or reduction of the effects of gravity allow the use of smaller power sources, gears and/or less effort exerted by a manual user. This is desirable from a cost standpoint and allows for a more compact design which, in turn, allows greater accessibility to the workspace. 
         [0005]    Several counterbalancing mechanisms have been previously disclosed, for example, U.S. Pat. No. 4,756,204, U.S. Pat. No. 4,546,233, or U.S. Pat. No. 4,500,251. 
         [0006]    Balancing mechanisms used on articulated arms and hinge mechanisms include counterweights. However, the use of counterweights can result in added mass and increase in arm inertia. 
         [0007]    A tension spring or passive pneumatic balancer may be used for balancing within a small angle or within a single quadrant (i.e. from a horizontal to vertically upward orientation). However, conventional tension springs typically do not adequately balance the gravitational load. Also, it is inherent in most spring balancing methods that complete balance is possible only for one or two configurations of the arm and spring combination. As the robot arm moves away from that configuration in either of two possible directions, an unbalance is generated. Thus, a danger of this mechanism may be drifting or falling under the force of gravity when actuation is removed or reduced. Therefore, such mechanisms are usually provided with brakes to alleviate the potential danger, or are overbalanced against gravity. 
         [0008]    Compression springs operating on small moment arms may overcome an angular limitation problem and offer better balance over the entire range of travel of the robot&#39;s arm. However, the problem of drift or falling under gravity also exists with compression springs. 
         [0009]    It is an object of an aspect of the present invention to provide a counterbalance assembly for a joint of a mechanical arm. 
       SUMMARY OF THE INVENTION 
       [0010]    In an aspect, there is provided a counterbalance assembly for a joint of a mechanical arm comprising: 
         [0011]    a first force generating device; 
         [0012]    a second force generating device; 
         [0013]    the first and second force generating devices interacting with at least first and second cams, respectively; 
         [0014]    the first and second cams fixed eccentrically relative to the pivot of a joint; 
         [0015]    and the relationship of the first spring to the second spring and the first cam to the second cam being preserved throughout rotation of the joint. 
         [0016]    In another aspect, there is provided a mechanical arm assembly comprising: 
         [0017]    an arm rotatable about a pivot, 
         [0018]    a first force generating device for maintaining the arm at a datum, 
         [0019]    a second force generating device for compensating for the first generating device to maintain the arm in positions other than the datum. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0020]    Embodiments will now be described, by way of example only, with reference to the attached Figures, wherein: 
           [0021]      FIG. 1   a  illustrates a dual spring counterbalance assembly at a joint of a mechanical arm using springs that are fixed to a ground and cams set eccentrically relative to the pivot of the joint; 
           [0022]      FIG. 1   b  illustrates a variant of the counterbalance assembly shown in  FIG. 1   a  with a different orientation of springs and cams; 
           [0023]      FIG. 1   c  illustrates a dual spring counterbalance assembly having springs attached to the payload arm; 
           [0024]      FIG. 1   d  illustrates a triple spring counterbalance assembly with an additional spring and an additional cam being added to the counterbalance assembly shown in  FIG. 1   b;    
           [0025]      FIG. 1   e  illustrates a simplified variant of the counterbalance assembly shown in  FIG. 1   d  with removal of a spring resulting in two springs interacting with three cams; 
           [0026]      FIG. 1   f  illustrates a mechanical arm of the counterbalance assembly shown in  FIG. 1   d ; spring/cam relationship in a spring balance mechanism for a mechanical arm; 
           [0027]      FIG. 1   g  is the same as  FIG. 1   f  except that the bolt head extension of a spring is cut away to more clearly show two cams; 
           [0028]      FIG. 2   a  illustrates a cross-sectional view of a dual spring counterbalance assembly showing springs coupled to cams set eccentrically relative to a pivot of a joint; 
           [0029]      FIG. 2   b  is a schematic diagram illustrating the geometric relationship between each spring-cam assembly shown in  FIG. 2   a;    
           [0030]      FIG. 3  illustrates a cross-sectional view of a mechanical arm comprising a variant of the spring balance mechanism shown in  FIG. 2 ; 
           [0031]      FIG. 4  illustrates the phase relationship between springs and cams in various configurations of mechanical arm rotation; 
           [0032]      FIG. 5  illustrates a variant to the design presented in  FIG. 3 ; and 
           [0033]      FIG. 6  illustrates an example of a medical guide apparatus that can comprise the spring balance mechanism shown in  FIG. 1 . 
       
    
    
     DETAILED DESCRIPTION 
       [0034]      FIGS. 1   a  to  1   e  are schematic illustrations of spring counterbalance assemblies which show the geometric relationship of spring and cams. Referring to  FIG. 1   a  and  1   b , the spring counterbalance assembly comprises two compression springs ( 101 ,  102 ), each of which are fixed at the base (or grounded fixture) and the other end(s) are connected to eccentric circular cams ( 103 ,  104 ) by a yoke (not shown), such that each cam is free to rotate about the fulcrum or pivot ( 120 ) of a joint, and the springs are free to compress (or stretch). The springs may be adjustable. Cam  103  is eccentrically set relative to the pivot ( 120 ) of a joint by a distance equal to e 1  ( 110 ), and cam  104  is eccentrically set relative to the pivot ( 120 ) of the joint by a distance of e 2  ( 115 ). 
         [0035]    Spring ( 101 ) interacts only with cam ( 103 ), and spring ( 102 ) interacts with cam ( 104 ). Both of the cams are in turn pinned to the lever/arm ( 105 ) that supports the payload ( 125 ). The compressive (or tensile) force exerted by each spring results in a net torque being exerted about the pivot ( 120 ) of the lever supporting the load. 
         [0036]      FIGS. 1   a  and  1   b  schematically illustrate different orientations of springs and cams in a counterbalance assembly designed to fully support the weight of a payload about a hinged connection which is connected to a ground or stable fixture. The base of each spring is anchored to the ground (or fixture) while the lever/arm ( 105 ), pinned to the cams ( 103 ,  104 ) is free to rotate about the pivot ( 120 ) of a joint of a mechanical arm. The ability to establish equilibrium of torque relative to pivot ( 120 ) is not limited to specific spring-cam orientations shown in  FIGS. 1   a  and  1   b  as will be apparent from equilibrium equations provided below. 
         [0037]    In  FIG. 1   a  the relationship between spring ( 101 ) and cam ( 103 ) to the lever/arm supporting the load is orientated such that the line joining the pivot ( 120 ) and e 1  ( 110 ) is not coincident with the line joining the pivot ( 120 ) to the center of gravity of the payload ( 125 ), which includes mass of the lever/arm ( 105 ). In an example of an alternate orientation shown in  FIG. 1   b  the relationship between spring ( 101 ) and cam ( 103 ) to the lever/arm supporting the load is orientated such that the line joining the pivot ( 120 ) and e 1  ( 110 ) is coincident with the line joining the pivot ( 120 ) to the center of gravity of the payload ( 125 ), which includes mass of the lever/arm ( 105 ). In both  FIGS. 1   a  and  1   b  the orientation of the spring/cam relationship is preserved throughout rotation. Thus, if the cam is in a desired position with respect to the pivot, that will define the orientation of the spring in space. If the spring is in a desired position in space, that will define the position of the cam with respect to the pivot. 
         [0038]    In the configuration shown in  FIG. 1   b , the orientation of the cam to the lever/arm constrains spring ( 101 ) to a vertical position. If the eccentric point is in between the pivot/fulcrum and center of gravity as shown in  FIG. 1   b , spring ( 101 ) will exert a compressive force in its current configuration to offset the payload when the arm is horizontal (theta ( 130 )=0 degrees). If the pivot/fulcrum is in between eccentric point and center of gravity (not shown), spring ( 101 ) will exert a tensile force to offset the weight of the payload. The user can initially set spring ( 101 ) such that its initial compression offsets the mass of the payload, for example when the arm is in the horizontal position (ie, when the cam  103  is 90 degrees out of phase with spring  101 ). The pre-compression of spring ( 101 ) will typically be set with the arm ( 105 ) in the horizontal position since the torque exerted by the arm is greatest at this point. However, pre-compression may also be set with the arm being above or below horizontal by extrapolation. 
         [0039]    In  FIG. 1   b , the relationship between spring ( 102 ) and cam ( 104 ) to the lever/arm supporting the load is orientated such that the line joining the pivot ( 120 ) and e 1  ( 10 ) is coincident with the line joining the pivot ( 120 ) to the center of gravity of the payload ( 125 ), which includes mass of the lever/arm ( 105 ). The orientation of the cam to the lever constrains spring ( 102 ) to a horizontal position. If the eccentric point is in between the pivot and center of gravity (not shown), spring ( 102 ) will exert a tensile force in its current configuration to offset the linear change in force of spring ( 101 ). If the pivot ( 120 ) is in between eccentric point and center of gravity as shown in  FIG. 1   b , spring ( 102 ) will exert a compressive force. In the specific example shown in  FIG. 1   b , spring ( 102 ) is not adjustable, and is set by design such that the spring exerts no load on cam ( 104 ) when the arm ( 105 ) is in a vertical orientation (90 or 270 degrees relative to a Cartesian coordinate system where 0 degree corresponds to the positive X axis). 
         [0040]    Still referring to  FIG. 1   b , the relationship between each cam-spring pair is such that each cam is 180 degrees out of phase with each other (pivot ( 120 ) is in-between the eccentric points ( 110 ) and ( 115 )). In this configuration, each of the springs is constrained to be 90 degrees out of phase with each other (perpendicular). The relationship created from the constrained relationship between each spring/cam pair is the torque exerted by spring ( 101 ) leads spring ( 102 ) by 90 degrees. 
         [0041]    In an alternate embodiment, each spring/cam pair can be rotated about the pivot ( 120 ) to any position (for example, springs are aligned, 0 or 180 degrees) as long as the relationship between the cam and corresponding spring is maintained. 
         [0042]    Thus, the ability to establish equilibrium relative to pivot ( 120 ) is not limited to specific spring-cam orientations shown in  FIGS. 1   a  and  1   b  as will also be apparent from equilibrium equations provided in the following paragraphs. 
         [0043]    Alternatives to  FIGS. 1   a  and  1   b  are shown in  FIGS. 1   c - 1   e .  FIG. 1   c  is an alternate embodiment of the mechanism illustrated in  FIGS. 1   a  and  1   b  where the springs are attached to the arm ( 105 ) and the cams are attached to the ground (or fixture).  FIG. 1   d  adds an additional spring ( 140 ) and cam ( 145 ) to the spring/cam relationships shown in  FIGS. 1   a  and  1   b  and thus eliminates the need for spring ( 102 ) to exert both compressive and tensile loads. Spring ( 102 ) as shown in  FIGS. 1   a  and  1   b  when coupled by a yoke to cam ( 104 ) can be required to exert both tensile and compressive loads. Addition of spring ( 140 ) and cam ( 145 ) shown under the cutaway portion of cam ( 104 ) in  FIG. 1   d , allows the use of compression springs ( 102  and  140 ) that abut their respective cams ( 104  and  145 ) and exert only compressive loads.  FIG. 1   e  shows a further simplification of the assembly illustrated in  FIG. 1   d  with spring  102  interacting with both cams ( 145  and  104 ). Cam  145  is shown under the cutaway of cam ( 103 ). The assembly design shown in  FIG. 1   d  allows for the use of compression spring ( 102 ) to abut cams and only exert a compressive load, while removing the need for spring ( 140 ). The assembly shown in  FIG. 1   e  can be even further simplified by setting spring ( 102 ) to interact with both cams ( 103  and  104 ), thus removing the need for spring ( 140 ) and cam ( 145 ).  FIGS. 1   f  and  1   g  show the assembly design of  FIG. 1   d  as implemented on a mechanical arm. 
         [0044]    The following is a description of the equilibrium equations that govern the geometric spring/cam relationships shown in  FIG. 1   a - 1   e . The force friction has been omitted from this analysis as it has no bearing on the equilibrium equations when the machine is at rest. Friction can be used as an advantage to construct inexpensive mechanisms that behave in a similar manner to the case illustrated in  FIG. 1  but do not fully balance the load. The sum of all the frictional forces between every moving part within the mechanism would prevent drift. 
         [0045]    Referring to  FIG. 1   a , equilibrium about the pivot ( 120 ) is established when the net torque is zero, i.e.: 
         [0000]        T   g   +T   x   +T   y =0  (1),
 
         [0000]    where Tg is the unbalanced torque due to the payload ( 125 ), and the unbalanced torque produced from spring ( 101 ) and ( 102 ) are Tx and Ty respectively. The unbalanced torque produced by the weight is the product of the gravitational force due to the payload M, and the shortest distance between the force vector (M=mg) and the point ( 120 ): 
         [0000]        T   g   =Mr  cos(θ)  (2).
 
         [0000]    The net torque of spring ( 101 ) about ( 120 ) is equal to the sum of the torque produced from the compression of the spring due to the arm displacement ( 130 ) and the pre-compression of the spring when the arm is horizontal ( 130 : θ=0), and is given by: 
         [0000]        T   y =−( K   y   e   1  sin(θ)+ K   y   Δy )( e   1  cos(θ))  (3),
 
         [0000]    where Ky is the spring rate of ( 101 ), and Δy is the displacement of the spring from rest when the arm is horizontal. The net torque produced from spring ( 102 ) is given by: 
         [0000]        T   x   =K   x   e   2   2  cos(θ)sin(θ)  (4),
 
         [0000]    where Kx is the spring rate of ( 102 ) and is uncompressed when the arm is in a vertical orientation (up or down). Substituting equations (2-4) into 1 gives the following: 
         [0000]        Mr  cos(θ)− K   y   Δye   1  cos(θ)+ K   x   e   2   2  cos(θ)sin(θ)− K   y   e   1   2  sin(θ)cos(θ)=0  (5).
 
         [0000]    Equation 5 is equal to zero and independent of the angle θ, and the spring-cam orientations ( 135 : a) and ( 140 : b) under the following conditions: 
         [0000]      Mr=K y Δye 1   (6),
 
         [0000]      K x e 2   2 =K y e 1   2   (7).
 
         [0000]    Equation 6 provides that spring ( 101 ) pre-compression is set to counterbalance the payload ( 125 ) at the arm position within the desired rotation where the torque exerted is greatest, typically when the arm is horizontal. Equation 7 provides the physical constraints which govern the relationship of each spring cam pair. 
         [0046]    Equation 5 can be expanded and written in the following form: 
         [0000]        Mr  cos(θ)−( K   ya   Δy   a   e   1a   +K   yb   Δy   b   e   1b + . . . )cos(θ)+( K   xa   e   2a   2   +K   xb   e   2b   2 + . . . )cos(θ)sin(θ)−( K   ya   e   1a   2   +K   yb   e   1b   2 + . . . )sin(θ)cos(θ)=0  (8).
 
         [0000]    Equation 8 is equal to zero and independent of the angle θ, and the spring-cam orientations (a: 135 ) and (b: 140 ) under the following conditions: 
         [0000]        Mr=K   ya   Δy   a   e   1a   +K   yb   Δy   b   e   1b + . . .  (9),
 
         [0000]        K   xa   e   2a   2   +K   xb   e   2b   2   + . . . =K   ya   e   1a   2   +K   yb   e   1b   2 + . . .  (10).
 
         [0047]    From equations 9 and 10, the following illustrative embodiments are apparent:
       The spring ( 101 ), and cam ( 103 ) can be replaced with multiple spring and cam assemblies.   If (e 1a   2 =e 1b   2 = . . . ), and (K ya =K yb = . . . ) then the spring ( 101 ) can be replaced by multiple springs acting against the cam ( 103 ).   The spring ( 102 ), and cam ( 104 ) can be replaced with multiple spring and cam assemblies.   If (e 2a   2 =e 2b   2 = . . . ), and (K xa =K xb = . . . ) then the spring ( 102 ) can be replaced by multiple springs acting against the cam ( 104 ).   If multiple springs are used in place of ( 101 ), then each spring can be preloaded a different amount to offset the payload when the arm is horizontal.       
 
         [0053]    Now referring to  FIG. 1   c , an alternate embodiment of the mechanism illustrated in  FIGS. 1   a  and  1   b  is shown where the springs are attached to the arm ( 105 ) and the cams are attached to the ground (or fixture). Consistent with the embodiments shown in  FIGS. 1   a  and  1   b , in  FIG. 1   c  equilibrium about the pivot ( 120 ) is established when the net torque is zero, i.e.: 
         [0000]        T   g   +T   x   +T   y =0  (1),
 
         [0000]    where Tg is the unbalanced torque due to the payload ( 125 ), and the unbalanced torque produced from spring ( 101 ) and ( 102 ) are Tx and Ty respectively. The unbalanced torque produced by the weight is the product of the gravitational force due to the payload M, and the shortest distance between the force vector (M=mg) and the point ( 120 ): 
         [0000]        T   g   =Mr  cos(θ)  (2).
 
         [0000]    The net torque of spring ( 101 ) about ( 120 ) is equal to the sum of the torque produced from the compression of the spring due to the arm displacement ( 130 ) and the pre-compression of the spring when the arm is horizontal ( 130 : θ=0), and is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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         [0000]    where Ky is the spring rate of ( 101 ), and Δy is the displacement of the spring from rest when the arm is horizontal. This spring force is equal and opposite of the spring in  FIG. 1   a , and the cams are 180 degrees out of phase to the cam arrangement in  FIG. 1   a.  
 
The net torque produced from spring ( 102 ) is given by:
 
         [0000]        T   x   =−K   x   e   2   2  cos(θ+π)sin(θ+π)  (12a),
 
         [0000]        T   x   =−K   x   e   2   2  cos(θ)sin(θ)  (12b),
 
         [0000]    where Kx is the spring rate of ( 102 ) and is uncompressed when the arm is in a vertical orientation (up or down).
 
Substituting equations (2), (11) and (12) into (1) gives the following:
 
         [0000]        Mr  cos(θ)− K   y   Δye   1  cos(θ)− K   x   e   2   2  cos(θ)sin(θ)+ K   y   e   1   2  sin(θ)cos(θ)=0  (13).
 
         [0000]    Equation (13) is equivalent to equation (5). 
         [0054]    In  FIGS. 1   a - 1   e  when the illustrated mechanism is in balance, the torque exerted by the payload is equal and opposite to the torque exerted by the springs, regardless of the angular orientation of the arm ( 105 ). As illustrated in equation (7), this condition is met when the product of e 1  squared and Ky is equal to the product of e 2  squared and Kx. If e 1  and e 2  are equal, then both springs must have the same spring rate (Kx=Ky). 
         [0055]    If tension springs are used in place of compression springs in  FIG. 1   a , then placing the payload on the opposite side of the pivot (or rotating both cams 180 degrees), equilibrium about the pivot ( 120 ) is established when the net torque is zero, i.e.: 
         [0000]      − T   g   −T   x   −T   y =0  (1),
 
         [0000]    where −Tg is the unbalanced torque due to the payload ( 125 ), on the opposite side of the fulcrum illustrated in  FIG. 1   a , and the unbalanced torque produced from tension spring ( 101 ) and ( 102 ) are −Tx and −Ty respectively. The unbalanced torque produced by the weight is the product of the gravitational force due to the payload M, and the shortest distance between the vector (M) and the point ( 120 ): 
         [0000]      − T   g   =−Mr  cos(θ)  (2).
 
         [0000]    The net torque of spring ( 101 ) about ( 120 ) is equal to the sum of the torque produced from the extension of the spring due to the arm displacement ( 130 ) and the pre-tension of the spring when the arm is horizontal ( 130 : θ=0), and is given by: 
         [0000]        T   y =+( K   y   e   1  sin(θ)+ K   y   Δy )( e   1  cos(θ))  (3),
 
         [0000]    where Ky is the spring rate of ( 101 ), and Δy is the displacement of the spring from rest when the arm is horizontal. The net torque produced from spring ( 102 ) is given by: 
         [0000]        T   x   =−K   x   e   2   2  cos(θ)sin(θ)  (4),
 
         [0000]    where Kx is the spring rate of ( 102 ) and is uncompressed when the arm is in a vertical orientation (up or down).
 
Substituting equations (2-4) into 1 gives the following:
 
         [0000]      − Mr  cos(θ)+ K   y   Δye   1  cos(θ)− K   x   e   2   2  cos(θ)sin(θ)+ K   y   e   1   2  sin(θ)cos(θ)=0  (5).
 
         [0000]    Since this is equation 5, then it becomes apparent that tension springs can be used as a replacement for compression springs 
         [0056]    Now referring to  FIG. 2   a , an alternate embodiment is illustrated, where both of the compression springs are pivotally attached ( 250 ) at the base (or grounded fixture) and the other ends are fixed to the cams by a hinged connection (roller bearings  255  and  260 ). This mechanism exerts its torque through the pins ( 265 ) and ( 270 ) to the arm ( 205 ) supporting the payload ( 225 ). 
         [0057]    The section view of this assembly illustrates that spring ( 201 ) and ( 202 ) can only exert compressive loads on the cams. Spring ( 201 ) is compressed between the adjustment screw ( 275 ) attached to the base ( 290 ) and the bushing ( 285 ), resulting in a compressive load on cam ( 203 ). Spring ( 202 ) is compressed in a similar manner between adjustment screw ( 280 ) and bushing ( 290 ) to exert compressive loads on cam ( 204 ). As a result this variation is capable of fully supporting the weight of the payload to a maximum of ±90 degrees from its rest position. The rest position of the arm is in the horizontal position (not shown in  FIG. 2   a ). 
         [0058]    Adjustment screw ( 275 ) is used to set the pre-compression load on spring ( 201 ) to support the weight of the payload when the arm is in the horizontal position (preload=Mr). Adjustment screw is set such that the spring ( 202 ) exerts no load on cam ( 204 ) when the arm ( 205 ) is in a vertical orientation (illustrated in  FIG. 2   a ). 
         [0059]      FIG. 2   b  is a schematic diagram illustrating the geometric relationship between each spring/cam pair shown in  FIG. 2   a.    
         [0060]    Equilibrium equations will now be described with reference to  FIG. 2   b . In  FIG. 2   b , equilibrium about the pivot ( 220 ) is established when the net torque is zero, i.e.: 
         [0000]        T   g   +T   u   +T   v =0  (14),
 
         [0000]    where Tg is the unbalanced torque due to the payload ( 225 ), and the unbalanced torque produced from spring ( 201 ) and ( 202 ) are Tu and Tv respectively. The unbalanced torque produced by the weight is the product of the gravitational force due to the payload M, and the shortest distance between the force vector (M=mg) and the point ( 220 ): 
         [0000]        T   g   =Mr  cos(θ)  (2).
 
         [0000]    The net torque of spring ( 201 ) about ( 220 ) is equal to the sum of the torque produced from the compression of the spring due to the arm displacement ( 230 ) and the pre-compression of the spring when the arm is horizontal ( 230 : θ=0), and is given by: 
         [0000]        T   v   =K   y   e   1  cos(θ− a   1 )[( l   1   2   +e   1   2 ) 1/2 −( l   1   2 −2 e   1   l   1  sin(θ)+ e   1   2 ) 1/2   +K   y   Δy )  (15),
 
         [0000]    where Ky is the spring rate of ( 201 ), and Δy is the displacement of the spring from rest when the arm is horizontal and l 1  and l 2  is the distance between the pivot ( 220 ) and a pivot ( 250 ) where the springs  201  and  202 , respectively, are coupled to the ground (or fixture). The net torque produced from spring ( 202 ) is given by: 
         [0000]        T   u   =K   x   e   2  cos(θ− a   2 )[( l   2   2   +e   2   2 ) 1/2 −( l   2   2 −2 e   2   l   2  cos(θ)+ e   2   2 ) 1/2 )  (16),
 
         [0000]    where Kx is the spring rate of ( 202 ). If l 1 &gt;&gt;e 1  and l 2 &gt;&gt;e 2 , then equation (14) can be reduced to equation (5) or (13) as the directions of the force vectors Fu and Fv become horizontal and vertical respectively in the limit as l 1 ,l 2 →∞. 
         [0061]      FIG. 3  illustrates a variation to the design presented in  FIG. 2 . A shoulder bolt ( 395 ) was integrated into the previous design to allow compression spring ( 302 ) to exert both compressive and tensile loads on cam ( 304 ). This assembly was designed to support a payload exerting a maximum torque of 27.5 in-lb. This device can support the payload to a maximum of ±180 degrees from the horizontal rest position of the arm. 
         [0062]    When the housing ( 305 ) supporting the cam ( 304 ) is moved away from the base ( 300 ), the spring in turn is trapped between the head of the shoulder bolt (or washer  310 ) attached to the base ( 300 ) and washer  315  (attached to housing  305 ). Thus, the compression of the spring ( 302 ) is converted into a tensile load that is in turn exerted on cam  304 . 
         [0063]    Alternately, if the housing ( 305 ) is displaced toward the base ( 300 ), the compression spring ( 302 ) is now trapped between washer  310  (now fixed to the housing  305  instead of the shoulder bolt  395  previously described) and the base  300  (and washer  315 ). Thus, the compression spring is now exerting a compressive load on cam  304 . 
         [0064]      FIG. 4  illustrates the phase relationship between springs  201  and  202  of the counterbalance assembly shown in  FIG. 2  with the addition of a shoulder bolt ( 295 ). The shoulder bolt ( 295 ) in this design allows the mechanism to apply both compressive and tensile loads to the cam ( 204 ). Since the maximum spring compression is not equal to the maximum spring tension, this system will support 97.5% of the payload through its full range of motion. However, if the shoulder bolt were applied to both springs  1  and  2  in the embodiment illustrated in  FIG. 2 , substantially all of the load but not 100% would be supported through a full 360 degrees of rotation. If the shoulder bolt were applied to both springs  101  and  102  in the embodiment illustrated in  FIG. 1   a  or  1   b , substantially all of the load, and up to 100% would be supported through a full 360 degrees of rotation. As ‘l 1 ’ and ‘l 2 ’ approach infinity then the embodiment shown in  FIG. 2  becomes equivalent to  FIG. 1   a  or  1   b.    
         [0065]      FIG. 4  shows a side view of the springs  201  and  202  illustrating the phase relationship between each spring-cam pair for various arm rotations, with rotational positions stated in relation to a Cartesian coordinate system with 0 degree corresponding to positive X axis. This device was designed to support a payload exerting a maximum torque of 200 in-lb:
       Arm at 180 degrees (left column): In this orientation, the preload of spring ( 201 : bottom left) is set to exert a torque to balance the payload. The spring ( 202 ) does not exert an unbalanced torque in this rotational position.   Arm at 270 degrees (center column): Spring ( 201 : bottom center) does not exert an unbalanced torque in this configuration. Spring ( 202 : top center) is relaxed and does not exert an unbalanced torque to the arm. Since the payload is directly over the pivot, the system is in equilibrium.   Arm at 0 degrees (right column): In this arm rotational position, the preload of spring ( 201 : bottom right) is set exert a torque to balance the payload. The spring ( 202 ) does not exert an unbalanced torque in this arm position.       
 
         [0069]      FIG. 5 : illustrates an alternate variation to the design presented in  FIG. 3 . The spring cam pair(s) illustrated in  FIG. 3  were rotated to align both springs in a vertical orientation. However, the relationship between the cam and corresponding spring is still maintained. This design modification supports 97.5% of the load to a maximum of ±90 degrees from its rest position. The rest position of the arm is in the vertical position. 
         [0070]    While the Figures show counterbalance assemblies for a joint of a mechanical arm where the assembly comprises two or three springs, the skilled person having the benefit of reviewing the Figures will recognize that the counterbalance assemblies need not be restricted to spring balance mechanisms and will further recognize equivalent counterbalance assemblies. 
         [0071]    While springs have been used in the Figures it will be recognized that any force generating device may be used in the counterbalance assembly described herein. A force generating device refers to any structure or device which provides resistance to compressive or tensile forces in response to linear deflection imposed thereon. More specifically, any structure or device that exhibits resistance to linear compression or tension along a longitudinal axis thereof may be useful as a force generating device. Thus, a force generating device includes a longitudinal axis along which linear forces shall be imposed as a result of rotational movement of a mechanical arm. The force generating device interacts with a cam to converts rotational movement of the arm into linear deflection of the force generating device. An example of a force generating device is a spring-like device. A spring-like device is any device or structure that acts like a compression or tension spring in providing resistance to a linear compression and/or tension along a longitudinal axis. An example of a spring-like device is a unit of rubber or other resilient material, or a hydraulic or pneumatic pressurized cylinder any one of which may be used in an equivalent manner to a compression or tension spring by providing resistance to a linear force along a longitudinal axis. Another example of a spring-like device is a spring, such as a compression spring or a tension spring. Compression springs is an example of a low cost force generating device that may be utilized to provide a simplified arrangement within the counterbalance assembly. A compression spring includes a longitudinal axis along which linear compressive forces may be imposed as a result of rotational movement of a mechanical arm. Examples of compression springs include relatively standard die springs as commonly available in the industry. The exact number and size of such springs used in the counterbalance assembly described herein can vary depending upon the counterbalance torque desired, the size of the robotic arm involved, and the like, as will be recognized by the skilled person. The force generating device may be adjustable such that the resistive force provided by the force generating device may be increased or decreased to allow for variation in mechanical arms. 
         [0072]    A force generating device will interact with at least one cam in the counterbalance assemblies described herein. A cam is a general term pertaining to a component that rotates or reciprocates to create a prescribed motion in an interacting element, which is often termed the follower. In the context of the counterbalance assembly described herein, a cam may be any structure or device that is set relative to a pivot of a joint, to exert a variable motion on a interacting portion of a force generating device as a function of the rotation of the joint. More specifically, a cam refers to any structure or device that can convert rotational movement of a mechanical arm into a linear movement parallel to a longitudinal axis of a force generating device. A cam is typically set eccentrically relative to a pivot of a joint of the mechanical arm. A cam may be mounted within the circumference of a joint. Alternatively, a cam need not be mounted entirely within the circumference of a joint, and may readily be set outside the circumference of a joint where full rotation is unnecessary or where physical collision or interference of mechanical components is not a concern, for example as may be the case for large industrial robotic arms. One example of a cam is an eccentric bearing. Another example of a cam is a lever extending from the joint that can interact with a force generating device. Cams can be varied shape so as impart a desired linear deflection of the force generating device. 
         [0073]    Any technique for achieving an interaction of a cam to its follower known in the art may be used to achieve interaction of a force generating device and a cam in the counterbalance assembly described herein. The Figures show various alternatives of a spring interacting with a cam. For example,  FIGS. 1   d - 1   g  show various alternatives of a spring abutting a cam. As another example,  FIG. 2  shows a spring hingedly coupled to an eccentric bearing. As yet another example,  FIGS. 1   a - 1   c  show a spring coupled to a cam through a yoke. Each of the examples described in the Figures may be used to achieve an interaction between a force generating device and a cam. Still other forms of coupling using slots, pegs or other techniques known in the art can be used to achieve the interaction of a force generating device and a cam. Interaction as used herein contemplates a force generating device abutting or engaging a cam, and a force generating device being linked or coupled to a cam. 
         [0074]    The counterbalance assembly has been structurally shown in the Figures using at least two springs with each spring interacting with at least one cam that is mounted eccentrically relative to a pivot of a joint of a mechanical arm. Functionally, the spring/cam relationships can be divided into first and second groups. The purpose of each group is to generate torque. The torque generated by the first and second groups together allows the counterbalance assembly to maintain an equilibrium of torque exerted on a joint throughout the desired rotation of the joint. The torque provided by the first group is used to counteract the torque exerted by the mechanical arm and its associated payload at a rotational position, typically horizontal, where torque exerted by the arm is greatest. The torque provided by the second group is to counteract the linear change in force exerted by the first group. For example, the linear change in force due to linear displacement of springs in the first group when the arm is above horizontal results in the torque exerted by the mechanical arm being greater than the torque exerted by spring/cam pairs in the first group causing the arm to drift back to horizontal. In contrast, the linear change in force due to linear displacement of springs in the first group when the arm is below horizontal results in the torque exerted by the mechanical arm being less than the torque exerted by spring/cam pairs in the first group causing the arm to drift back to horizontal. The torque provided by the second group can maintain equilibrium when the arm is below and above the horizontal. Thus, the torque provided by the second group compensates for the first group to maintain the arm in positions other than the horizontal. The horizontal is the rest position or datum. 
         [0075]    Using the specific example shown in  FIG. 2  for illustration only, the purpose of spring  201  is to offset for the weight of the payload. To account for its weight, the initial compression of the spring is set with an adjustment screw (for example, item  275 ,  FIG. 2 ) such that the torque exerted by the spring through the cam is equal to the counter torque resulting from the weight of the payload. The purpose of the second spring is to offset for the linear change in force with compression of the first spring. 
         [0076]    For example, the pre-compression load of spring  201  may be set with the arm in a rotational position, typically horizontal, where the arm exerts its greatest torque. Thus, the torque exerted by spring  201  maintains the system in equilibrium with the arm in the horizontal position. This arm position is the datum or rest position. When the arm is displaced from its horizontal position when with the pre-compression load of spring  201  set, the lever will return to its initial rest position (horizontal) without spring  202  present due to change in force exerted by the spring  201  due to linear displacement of the spring. With spring  202  in place, when the arm is displaced from the horizontal, the change in force applied by spring  201  is counteracted by spring  202 . The result is the lever will not return to its initial equilibrium position defined by spring  201 . With the addition of spring  202 , its equilibrium position is no longer related to orientation ( 230 ) of the lever/arm. 
         [0077]    Counterbalance assemblies described herein may maintain equilibrium of torque for an unlimited degree of rotation. Torque equilibrium may be maintained for arm rotations greater than 1 degree, 45 degrees, 90 degrees, 135 degrees, 180 degrees, 225 degrees, 270 degrees, 315 degrees, 360 degrees, and even greater, in both positive and negative directions. 
         [0078]    Counterbalance assemblies described herein may be used for one or more than one joint in a mechanical arm. 
         [0079]    The following relationship as described with reference to  FIG. 1   b  holds true for the counterbalance assemblies shown throughout the Figures. Pre-compression of a first spring to counteract torque of a mechanical arm is set for an arm position which exerts its greatest torque, ie horizontal in  FIG. 1   b . With the arm in this position, the line between the pivot ( 120 ) and the center of eccentric cam ( 103 ) is substantially perpendicular to the longitudinal axis of spring  101 . At this same arm position, the line between the pivot ( 120 ) and the center of eccentric cam ( 104 ) is substantially parallel to the longitudinal axis of spring  102 . In certain examples, with the arm in this position, the line between the pivot ( 120 ) and the center of eccentric cam ( 103 ) is perpendicular to the longitudinal axis of spring  101 , and the line between the pivot ( 120 ) and the center of eccentric cam ( 104 ) is substantially parallel to the longitudinal axis of spring  102 . 
         [0080]    Counterbalance assemblies, for example spring balance assemblies, described herein may be used in conjunction with further components as desired to aid in the orientation of mechanical arms, for example, without limitation, brakes for locking a hinged arm, encoders for measuring rotational angles of a hinged coupling, counterweights and/or other balances to offset the mass of the system, computer controlled actuators for automating actuation of a hinged coupling. Further components that may be incorporated into the mechanical arm will be apparent to the skilled person, and suitable combinations of optional components will also be apparent depending on the particular mechanical arm and the particular use of the mechanical arm. 
         [0081]    As one example of an optional component, a counterweight may be mounted to the arm to offset the mass of a payload and/or mass of one or more elements of an articulated arm. Although the counterbalance mechanism described herein can eliminate the need for counterweights, counterweights may, if desired, be used in conjunction to offset the mass of the system. 
         [0082]    As yet another example of an optional component, a braking mechanism may be mounted within the mechanical arm to inhibit or stop motion of arm elements relative to each other. 
         [0083]    As still another example of an optional component, the mechanical arm may be equipped with motors (not shown), for example servo motors that may be controlled by a computer to automate the motion of various linkage elements. The counterbalance mechanism described herein reduces the force required by motors to actuate the mechanical arm. 
         [0084]    As another example of an optional component, in embodiments where springs are used in a counterbalance assembly the compression or tension of one or more springs is adjustable. 
         [0085]    Still further optional features will be apparent to the skilled person. 
         [0086]    The spring balance mechanism may be used in conjunction with many different types of mechanical arms, for example, arms having industrial or medical uses. 
         [0087]    A specific illustrative example of a mechanical arm where the counterbalance assembly may be used is a guide apparatus  601  that may be used for 3D orientation of a medical tool relative to and through a fixed point in space, a remote fulcrum ( FIG. 6 ). The guide apparatus comprises two linkage elements, a crank  602  and a link  604 . The crank  602  and the link  604  may be of any size, or shape that allows for the remote fulcrum  600 . 
         [0088]    The linkage elements may be hingedly coupled to form positioning elements. In  FIG. 6  the crank  602  and link  604  both have an arcuate structure having a central angle of about 45 degrees. The crank has a first end  612  and a second end  614 . The link also has first and second ends  622 ,  624 . When the guide apparatus is in use the first end  612  of the crank is hingedly coupled to a base or stabilizer. The first end  612  may comprise a full hinged coupling that is attached to a member that is rigidly fixed to the base or ground arm. 
         [0089]    Alternatively, the first end  612  may comprise a portion of a hinged coupling  610  with the remainder of the hinged coupling being provided by the base or stabilizer. The second end  614  of the crank forms a hinged coupling  616  with the first end  622  of the link. The second end  614  of the crank comprises a portion  618  of the hinged coupling  616 , while the first end  622  of the link comprises the remaining portion  620  of the hinged coupling  616 . The second end  624  of the link is coupled to a tool holder  606 . The tool holder may be in the form of an adaptable cradle for securing a shaft  632  that may be used to actuate a medical tool  640 . The spring balance assembly  650  is provided for the joint between first end  612  and the base or ground arm. A counterweight  652  is provided to offset the weight of the payload. However, if desired counterweight  652  may be replaced with a spring balance assembly. 
         [0090]    The above-described embodiments are intended to be examples and alterations and modifications may be effected thereto, by those of skill in the art, without departing from the scope of the invention which is defined by the claims appended hereto.