Patent Publication Number: US-9847045-B2

Title: Apparatus for upper body movement

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a 371 National Stage of International Application PCT/SG2013/000520 filed on Dec. 10, 2013 entitled, “AN APPARATUS FOR UPPER BODY MOVEMENT”, which claims priority to U.S. Provisional Application No. 61/735,295 filed on Dec. 10, 2012 entitled, “AN APPARATUS FOR UPPER BODY MOVEMENT”, both of which are incorporated herein by reference in their entirety for all purposes. 
    
    
     FIELD OF INVENTION 
     The invention relates to an apparatus for upper body movement, specifically for elbows and shoulders. 
     BACKGROUND 
     Stroke is a cerebrovascular accident recognized as the leading cause of neurological disability worldwide. Stroke can affect different areas of the brain and, due to death of affected neurological cells, the functionality of specific areas of the brain might be seriously compromised or lost. It has been estimated that among the 75% of stroke survivors, more than half will require specialized rehabilitation. Individuals are left with a broad range of disabilities, from mild paresis to complete paralysis of both the upper and lower extremities. Results from studies exploring the time course of recovery report that approximately 50% of the patients regain some functional abilities in the paretic upper extremity, whereas only 10% to 20% experience complete recovery [Kwak07]. 
     Although neurological cells lose the ability to reproduce soon after the first years of life, there exists a spontaneous recovery process after stroke. A first physiological factor taking place at an early, or acute, phase after stroke is the resolution of the damaged tissue, with a decrease of swelling and bleeding. At the same time, lost functionalities are partly replaced by compensatory behaviors, which allow survivors to keep performing everyday motor tasks, although in an inefficient way. A second physiological factor taking place after stroke but with slower dynamics is phenomenon of plasticity. Despite the death of specific neurological cells, their function can be dynamically reallocated thanks to a diffuse and redundant network connecting different areas of the brain. The plasticity is an ongoing phenomenon since birth but it is enhanced soon after stroke and is strongly affected by the environment and “experience-associated neural changes have the potential to either hinder or enhance functional recovery” [Sch00]. 
     The principle that plasticity is induced by motor practice, both active and passive, has inspired several neuro-rehabilitation techniques. However, the optimal training strategy for facilitating plasticity and functional reorganization has remained unclear thus far. One of the main reasons is that dose and consistency of therapy delivered by a therapist and outcomes as assessed via available clinical scales can be hardly compared across therapists. In this sense, robotic devices emerged as an objective means to deliver therapy and measure outcomes. Another reason is also due to the limited amount of therapy which a stroke survivor can be exposed to, exacerbated by an aging population, cost of health-care/therapy and insurance policies. 
     In this regard, rehabilitation robots have been developed to alleviate the burden on therapists and healthcare systems, while simultaneously increasing patient access to rehabilitation. Several studies have shown similar improvement in stroke survivor outcomes with the use of rehabilitation robotic devices when compared with conventional therapy. Robot-aided therapy complements conventional therapy with features such as exact repetitive movements, programmable resistance/assistance levels, objective evaluation, and motion sensing capabilities. Robots also represent a potential aid for therapists to extend rehabilitation to remote locations or to a patient&#39;s home. 
     Active participation to the therapy can be enhanced by virtual reality environments, where the concomitance of haptic and visual stimuli further increase the so-called Hebbian learning processes behind plasticity. In addition to this, robotic devices can accurately measure kinematic (e.g. position, speed) and dynamic (interaction forces) parameters, providing fine and objective assessment which complements the available clinical scales, such as the Fugl-Meyer, Wolf Motor Function, Stroke Impact Scale. 
     Many robotic devices have been developed which target post-stroke rehabilitation of the upper-limb [Bre07], however very few are commercially available and, in any case, their use in hospitals and clinics is still very limited due to high costs and complexity. 
     At the moment, the only commercially available robots for elbow/shoulder rehabilitation are shown in  FIG. 1 . Other robots only exist as research prototypes, e.g [Gurg00], [Lum02], [Mice05], [Rein00], [Kre98], [Vol00], and have been used in clinical studies to validate their efficacy in rehabilitation. Sample sizes used in initial, pilot studies to prove clinical usefulness (for some robots more than two studies are available) are shown in  FIG. 2 . Among these, only four devices are of 2D planar, end-effector type, namely MIT-MANUS [Kre98], Braccio-di-Ferro [Casa09], MEMOS [Mice05], and Reha-Slide [Hess08]. Only the first three are in fact robots (as they entail actuation) while the Reha-slide is passive machine, as described later. 
     As shown in  FIGS. 3( a ) and 3( c )  respectively, MIT-MANUS [Kre98] and Braccio-di-Ferro [Casa09] are functionally very similar. Meant for rehabilitation of the shoulder and elbow, both robots are based on the so-called pantographic mechanism ( FIG. 3( b ) ) which ensures a so-called low intrinsic end-point impedance due to the very low inertia and friction properties of the mechanism, while able to impose large forces at the handle (up to 5 kg of continuous force). These characteristics allow both the MIT-MANUS and Braccio-di-Ferro to rapidly comply with the subject&#39;s movements. Both robots are also endowed with sensors which allow measuring the position and velocity of the handle as well as interaction forces between robot and patient. During the therapy, the subject&#39;s arm is attached to the end-effector (handle) of the robot. The subject moves the handle and performs goal-directed tasks, such as reaching a target, often guided by a videogame. The robots senses the current position and velocity (e.g. direction) of the reaching movement and is capable of exerting assistive or disturbing forces, or more general force fields, according to the therapy to be imparted. From a clinical evaluation perspective, the MIT-MANUS is the only commercially available robot in this category and also the most clinically studied device for upper-limb neuro-rehabilitation. Many random controlled trials (RCT) have shown statistically significant decrease of impairment, at the level of shoulder and elbow, for acute, sub-acute as well as chronic stroke survivors. These studies were performed on sample sizes which varied from twenty to one hundred and twenty seven subjects. A recent, multi-centre RCT study involving one hundred and twenty seven patients, showed that robot-assisted therapy was no better than usual therapy and intensive therapy after 12 weeks but that it was better than usual therapy after three months [Lo10]. 
     Unfortunately, the MIT-MANUS and Braccio-di-Ferro robots (and similar devices) share the following drawbacks:
         lack of portability, limiting the potential use at home or community centres;   high complexity, requiring highly trained personnel (to ensure safe operations as well); and   high costs, meaning that only few and specialized clinics can afford (at most) one, thus limiting their availability to most of impaired subjects, especially those with mild impairments.       

     Referring to  FIG. 4 , the MEMOS [Mice05], ARM guide [Rein00] and the Reha-Slide [Hess08] are examples of two planar devices for neuro-rehabilitation of the shoulder/elbow meant to represent a trade-off between the best clinical efficacy and the least amount of robotic complexity. The Reha-Slide device, in fact, is not a robot but a lower cost passive machine designed for bi-manual arm training. The Reha-Slide is a one degree-of-freedom passive device whereby the patient uses the unaffected arm to aid the affected one, exercising the shoulder, elbow, and wrist. In a multi-centre RCT study, fifty-four sub-acute stroke survivors, over a six week period, received therapy with the Reha-Slide or electrical stimulation in addition to standard care. Significant improvement was found in both groups but no statistically significant difference [Hess08]. 
     The ARM guide robot was designed to assess multi-joint coordination during fundamental to many activities of daily living such as reaching tasks. As reaching movements in healthy subjects are known to approximately follow straight-line trajectories, a passive, linear constraint with a single motor robot was used to assist in arm movement and to reduce complexity and costs typical of multi-degrees-of-freedom robots [Rein00]. A RCT study including nineteen patients showed that the therapy based on the ARM guide robot improved arm movement ability, although no difference was detectable with a group performing task-matched unassisted reaching tasks. 
     Unlike the ARM guide and the Reha-Slide, the MEMOS robot is based on a 2D planar mechanism in a Cartesian configuration. While this simplifies the kinematics and therefore the control, the issue with the MEMOS is that it simply readapts industrial robots design. Industrial robots, well known to be repeatable, implement position-controlled architectures, not suitable for the flexibility required for interacting with humans, whether healthy or impaired. Such flexibility can be achieved by means of admittance control, whereby force sensors are used to sense the human reaction forces and command appropriate actions. However, this approach has several limitations. Firstly, it relies on force sensors, typically expensive and noisy, making the system insensible to weak interactions. Secondly, in order to adapt quickly to changes of interaction forces, large motors should be used, making the system intrinsically unsafe for humans and exceedingly expensive. The inertia and friction of mechanisms, as perceived by the user, are typically high and cannot be sufficiently compensated for by means of active control. This is clearly an issue in rehabilitation as subject&#39;s movements are strongly influenced by the mechanical impedance of the robot [Cam09] while ‘assist-as-needed’ strategies are fundamental for increasing recovery. 
     SUMMARY 
     There is provided an apparatus for upper body movement. The apparatus comprises a H-shaped cable-driven mechanism; two motors for driving the H-shaped cable-driven mechanism; and a manipulandum coupled to the H-shaped cable-driven mechanism for independent movement along x and y axes. Each motor may be of a type selected from, for example DC motor, AC motor, magnetic linear actuator, pneumatic linear actuator and the like. The two motors may be controlled by a motor driver and a driving force of the two DC motors may be determined by a position of the manipulandum. The driving force of the two DC motors is determined using the following equations: 
     
       
         
           
             
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     Preferably, the H-shaped mechanism is configured in a form of a differential mechanism such that a user holding the manipulandum experiences low inertia. The manipulandum includes a horizontal carriage; a solid base mounted to the horizontal carriage; a six degree of freedom force/torque sensor mounted to the solid base; a plurality of idler pulleys; and a plurality of vertical carriages. The manipulandum can also include a handle, which may be a separate part of the manipulandum. 
     The apparatus can also include a plurality of guides arranged along the x and y axes; a plurality of idler pulleys; and a driving pulley coupled to each motor. It is preferable that a cable of the H-shaped cable-driven mechanism is wound at least four turns around the driving pulley coupled to each motor. 
     Advantageously, four force channels are available, horizontal and vertical channels being obtained by mechanically blocking the horizontal/vertical carriages, and 45° channels being obtained by blocking the driver pulley. 
    
    
     
       DESCRIPTION OF FIGURES 
       In order that the present invention may be fully understood and readily put into practical effect, there shall now be described by way of non-limitative example only preferred embodiments of the present invention, the description being with reference to the accompanying illustrative figures. 
         FIG. 1  shows examples of commercially available robots for shoulder/elbow rehabilitation. 
         FIG. 2  shows a graph of sample sizes used in clinical studies for various robots. 
         FIGS. 3 ( a )-( c )  show examples of 2D planar robots based on a pantographic mechanism. 
         FIG. 4  shows examples of 2D cartesian robots and passive machines. 
         FIG. 5  shows a possible application of the present invention. 
         FIG. 6  shows a schematic top view of the present invention. 
         FIGS. 7 ( a )-( b )  show graphical representations of differential movements which the present invention can undergo. 
         FIG. 8  shows graphical representations of movements which the present invention can undergo. 
         FIG. 9  shows a mechanical drawing of the present invention. 
         FIG. 10  shows a photograph of the present invention. 
         FIGS. 11 ( a )-( e )  show photographs of various pulleys used in the present invention. 
         FIG. 12  shows a DC motor electromechanical model which is employed in the present invention. 
         FIGS. 13 ( a )-( b )  show a further enhancement of the present invention. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     The preferred embodiments of the present invention may provide an apparatus for upper body movement, specifically for elbows and shoulders. The apparatus can be used for applications such as, for example, surgical training, tele-operation, game playing, and most pertinently, rehabilitation. For example, a surgeon grasps a manipulator&#39;s handle of the apparatus as if it were a scalpel, and a virtual organ is displayed on a computer screen. The surgeon then moves the handle as if he were cutting the organ with a scalpel. The apparatus then records the trajectory/force and the apparatus can introduce disturbances along the path to simulate anomalies in the organ. Although the apparatus is not suitable to all patients (e.g. the severely impaired ones) undergoing rehabilitation, a large proportion of patients will be able to benefit from use of the apparatus. The low cost to fabricate the apparatus ensures that the apparatus is able to be readily deployed in hospitals, community centres and private homes. Furthermore, the apparatus complements current robotic therapies and allows patient-robot interaction, enabling early discharge and continuous monitoring/training of patients. 
       FIG. 6  shows a schematic top view of the apparatus  20  (in this instance used for upper body rehabilitation),  FIG. 9  shows the schematic diagram of the apparatus  20  and  FIG. 10  shows a photograph of an example implementation of the apparatus  20 . The apparatus  20  includes a handle  36  on a manipulandum  22 , a six degree of freedom force/torque sensor  23  (for example, ATI Mini40 with 80 N and 4 Nm sensing range), two DC-motors  24 ,  26  controlled by a motor driver and a PC with a data acquisition system (not shown). The handle  36  is a main component of the apparatus-user interface, but it should be appreciated that the handle  36  need not be a separate object. The manipulandum  22  can be shaped in a physical form which facilitates gripping by a user&#39;s hand. The force/torque sensor  23  is configured to measure the force/torque transmitted between the manipulandum  22  and the user&#39;s hand while gripping the handle  36 . 
     The driver and the PC with a data acquisition system may be scalable down to a microcontroller form. For a haptic device, a data acquisition system is required to read the position of the manipulandum  22  and to provide instructions to control an output force of the motors  24 ,  26  which will be transferred to the manipulandum  22 . In our current implementation, a PC with a real-time control platform (dSPACE, Germany) is used to read the position of the manipulandum  22  (via a linear encoder attached to the motors  24 ,  26 ) and to send an output signal to control the output current to the motors  24 ,  26  via the motor driver. 
     The force transmission from DC-motors  24 ,  26  to the manipulandum  22  is carried out through an H-shaped cable-driven mechanism  28 . It may be possible to adopt an A-shaped cable-driven mechanism, but such a shape would introduce more issues/complexity, such as, for example, asymmetric friction, position-dependant impedance, more complex kinematics and so forth. The DC-motors  24 ,  26  are shown with driving pulleys  25 ,  27  directly connected to the motors  24 ,  26  respectively. The driving pulleys  25 ,  27  transfer the force to a cable  32  which is routed through eight idler pulleys  30  (for example, diameter of 20 mm with 6 mm bearing inside, Misumi AFBD9-20) in the H-shaped cable-driven mechanism  28 . Ultimately the force is directly transferred to the carriages (and ultimately the manipulandum  22 ), with minimal friction losses. 
     The handle  36  (made from peek rod) is connected rigidly to a horizontal carriage  38 . A mounting is fixed to a solid base  40  to mount the six degree of freedom force/torque sensor. The handle  36  (of sample dimensions 25 mm×65 mm) is mounted on top of the six degree of freedom force/torque sensor  23 . The solid base  40  is mounted to the horizontal carriage  38 . The manipulandum  22  also includes four idler pulleys  30  (from the eight idler pulleys  30  mentioned earlier) and two vertical carriages  39 . 
     The apparatus  20  has a configuration in a form of a differential mechanism which enables independent movement of the manipulandum  22  along x and y axes despite having just one cable loop. Another advantage of this configuration is that both actuators are grounded hence a user holding the manipulandum  22  experiences low inertia. Moreover, a Cartesian approach in the manipulandum  22  is obtained by the linear guides/rails of the H-shaped cable-driven mechanism  28 . This configuration ensures homogeneous inertia and friction throughout a whole workspace of the apparatus  20 . 
     The apparatus  20  is configured to provide planar (i.e. in the xy plane) differential motion. A differential mechanism is a device that produces resultant motion as sum or difference of the component motions, an example of cabled differential for rotary motions can be found in [Sal193]. In the apparatus  20 , one movement in one axis is obtained by the sum of the rotation of the motors, while the other is obtained by the difference. This differential movement is represented graphically in  FIG. 7 . To produce movement in the x axis, DC-motors  24 ,  26  must rotate in same directions (i.e. either both clockwise or both counter-clockwise), while for that in y axis, in opposite directions. So,  FIG. 7( a )  shows both DC-motors  24 ,  26  rotating in a clockwise direction to produce movement of the manipulandum  22  in a positive x direction and in  FIG. 7( b ) , both DC-motors  24 ,  26  rotate in opposite directions to produce movement of the manipulandum  22  in positive y direction. It should be noted that during x axis movement, only the horizontal carriage  38  moves (together with the handle  36  and force/torque sensor  23 ). However for y axis movement, the moving parts are more, i.e. all carriages  38 ,  39  with 4 idler pulleys  30 . Hence, in order to reduce the inertia experienced by the user, lightweight components are necessary. It should be appreciated that the motors  24 ,  26  can also be in a form of AC motors, linear actuators (magnetic or pneumatic), or any device which is able to produce actuation. 
     The apparatus  20  sits on an aluminum table structure (for example, a 30×60 mm aluminum frame), and is suitable for table-top use. Two sets of lightweight stainless steel parallel rails, one on top of the other, are used to implement a 2D Cartesian mechanism. Vertical rails  50  allow for movement of the manipulandum  22  in Y axis, and may be 470 mm long miniature linear guides from Misumi (SSELB13-470), mounted 108 mm apart on a 6 mm clear plastic plate. Horizontal rails  52  mounted above the vertical rails  50  allow for movement of the manipulandum  22  in X axis, and may be 275 mm long miniature linear guides from Misumi (SEBZ10-275). The smaller set of rails  52  contributes to the total inertia that the subject has to move for movement in y axis. In this example, by leaving out the length of the carriage (45 mm) and end stoppers at the linear guides, the total Cartesian work space of the mechanism is 221 mm (x)×441 mm (y). 
     An H configuration of cable  32  is required for the differential driving system for the mechanism  28  with two driving motors  24 ,  26 . As shown in  FIG. 10 , the H-shaped cable-driven mechanism  28  is constructed using eight idler pulleys  30 , four of which are fixed to two T-shaped custom made mounting plates (as shown in  FIG. 10( a ) ) which are fixed at the bottom side of the top rails. Six mm male end threaded cantilever shafts are used to fix the pulleys  30  to the mounting plates. The other four idler pulleys  30  are installed at the 4 ends of the mechanism  28 , three of which are fixed to the aluminum table structure while one at the bottom right hand side is mounted on top of the lead screw guide unit (for example, Misumi XKNEJ20, as shown in  FIG. 10( b ) ) to enable the adjustment of pretension of the cable  32 . Clear plastic spacers are used to adjust the height of the idler pulleys  30  to align the grooves of the idler pulleys  30  into a single horizontal plane. The use of spacers ensures that the cable  32  is maintained in a substantially horizontal plane to minimize vertical loading of the idler pulleys  30  which will cause additional friction. 
     For the actuation of the mechanism  28 , the driving pulleys  25 ,  27  (for example, having diameter 27.5 mm) are used at the middle in tangent to the long side of the outer cable line of the mechanism  28 . The driving pulleys  25 ,  27  are mounted on a clear plastic plate with a double bearing unit (for example, Misumi BGCBB623ZZ-20) driving shaft. The motors  24 ,  26  are mounted directly under the driving pulleys  25 ,  27  with four circular posts (both-ends female thread, for example, Misumi ETKR6-15) connecting motor mounting plate and pulley mounting plate ( FIGS. 10( c ) and 10( d )  respectively). A six mm coupler (for example, Misumi MCO15-6) connects the motors  24 ,  26  and the driving pulley shaft. There is a need for two motors  24 ,  26 , as in an instance when only a single motor is used, there can only be one degree of freedom. Even if a set of gears is incorporated to establish a mechanical relation between the driving pulleys  25 ,  27 , the manipulandum  22  will only be able to move at one speed/trajectory. For example, if the driving pulleys  25 ,  27  are coupled with a 1:1 transmission, the manipulandum  22  will only move in a left-right manner. If the driving pulleys  25 ,  27  are coupled with a −1:1 transmission, the manipulandum  22  will only move in an up-down manner. If the driving pulleys  25 ,  27  are coupled with a 1:2 transmission, the manipulandum  22  will only be able to move along a straight line at a pre-defined angle. It should be appreciated that varying the gear ratios (akin to a continuous variable transmission gear system in cars) would require a second motor. 
     In this embodiment, 0.54 mm nylon coated steel wire rope (7×7) (for example, Asahi Intecc NB45-61) was selected for the cable  32 . Due to its flexibility, it is easy to combine it for use with small pulleys like those used in the mechanism  28 , hence allowing the possibility to scale down the working space with minimum effort. The cable  32  is routed through eight pulleys as shown in  FIG. 9  to form an H configuration and is wrapped at least four turns around the each driving pulley  25 ,  27  (as shown in  FIG. 10( e ) ). The more turns around each driving pulley  25 ,  27 , the lower the likelihood of slippage due to the higher friction. However, the pulley  25 ,  27  will have to be able to have the physical dimensions to accommodate the winding of the cable  32 . The friction provided from the at least four turns of the cable  32  at each driving pulley  25 ,  27  can hold 50 N of force at the handle  36  when both driving pulleys  25 ,  27  are hampered. Both ends of the cable  32  are fixed to a bottom mounting plate of a torque sensor at a distal side of the mechanism  28 . 
     As an example, Faulhaber&#39;s DC Micromotors (3863H012C) are chosen to drive the manipulandum  22 . They are light and compact (400 gram, 38 mm diameter, 63 mm length) but it can produce significant amount of torque (1424 mNm stall torque). By attaching a 27.5 mm diameter pulley to the motor shaft, 25 N force can be generated by each motor to move the driving pulley. This amount of force is at the same order as the arm force to move the handle in general, though still below what the arm can produce maximally. For rehabilitation purpose, a more powerful motor may be needed if for example the patient has a very minimum muscle power and the robot is required to assist his/her motion to achieve a certain goal. For motor control experiments, the force generated by this particular setup is sufficient to provide perturbation. 
     To drive the motor, Faulhaber 4 quadrant PWM motion controller (MCDC3006, 65×58×27.5 mm 3 ) may be used. It has its own ROM, an RS232 interface, and an analog input so that it can be programmed to accept a voltage input to be used as the voltage sent to the motor. Using a simple DC motor allows control of current supply by controlling the voltage sent to the motor. 
     Faulhaber optical encoder (HEDL5540) may be attached to the shaft of each motor. It has a resolution of 500 lines per revolution, thus for a 27.5 mm pulley diameter, its resolution is &lt;0.2 mm in the xy plane. The encoder count is acquired through an input port on the dSPACE system. The dSPACE system is then programmed to provide an analog output which controls the voltage to be sent to the motor through the driver. The programming is done using Simulink and the program is compiled to the dSPACE memory with Simulink Coder. 
     Due to the differential mechanism of the apparatus  20 , the forces at the end-effector depend on the torque generated at the motor shaft according to the following equations: 
                     [           F   x               F   y           ]     =     A   ⁡     [           τ   L               τ   R           ]               (   1   )                   [           v   x               v   y           ]     =         (     A     -   1       )     T     ⁡     [           ω   L               ω   R           ]         ⁢     
     ⁢     A   =       1   r     ⁡     [           -   1         1             -   1           -   1           ]                 (   2   )               
where the variables with x and y subscript are with respect to the xy coordinate frame as defined in  FIG. 6 , and the variables with L and R subscript are with respect to the DC-motors  24 ,  26  respectively. So τ L  and τ R  are the torques exerted by the DC-motors  24 ,  26 , while the ω&#39;s are the angular velocity of the shaft of DC-motors  24 ,  26 . F x  and F y  are the force components at the handle. v x  and v y  are the velocity components at the handle  36 . The variable r is the radius of the driving pulleys  25 ,  27  attached to the motor shaft, i.e. 0.5*25.5 mm=13.75 mm.
 
     A possible family of perturbation force fields is the velocity dependent fields, which can comprises damping and/or Coriolis&#39; fields. In both cases the force F H  at the handle is proportional to the handle velocity v H   
     
       
         
           
             
               
                 
                   
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     The perturbation B in our setup may consist of two components, Coriolis field—B c , and damping field—B d , parameterized as α and β 
                     B   =       α   ⁢           ⁢     B   c       +     β   ⁢           ⁢     B   d           ⁢     
     ⁢     B   =       α   ⁡     [         0         b   cz               -     b   cy           0         ]       -     β   ⁡     [           b   dx         0           0         b   dy           ]                   (   4   )               
where all the b&#39;s are positive numbers.
 
     Substituting eqs (1) and (2) to (3), we can rewrite the perturbation equation with respect to the motors 
     
       
         
           
             
               
                 
                   
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     Hence once we obtain the angular velocity of the shaft of the DC-motors  24 ,  26 , read via encoders, we can calculate the amount of torque that the DC-motors  24 ,  26  have to produce for the perturbation. To control the generated torque, we will assume that it is linearly proportional to the amount of current supplied to the DC-motors  24 ,  26 . 
                     [           i   L               i   R           ]     =           [           K     i   ,   L           0           0         K     i   ,   R             ]     ⁡     [           τ   L               τ   R           ]       ⁢     
     [           i   L               i   R           ]     =       K   i     ⁡     [           τ   L               τ   R           ]                 (   6   )               
where K i,L,R  are the current constant (K i  is 1/K t  in  FIG. 7 ).
 
     In conclusion, the feedforward model is 
     
       
         
           
             
               
                 
                   
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     Apart from the input (angular velocity) and output (current), all the variables are constant numbers and all the operations are just matrix multiplication. The inverse of matrix A can be calculated beforehand since A is known. The system is programmed to receive values of α and β from the user to determine the type of perturbation. The simplicity of this model enables it to be implemented in the low cost microprocessor. 
     As mentioned earlier, the motor driver only supports voltage control and not current control. So we have to provide a model relating the current and voltage. Based on classical DC motor models, as shown in  FIG. 12 , the following equations can be applicable for the 2-motor system: 
                     [           V   L               V   R           ]     =         [           R   L         0           0         R   R           ]     ⁡     [           i   L               i   R           ]       +       [           K     e   ,   L           0           0         K     e   ,   R             ]     ⁡     [           ω   L               ω   R           ]                 (   8   )               
where V L,R  and i L,R  are the voltages and currents at the terminals of M 1  and M 2 , R L,R  is the electrical resistance of the armature, and K e,L,R  is the back-EMF constant.
 
     Putting everything together in equation, we have the feedforward model 
                     [           V   L               V   R           ]     =       (         RK   i     ⁢     A     -   1       ⁢       B   ⁡     (     A     -   1       )       T       +     K   e       )     ⁡     [           ω   L               ω   R           ]               (   9   )               
with B defined in eq (6). It should be noted that eq (9) is needed because of the particular motor driver that we use here, otherwise for a driver that is able to incorporate current control, eq (7) and (8) are sufficient.
 
     A basic requirement for the next generation of the apparatus  20  is the possibility to implement adaptive impedance control which is currently used in commercial MIT-MANUS and which is key to the Performance-Based Progressive Therapy (PBPT) used on the largest clinical study (127 patients) with a MIT-MANUS [Lo10] to date. This approach incorporates the concept of ‘assist-as-needed’ whereby the patient attempts a movement and the therapist manually helps complete the movement, only when needed. 
     The details of the adaptive impedance control are fully described in [Kre03], here we will just recall the basic characteristics. Subjects are asked to perform goal-directed reaching, as shown in  FIG. 12 - a , from a central target (x 0 ) to a peripheral target (x T ). 
     Healthy subjects are known to perform reaching movements along straight lines and following a so-called minimum-jerk trajectory [Kre03]: 
               s   ⁡     (   t   )       =       x   0     +       (       x   T     -     x   0       )     ·     [       10   ⁢       (     t     t   f       )     3       -     15   ⁢       (     t     t   f       )     4       +     6   ⁢       (     t     t   f       )     5         ]               
so that s(t)=x 0  at start (t=0) and s(t)=x− T  at final time t=t f  
 
     Impaired subjects, in general, will neither follow straight lines nor move along smooth trajectories. Some subjects might not even be able to start moving and will require assistance. Unlike standard industrial robotic devices, robots such as the MIT-MANUS and the apparatus  20  will be able to generate impedance-like force fields to guide the movement, just like a therapist guiding the patient hand-in-hand. 
     The trajectory s(t) can be seen as a ‘virtual hand’, moving from x 0  to x− T . If the subject is able to move fast enough, his/her hand would in general move ahead of the virtual hand. If a subject is unable to move or is too slow, the position of the subject&#39;s hand x(t) at a certain time t will lag behind the virtual hand s(t).  FIG. 13( a )  shows the apparatus  20  in use. 
     As shown in  FIG. 13( b ) , whenever x(t) lags behind s(t) the subject will experience an assistive force field ( ). If a subject overshoots the target, he/she would then experience a resistive force field ( ). Similarly, lateral fields (acting perpendicularly to the x-direction, but not shown in  FIG. 13 ) will help the subject follow straight lines. 
     The force fields implemented in the impedance controller are a combination of elastic and damping fields. Damping fields produce torques proportional, via a coefficient typically set around B=10 Ns/m, to movement speed and always against the actual movement direction. Also for very jerky motions, speed will rarely exceed 20 cm/s, therefore damping torques will rarely exceed 2 N (approximately 0.2 Kg of force) which can be considered a very low force. On the other hand, elastic fields might produce much larger forces, depending on the specific subject, and this needs to be taken into account in the early phases of design as well as recruitment. For example, the assistive field ( ) in  FIG. 13( b )  schematically represents the field of a virtual spring connected between the subject&#39;s hand at position x(t) and the virtual hand at position s(t). The virtual spring implemented in the MIT-MANUS has a stiffness coefficient k=200 N/m, so that an elastic force F=k*(x−s), i.e. a force proportional to the distance between subject&#39;s hand (x) and virtual hand(s). Peripheral targets are 15 cm away from the central target. This means that if a severely impaired subject is unable to move towards a target, the virtual spring should generate forces as high as 200 N/m*15 cm=30 N, i.e. approximately 3 Kg of force. 
     This is a considerable amount of force, in fact close to the limits of the apparatus  20 . Larger forces require larger motors, making the system more expensive and less safe. As the apparatus  20  is meant for subjects with mild impairments who would require some level of assistance but who would still be able to move, smaller motors would be preferable. 
     The behavior of the user (e.g. speed, jerkiness and so forth) will be monitored during the task. The movement time of the virtual hand t f , can be adjusted from trial to trial in order to assist-as-needed or to challenge the subject to do better/faster. Krebs et al [Kre03] describe in detail the adaptive algorithm used to tune the reaching time t f  to a specific subject&#39;s needs, based on his/her performance during previous trials. This concept is at the basis of the Performance-Based Progressive Therapy. 
     A fundamental part of the robot-aided therapy is the goal-directed therapeutic gaming aspect, which is used to motivate and guide the patient through the training session. A possible rehabilitation scenario is shown in  FIG. 5  whereby the apparatus can be placed on an inclined surface. It should be appreciated that due to homogeneous inertia, a simple counter weight can be used to balance against gravity when using the inclined surface. The user sits in front of the apparatus  20  and faces a computer screen with a video-game which motivates and guides the user through a series of motor tasks, typically reaching peripheral targets starting from a central one. Healthy subjects are expected to perform reaching tasks by moving along straight lines, with the apparatus  20  being used to generate assistive/resistive force fields to correct the trajectories of the user, as described in the preceding paragraphs. 
     The apparatus  20  can be easily manufactured mostly with off-the-shelf components and via a microcontroller, implementing the real-time control, connected to a regular PC (where the video games would be implemented). With its low cost, multiple systems can be employed in hospitals or even community centres, enabling step-down care. It is possible to separate the software for the control of the robot from the user interface. The robotic platform can be made portable with a serial port connectivity as its output. This serial port can be connected directly to any computer which has the user interface software installed within. Hence an understanding of the user interface and of the apparatus  20  is all which is required. 
     The use of the planar differential mechanism used in the apparatus  20  provides the following advantages:
         i. The user will experience the same inertia, friction, and damping in every point of the workspace, i.e. homogeneous impedance. This feature is not necessarily available in any robotic manipulandum and non-homogenous impedance might lead to arm trajectories which are curved rather than straight as expected, for example, during reaching tasks.   ii. Another significant advantage of having this type of Cartesian differential mechanism is the simplicity of the mechanism resulting in easier control. It will be shown later that the calculations for controlling the mechanism involve only simple algebra without any trigonometric/logarithmic functions or online matrix inversions. As a result, a simple microcontroller can execute all the operations in real time, hence reducing the complexity and therefore the cost of the system.   iii. Finally, the so-called “force channels” can be implemented by means of simple mechanical stops. Some experimental paradigms make use of force channels to guide the subject&#39;s arm along predefined straight lines (e.g. horizontal, vertical, or oblique). Typically, the channel is implemented by actively, i.e. by means of very powerful actuators which generate canyon-like potentials with steep walls to allow motion only along the canyon, e.g. see [Krebs03]. When using the apparatus  20 , channels in four different directions are passively obtained by mechanical stops. The actuator does not need to be oversized to generate large channel forces, hence increasing the safety of the system by using low power actuators. Four channels are available in our system (see  FIG. 8 ), the horizontal and vertical channels are obtained by mechanically blocking the carriages, while the 45° channels by blocking the driving pulleys or motor shafts. Passive vertical and horizontal channels are possible only in Cartesian mechanisms like the apparatus  20 . Oblique channels are a direct consequence of the differential transmission.       

     Unlike conventional machines or robots which are based on complex designs (often readapting industrial mechanisms) to match all possible conditions and severities of impairments, the apparatus  20  has been primarily conceived to be intrinsically lightweight, portable and simple. In particular, its mechanism makes use of the planar cabled differential with properties potentially beneficial to rehabilitation:
         a) lightweight and therefore portable: as only these characteristics will allow use in remote locations and at home.   b) low-cost and therefore accessible: If only few and specialized clinics can afford (at most) one robot, only few patients will have access to it and for a very limited time.   c) intrinsically simple and safe: complex and strong robots can harm and therefore require highly trained personnel to be operated.       

     Whilst there have been described in the foregoing description preferred embodiments of the present invention, it will be understood by those skilled in the technology concerned that many variations or modifications in details of design or construction may be made without departing from the present invention. 
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