Abstract:
The present invention provides parallel, cable based robotic manipulators, for use in different applications such as ultra high-speed robots or positioning devices with between three to six degrees of freedom. The manipulators provide more options for the number of degrees of freedom and also more simplicity compared to the current cable-based robots. The general structure of these manipulators includes a base platform, a moving platform or end effector, an extensible or telescoping central post connecting the base to moving platform to apply a pushing force to the platforms. The central post can apply the force by an actuator (active), or spring or air pressure (passive) using telescoping cylinders. The robotic manipulators use a combination of active and passive tensile (cable) members, and collapsible and rigid links to maximize the benefits of both pure cable and conventional parallel mechanisms. Different embodiments of the robotic manipulators use either active cables only, passive cables only, or combinations of active and passive cables. An active cable is one whose length is varied by means of a winch. A passive cable is one whose length is constant and which is used to provide a mechanical constraint. These mechanisms reduce the moving inertia significantly to enhance the operational speed of the robots. They also provide a simpler, more cost effective way to manufacture parallel mechanisms for use in robotic applications.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]    This patent application relates to, and claims the priority benefit from, U.S. Provisional Patent Application Serial No. 60/394,272 filed on Jul. 9, 2002 and which is incorporated herein in its entirety. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    This invention relates to robotic manipulators for moving and positioning an object in space, and more particularly the present invention relates to light weight cable actuated active/passive parallel manipulators.  
         BACKGROUND OF THE INVENTION  
         [0003]    Robotic manipulators may be divided into two main categories, parallel and serial manipulators. Serial manipulators, which are more common in the industry, have several links in series usually connected by rotary or sliding joints. They are analogous to the human arm which has a series of links hinged at the shoulder, elbow and wrist. The configuration of serial manipulators necessitates the location of the driving motors to be at the joints themselves or the use of a heavy or complicated linkage for transferring the motion from the base of the robot to the joints. This is a disadvantage since it requires the movement of the large mass of the manipulator and drives even for a small payload. Further, the positional error of the end effector of a serial manipulator is the accumulation of the errors in the individual links so that by increasing the size or number of links the error associated with the position of the end effector increases.  
           [0004]    In contrast to serial manipulators, the links of a parallel manipulator function in parallel to determine the movement of the end effector. A flight simulator and camera tripod are two examples of this kind of mechanisms. If one of the legs of a tripod is extended or moved, it changes the position of the end point. Parallel manipulators have relatively lower mass to payload ratio since the links work together and the actuators are mounted on a stationary base. They also have better precision since the error in the end effector is in the same order of actuators&#39; error.  
           [0005]    Low inertia, and therefore, high speed manipulation is one of the main applications of parallel robots. U.S. Pat. No. 4,976,5821 issued to Clavel, entitled ‘Device for the Movement of and Positioning of an Element in Space’, and reported further in Clavel, ‘Delta, a Fast Robot with Parallel Geometry’, Proceeding of International Symposium on Industrial Robots, pp. 91-100, April 1988, discloses one of the most successful mechanisms of this kind which produces movement with three pure translational degrees of freedom at its end effector. In this manipulator of Clavel, rotating arms are connected to the end effector using three parallelograms. The parallelograms constrain the end effector to be parallel to the base plate at all times and therefore, three pure translational movements are achieved.  
           [0006]    Other manipulator designs such as disclosed in L-W. Tsai, ‘Kinematic of a Three-DOF Platform With Extensible Limbs’, Proceeding of the Conference of Recent Advances in Robot Kinematics, pp. 401-410,1996, also provide pure translational movement of the end effector with three translational degrees of freedom. In the Tsai mechanism, three linear actuators connect the end effector to the stationary platform with universal joints. The specific configuration of the universal joints guarantees the three translational motions of the end effector.  
           [0007]    There are also parallel mechanism robots with 6-DOF such as the hexa pod, see Griffis M., Crane C., et Duffy J., ‘A smart kinestatic interactive platform’, In  ARK , pp. 459-464, Ljubljana, 4-6 July 1994, and the hexa robot disclosed in U.S. Pat. No. 5,333,514 issued to Toyama et al. entitled ‘Parallel Robot’.  
           [0008]    In general, parallel mechanism robots have higher stiffness to weight ratio, moment and torque capacity, and better accuracy. They also benefit from a simpler mechanism due to the elimination of drive trains and, also lower moving mass due to the stationary location of the actuators. Further reduction in the moving inertia of parallel mechanisms may be achieved by replacing the rigid links with tensile means such as cables. Replacing the rigid arms not only reduces the moving inertia but it lowers manufacturing cost and simplifies the mechanism structure by eliminating many joints.  
           [0009]    Using cables in cranes such as disclosed in U.S. Pat. No. 3,286,851 issued to J. R. Sperg entitled ‘Cargo Handling Rig’, and similar applications, see U.S. Pat. No. 5,967,72910 issued to G. F. Foes entitled ‘Bottom Discharge Rotating Ring Drive Silo Unloader’, is older than robotics, however in recent years several attempts have been made to design cable actuated manipulators. Some of these manipulators are designed to imitate human arms and can be considered as serial manipulators with parallel actuators, see U.S. Pat. No. 3,631,737 issued to F. E. Wells entitled ‘Remote Control Manipulator for Zero Gravity Environment’; U.S. Pat. No. 3,497,083 issued to V. C. Anderson, R. C. Horn entitled ‘Tensor Arm Manipulator’; and U.S. Pat. No. 4,683,773 issued to G. Diamond entitled ‘Robotic Device’.  
           [0010]    A pure parallel cable actuated mechanism is disclosed in S. Kawamura, W. Choe, S. Tanaka, S. R. Pandian, ‘Development of an ultrahigh Speed Robot FALCON using Wire Drive System’, Proceeding of IEEE Conference on Robotics and Automation, pp. 215-220, 1995. This manipulator has seven active cables to provide 6-DOF for the end effector. This mechanism does not have any rigid link in its structure and the cables are extended in both sides to maintain tension in the cables.  
           [0011]    U.S. Pat. No. 4,666,362 issued to S. E. Landsberger and T. B. Sheridan entitled ‘Parallel Link Manipulator’ discloses a manipulator which uses six active cables and a passive collapsible link. The collapsible link applies a pushing force between the moving and stationary platforms in order to keep all cables in tension.  
           [0012]    U.S. Pat. No. 5,313,854 issued to H. A. Akeel entitled ‘Light Weight Robot Mechanism’, discloses another combined cable-collapsible mechanism which moves the end point of the collapsible shaft in the space but does not have any control on its orientation.  
         SUMMARY OF THE INVENTION  
         [0013]    Based on the advantages of parallel and cable based manipulators, some new designs are introduced in this work which can be used in ultra high-speed robots with 3 to 6 degrees of freedom. The robotic mechanisms disclosed herein provide more options for the number of degrees of freedom and also more simplicity compared to the current cable-based robots. In the proposed designs a combination of active and passive tensile members, collapsible and rigid links are used to maximize the benefits of both pure cable and parallel mechanisms.  
           [0014]    Applications of both passive and active cables in the new designs improve performance, simplicity and feasibility of the robots. An active cable is one whose length is varied by means of a rotating drum. A passive cable is one whose length is constant and which is used to provide a mechanical constraint. In general, compared to rigid link parallel mechanisms the robotic mechanisms disclosed herein advantageously reduce the moving inertia significantly to enhance the operational speed of the robots. They also provide a simpler, more cost effective way to manufacture parallel mechanisms for use in robotic applications, measurements, and entertainments.  
           [0015]    The design of new light weight parallel manipulators for high-speed robots using active/passive cables is explained herebelow. The general structure of these manipulators has the following main components (see FIGS. 1 and 2):  
           [0016]    a) A base platform  24 .  
           [0017]    b) A moving platform or end effector  22 .  
           [0018]    c) An extensible or telescoping central post  26  connecting the base  24  to moving platform  22  to apply a pushing force to the platforms. The central post can apply the force by an actuator (active) or spring or air pressure (passive); and  
           [0019]    d) Active cables  28 . Active cables are those whose lengths change using an actuator; and/or  
           [0020]    e) Passive cables  42 . Passive cables are cables whose lengths are fixed.  
           [0021]    The robotic mechanism may have just active cables, just passive cables, or a combination of both.  
           [0022]    In one aspect of the invention there is provided a robotic mechanism, comprising:  
           [0023]    a support base, an end effector and a biasing member having opposed ends and attached at one of said opposed ends to the support base and attached at the other of said opposed ends to the end effector; and  
           [0024]    at least three cables each connected at a first end thereof to said end effector and said at least three cables having second ends being attached to an associated positioning mechanism for retracting or deploying each of said at least three cables to position said end effector in a selected position in space, said biasing member applying force on the end effector with respect to the support base for maintaining tension in said at least three cables.  
           [0025]    The present invention also provides a robotic mechanism, comprising:  
           [0026]    a support base, an end effector and a biasing member having opposed ends and pivotally attached at one of said opposed ends to the support base and pivotally attached at the other of said opposed ends to the end effector; and  
           [0027]    six cables each connected at a first end thereof to said end effector and said six cables having second ends being attached to an associated positioning mechanism for moving the second ends of the associated cable independently of the other cables, said biasing member applying force on the end effector with respect to the support base for maintaining tension in said six cables, wherein movement of the second ends of the cables by the associated positioning mechanisms changes a position and orientation of the end effector so that the robotic mechanism has six degrees of freedom.  
           [0028]    The present invention also provides a five-degree-of-freedom robotic mechanism, comprising:  
           [0029]    a support base, an end-effector and a biasing member having opposed ends and pivotally attached at one of said opposed ends to the support base with a universal joint and pivotally attached at the other of said opposed ends to the end-effector with a universal joint; and  
           [0030]    five cables each connected at a first end thereof to said end effector and said five cables having second ends being attached to an associated positioning mechanism for moving the second ends of the associated cable independently of the other cables, said biasing member applying force on the end effector with respect to the support base for maintaining tension in said five cables, wherein movement of the second ends of the cables by the associated positioning mechanisms changes a position and orientation of the end-effector.  
           [0031]    The present invention also provides a robotic mechanism, comprising:  
           [0032]    an end effector, a post having opposed ends being pivotally connected at one of said opposed ends to the end effector;  
           [0033]    a support base defining a plane and having a hole extending therethrough, an outer ring structure pivotally connected to said support base within said hole for pivotal motion of said outer ring structure out of the plane of said support base, a first actuator for pivoting said outer ring structure, an inner ring structure pivotally mounted to said outer ring structure inside said outer ring structure, said inner ring structure being concentric with said outer ring structure, a second actuator for pivoting said inner ring structure, said inner ring structure having an axis of rotation in the plane of the outer ring, and perpendicular to the axis of rotation of said outer ring structure, said inner ring structure having a central web with a hole therethrough and a universal joint mounted in said hole to the central web, the other end of said post being slidably mounted in said universal joint, bias means connected to said post for biasing said end effector away from said support base;  
           [0034]    a first set of three cables each connected at one end thereof to said end effector and the other ends of said first set of three cables being attached to positioning means mounted on said support base for pulling said three cables independently of each other to position said end effector in a selected position in space; and  
           [0035]    a second set of three cables each connected at one end thereof to said end effector and the other ends thereof being attached to the other end of said post, said second set of three cables being mounted to said inner ring at substantially 120° with respect to each other and constrained to be parallel to each other between said end effector and said inner ring and wherein when said positioning means moves said end effector to a selected position in its workspace, said second set of three cables maintains said end effector in a plane parallel to the plane of said inner ring.  
           [0036]    The present invention also provides a robotic mechanism, comprising:  
           [0037]    an end effector, a post having opposed ends being pivotally connected at one of said opposed ends to the end effector using a universal joint, the post having an adjustable length;  
           [0038]    a support base defining a plane and having a hole extending therethrough, an outer ring structure pivotally connected to said support base within said hole for pivotal motion of said outer ring structure out of the plane of said support base, a first actuator for pivoting said outer ring structure, an inner ring structure pivotally mounted to said outer ring structure inside said outer ring structure, said inner ring structure being concentric with said outer ring structure, a second actuator for pivoting said inner ring structure, said inner ring structure having an axis of rotation in the plane of the outer ring, and perpendicular to the axis of rotation of said outer ring structure, said inner ring structure having a central web with a hole therethrough and a universal joint mounted in said hole to the central web, the other end of said post being slidably mounted in said universal joint,;  
           [0039]    a first set of three cables each connected at one end thereof to said end effector and the other ends of said first set of three cables being attached to a positioning mechanism mounted on said support base for pulling said three cables independently of each other to position said end effector in a selected position in space; and  
           [0040]    a second set of three cables each connected at one end thereof to said end effector and the other ends thereof being attached to, a winch mounted on said central web of the inner ring assembly, said second set of three cables being guided through pulleys mounted to said inner ring at substantially 120° with respect to each other and constrained to be parallel to each other between said end effector and said inner ring, wherein the winch retracts or deploys all three cables simultaneously and keeps the cable lengths between the inner ring and the end-effector equal so that when said positioning mechanism moves said end effector to a selected position in its workspace, said second set of three cables maintains said end effector in a plane parallel to the plane of said inner ring.  
           [0041]    The present invention also provides a robotic mechanism, comprising:  
           [0042]    an end effector, a post having opposed ends and an adjustable length being pivotally connected at one of said opposed ends to the end effector;  
           [0043]    a support base, the other end of said opposed ends of the post being pivotally connected on a top surface of said support base;  
           [0044]    a set of three cables each connected at one end thereof to the end of said post pivotally connected to said end effector and the other ends of each of said first set of three cables being attached to positioning means mounted on said support base for pulling said cables to position said end effector in a selected position in space;  
           [0045]    a first longitudinal shaft having a first longitudinal axis and a pulley being rigidly mounted on each end of said first shaft, said first longitudinal shaft being mounted on a bottom surface of said support base and parallel to said support base, the first longitudinal shaft is passing through a first sleeve, a first rotational spring mounted from one end to the first sleeve and from the other end to the first longitudinal shaft for applying a constant torque to the fist longitudinal shaft, including a first motor connected to said first longitudinal shaft for rotating said first longitudinal shaft about an axis parallel to the said support base and normal to said first longitudinal shaft, a second longitudinal shaft having a second longitudinal axis and a pulley rigidly mounted on each end of said second shaft, said second longitudinal shaft being mounted on the bottom surface of said support base and parallel thereto and oriented so said first longitudinal axis is perpendicular to said second longitudinal axis, the second longitudinal shaft is passing through a second sleeve, a second rotational spring mounted from one end to the sleeve and from the other end to the second longitudinal shaft applies a constant torque to the second longitudinal shaft, including a second motor connected to said second longitudinal shaft for rotating said second longitudinal shaft about an axis parallel to the said support base and normal to said second longitudinal shaft; and  
           [0046]    a first pair of cables with each cable connected at one end thereof to said end effector and the other end of one of the cables being collected by one of the pulleys at the end of the first longitudinal shaft and the other end of the other cable being collected by the other pulley at the other end of the first longitudinal shaft, the first rotational spring mounted in the first sleeve  148  which applies torque to the first longitudinal shaft has both the pulleys rotate and collect the first pair of cables so that the lengths of the cables of the said first pair of cables remain the same and therefore a parallelogram is maintained by the first pair of cables, a second pair of cables with each cable connected at one end thereof to said end effector and the other end of one of the cables being collected by one of the pulleys at the end of the second longitudinal shaft and the other end of the other cable being collected or deployed by the other pulley at the other end of the second longitudinal shaft as said second longitudinal shaft is rotated by the torque provided by the rotational spring mounted in the second sleeve  146  and therefore the length of the cables of said second pair of cables remains the same and thus a parallelogram is maintained by the second pair of cables, and wherein said cables of said first pair of cables are parallel and said cables of the second pair of cables are parallel so that a plane defined by said end effector is maintained parallel to a plane defined by said two longitudinal shafts.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0047]    The present invention will now be described by way of example only, reference being had to the accompanying drawings in which:  
         [0048]    [0048]FIG. 1 is a perspective view of a three degree of freedom (DOF) wire actuated parallel robot using active cables constructed in accordance with the present invention;  
         [0049]    [0049]FIG. 2 is a perspective view of a three degree of freedom wire actuated parallel robot using passive cables;  
         [0050]    [0050]FIG. 3 is a perspective view of another embodiment of three degree of freedom wire actuated parallel robot using passive cables;  
         [0051]    [0051]FIG. 4 is a perspective view of a six DOF parallel mechanism using passive cables;  
         [0052]    [0052]FIG. 5 is a perspective view of a three-to-five DOF parallel mechanism using active and passive cables;  
         [0053]    [0053]FIG. 6 shows a top view (view A-A in FIG. 5) of the base platform and rings of the mechanism of FIG. 5;  
         [0054]    [0054]FIG. 7( a ) shows an overall perspective view of the configuration of active cables in the mechanism of FIG. 5;  
         [0055]    [0055]FIG. 7( b ) shows a detailed view of the portion of FIG. 7( a ) in the square box;  
         [0056]    [0056]FIG. 8( a ) shows an overall perspective view of the configuration of the passive cables in the mechanism of FIG. 5;  
         [0057]    [0057]FIG. 8( b ) shows a detailed view of a portion of the passive cable mechanism of FIG. 8( a );  
         [0058]    [0058]FIG. 8( c ) shows a side view of the passive cable configuration of FIG. 8( a );  
         [0059]    [0059]FIG. 9 is a perspective view showing the connection of passive cables to the bottom end of the center post;  
         [0060]    [0060]FIG. 10 shows the mechanism of FIG. 5 in two positions, vertical and tilted at an angle from the vertical showing the moving platform remains parallel to the base platform;  
         [0061]    [0061]FIG. 11( a ) is an overall perspective view of a three-to-five DOF robotic mechanism;  
         [0062]    [0062]FIG. 11( b ) is a close up detailed perspective view of the wire tensioning mechanism of the robotic mechanism of FIG. 11( a );  
         [0063]    [0063]FIG. 12 is a top perspective view of the mechanism of FIG. 11 a  absent the end effector and central post showing the tensioning mechanism for the passive cables used to maintain the moving platform parallel to the base;  
         [0064]    [0064]FIG. 13 shows the configuration of active cables for positioning the central post of the mechanism of FIG. 11;  
         [0065]    [0065]FIG. 14 is a perspective view of a hybrid parallel mechanism using seven active cables that can produce between three and five degrees of freedom for the moving platform;  
         [0066]    [0066]FIG. 15 is a perspective view of the central extensible rod and three active cables for the mechanism of FIG. 14;  
         [0067]    [0067]FIG. 16 is a bottom view of the mechanism of FIG. 14;  
         [0068]    [0068]FIG. 17 is a perspective view of three degree of freedom parallel planar manipulator using active cable;  
         [0069]    [0069]FIG. 18 is a bottom view of the moving platform component connection for planar manipulator;  
         [0070]    [0070]FIG. 19 is a perspective view of two degree of freedom parallel planar manipulator using an active cable;  
         [0071]    [0071]FIG. 20 is a perspective view of a parallel planar manipulator using a passive cable;  
         [0072]    [0072]FIG. 21 is a bottom view of three degree of freedom parallel planar manipulator using a passive cable;  
         [0073]    [0073]FIG. 22 shows the parallelism of the moving platform enforced by two parallelograms;  
         [0074]    [0074]FIG. 23 is a perspective view of a two degree of freedom parallel planar manipulator driven by passive cables with the orientation constrained by a winch mechanism; and  
         [0075]    [0075]FIG. 24 shows a perspective view of a three degree of freedom parallel planar manipulator driven by passive cables with the orientation controlled by a cam and a winch mechanism. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0076]    1. Three-Degree-of-Freedom Parallel Mechanism Using Active Cables  
         [0077]    A three-degree-of-freedom parallel robotic mechanism using active cables constructed in accordance with the present invention is shown generally at  20  in FIG. 1 and includes a moving platform  22  that is attached to base platform  24  using an extensible or telescoping central post  26  and three sets of parallel cables  28  with one end of each of cable attached to platform  22  and the other ends of each pair of cables attached to an associated winch assembly  30 . Each winch assembly  30  includes a drum  32  mounted for rotation in a frame  36  which is attached to the base  24  to keep the drum  32  in place and also to guide the cables  28  to the drum via two holes  39  located in the top plate  38  of the frame  36 . The extensible post  26  is attached to the platform  22  (end-effector) and base  24  by universal joints  34  at both ends of the post to prevent the rotation of the moving platform  22 . The extensible center post  26  applies a compression force between the platforms  22  and  24  using a linear actuator such as a hydraulically, pneumatically, and electrically powered cylinder. Alternatively, a linear motor (active element) or using a preloaded spring, or air pressure (passive element) may be employed in alternative embodiments of the mechanism to maintain tension of cables  28 . Post  26  may be any one of a hydraulically, pneumatically, and electrically powered cylinder.  
         [0078]    The motion of the moving platform  22  is controlled by the three pairs of active cables  28 . The two cables of each pair of cables  28  are parallel to each other to make a parallelogram as shown by the closed loop of a-b-c-d in FIG. 1. A motor controller  31  is connected to the motors  33  for driving the motors as well as being connected to position/velocity sensors on each of the drums  32 . A computer  35  attached to the controller  31  is used to program/command the controller for positioning the cables on each of the winches. A tool  37  is mounted on top of end effector  22  and is controlled by controller  31  or by separate controller  41 . When the end effector  22  is to be positioned in a selected location in its workspace, signals are sent by controller  31  based on its existing program or command signals sent by computer  35  which in turn moves the drums  32  in each winch  30  to either roll up the parallel cables  28  or release them, depending on the particular winch and where in the robotic workspace space the end effector  22  is to be located. The lengths of the three pairs of the cables  28  are adjusted independently to provide three degrees of freedom to the end effector platform  22 .  
         [0079]    Due to the three cable-parallelogram structures the moving platform  22  will always be parallel to the base platform  24  and can undergo three translational degrees of motion. This is obtained because the edge a-b in parallelogram a-b-c-d (similarly in the other two parallelograms) is always parallel to edge c-d that is parallel to base platform  24 . Since the three intersecting edges (a-b and the other two similar edges) are always parallel to base platform  24 , the moving platform  22  remains parallel to base platform  24  regardless of the lengths of the pairs of cables  28 . The lengths of each pair of cables  28  are controlled independently by their associated rotating drums  32 . The lengths of each pair of cables  28  determines the center location of the moving platform  22  while the parallelograms keep the platform  22  parallel to the base  24 . The length of the central post  26  changes according to the location of the moving platform  22  and the compression force that is applied to the platform  22  from the central post  26 .  
         [0080]    2. Three-Degree-of-Freedom Parallel Mechanism Using Passive Cables  
         [0081]    A three-degree-of-freedom parallel robotic mechanism using passive cables constructed in accordance with the present invention is shown generally at  40  in FIG. 2 and includes moving platform  22  that is attached to base platform  24  using an extensible or telescoping central post  26 . As with robot  20  in FIG. 1, the extensible post  26  is attached to the platforms  22  and  24  by universal joints  34  at both ends of the post to prevent the rotation of the moving platform  22 . There are three pairs of fixed-length cables  42  attached to the moving platform  22  and each pair of cables  42  forms a parallelogram a-b-c-d as seen in FIG. 2. The ends of each pair of cables  42  at the lower edge c-d of the parallelogram are connected to a link arm  44  using a revolute joint  46  having an axis of rotation coincident with c-d. Each link arm  44  is connected to a bracket  48  using another revolute joint  50  whose axis of rotation is parallel to axis c-d. Frame  48  is attached to base  24  and link arm  44  is rotated by an actuator such as an electrical motor (not shown in the figure). When link arm  44  is rotated about the rotational axis of the lower revolute joint  50 , the upper axis a-b remains parallel to axis c-d which guarantees the moving platform  22  stays parallel to the base platform  24  during any motion.  
         [0082]    The same reasoning as to why the moving platform  22  remains parallel with the base  24  in apparatus  20  in FIG. 1 applies to base  24  and platform  22  of apparatus  40  regardless of the angles of arms  44 . Thus platform  22  has a pure translational motion along the X, Y and Z-axes. The extendable center post  26  pushes the platform  22  away from the base  24  and generates tension in the pairs of cables  42  which prevents them from becoming slack.  
         [0083]    [0083]FIG. 3 shows an alternative embodiment at  60  of a robot constructed following the same principle as robot  40  with the difference being link arm  44  (FIG. 2) is replaced by actuators that move edge c-d and the other two similar axes of the parallelograms parallel to the base platform. As an example, connection rod  46  can be moved horizontally or vertically by a linear actuator attached thereto (not shown) to change the location of rod  46  without modifying its angle with the base  24 . Similarly, connection rod  46  can be attached to a rotary actuator for movement in a plane parallel to the base platform  24  to provide the desired movement of the platform  22 . For all these different motions as long as the axis of connection rods  46  are maintained parallel to the base platform  24  the mechanism  60  will have three translational degrees of freedom in the X, Y and Z directions.  
         [0084]    Mechanisms  40  and  60  also include a computer controlled motor controller (not shown) such as computer  35  connected to controller  31  shown in FIG. 1.  
         [0085]    3. Six-Degree-of-Freedom Parallel Mechanism Using Passive Cables  
         [0086]    A generalization of the design shown in FIG. 3 can be extended to a 6 degree of freedom robot as shown generally at  66  in FIG. 4. In this design the extendible center post  26  is attached to the base  24  and moving platform  22  by two spherical joints  56 , or one spherical joint and one universal joint instead of two universal joints as is used in mechanisms  20 ,  40 , and  60  in FIGS. 1, 2, and  3 . The parallelograms in the previous mechanisms  20 ,  40  and  60  defined by the pairs of parallel cables are used to impose mechanical constraints to eliminate three rotational degrees of freedom. In the six degree of freedom robot  66  the ends of cables  42  are connected to separate actuators to provide three extra degrees of freedom. In this design the six cables  42  are still passive and are connected at one end to an associated arm  44  and at the other end to moving platform  22 . Each link arm  44  is connected to a frame  48  with a revolute joint  50 . Frame  48  is attached to the base  24  and link arm  44  is rotated by an actuator such as an electrical motor not shown but similar to the motors and controller shown in FIG. 1. When link arm  44  is rotated the end points of the cables connected to arms  44  change and as a result the position and orientation of the moving platform  22  can be controlled. The central extensible post  26  applies a pushing force through a spring or air cylinder (not shown in the figure) to keep cables  42  in tension. It should be noted that the design is not limited to the use of assembly  44 ,  48  and  50  to move the end points of the cables and any mechanism and actuator (linear or rotary) can be used to achieve the same number of degrees of freedom, as discussed with respect to the mechanism of FIG. 3. Also, there are no limitations on the location of cable  42  attachment to the moving platform, however, these locations will change the overall workspace of the robot. Mechanism  66  also include a computer controlled motor controller (not shown) such as computer  35  connected to controller  31  shown in FIG. 1 for controlling each of the actuators.  
         [0087]    The six degree-of-freedom robotic mechanism of FIG. 4 may be converted to a five degree-of-freedom device by replacing spherical joints  56  connecting post  26  to base  24  and end effector  22  with universal joints and removing one of the six cables  42  and associated link arm  44  and motor. The five degrees of freedom will include three translational and two rotational motions (pitch and yaw). The replacement of the spherical joints with universal joints will eliminate the roll motion of moving platform  22  with respect to post  26  and fixed platform  24 .  
         [0088]    4. Three-to-Five DOF Parallel Mechanism Using Passive and Active Cables  
         [0089]    Referring to FIG. 5, there is shown generally at  70  a hybrid parallel mechanism using a combination of active and passive cables to provide five degrees of freedom for moving platform  22 , including three translational and two rotational motions. In this embodiment of the invention, base platform  24  includes two rings  76  and  74 . The top view of base  24  and the two rings is shown in FIG. 6. Ring  76  is attached to base platform  24  by two revolute joints  87  diametrically located on opposite sides of ring  76  and having coextensive or coincident axis of rotation. Revolute joints  87  are fixed in ring  76 , and held by collars on base  24 .  
         [0090]    Actuator  84  is mounted on base  24  and its shaft is connected to one of the revolute joints  87  to provide a relative rotational motion of ring  76  with respect to base  24  so that ring  76  can be rotated out of the plane of base  24 . Similarly, ring  74  is attached to ring  76  by two revolute joints  86  diametrically located on opposite sides of ring  74  and with revolute joints  86  having coextensive or coincident axis of rotation. The revolute joints  86  are fixed in ring  76  and held by collars in ring  74 . The coextensive axes of rotation of the two revolute joints  86  are normal to the coextensive axes of rotation of the two revolute joints  87 . Actuator  82  is mounted on ring  74  and its shaft is connected to one of the revolute joints  86  to provide a relative rotational motion between rings  74  and  76  for rotating ring  74  out of the plane defined by ring  76 . As a result, ring  74  is connected to base  24  through ring  76  and has two rotational degrees of freedom (pitch and yaw) and its orientation is set by motors  82  and  84 .  
         [0091]    At the center of ring  74  there is collar  78  which is attached to ring  74  by a universal joint  80 . When the planes of rings  74 ,  76  are in the same plane as base  24  and collar  78  is normal to the base the axes of rotation of universal joint  80  and revolute joints  86  and  87  are all in a single plane. Also, center post  72  can only slide in collar  78  without any rotation. Platform  22  (FIG. 5) is connected to center post  72  by universal joint  89  (FIG. 7( a )). Universal joint  89  prevents the rotation of platform  22  with respect to the longitudinal axis of center post  72 .  
         [0092]    Referring again to FIG. 7( a ), the top end of center post  72  is attached to three active cables  88  which are used to orient the center post  72  in space. FIG. 7( a ) shows the mechanism without the passive cables  98  and movable platform  22  to show more clearly the active cables  88 . The active cables  88  are attached at one end thereof to the tip of center post  72 . Referring particularly to FIG. 7( b ), each of the active cables  88  is pulled and accumulated using an associated winch assembly that includes a pulley  92  and a motor  90  which rotates the pulley. Pulley  92  and motor  90  of each winch assembly is mounted in housing  96  which is attached to the base platform  22  and each of the cables  88  passes through a hole  94  located in the top of the associated housing  96 . The tip of center post  72  can be moved to any point in the workspace by changing the length of active cables  88 . The center post  72  applies a pushing force to cables  88  to keep them in tension at all times. This force can be generated by means of passive elements such as spring  73  which applies the force between collar  78  and center post  72 . In an alternative embodiment an active element such as a linear motor (not shown in the figures) may be used instead.  
         [0093]    There are three passive cables  98  (best seen in FIGS.  8 ( a ) and  8 ( b )) attached at one end to the moving platform  22  and at the other end to the bottom end of center post  72  (see FIG. 9). Passive cables  98  are parallel to each other in the section between ring  74  and platform  22  (FIG. 10) and are used to maintain the moving platform  22  parallel to ring  74  so that any orientation of ring  74  transfers to platform  22 .  
         [0094]    Referring to FIG. 8( a ), the passive cables  98  from platform  22  are guided through pulleys  100  which are mounted to brackets  103  (see FIG. 8( b )), which in turn are attached to ring  74  using revolute joints (not shown). The revolute joints allow the pulleys  100  to adjust themselves with respect to the direction of the associated cables  98 .  
         [0095]    Three other pulleys  104  (see FIG. 9) are mounted in brackets  106  which are mounted on a frame  108  which is attached to collar  78 . The axes of pulleys  100  are in the same plane which passes through the center of universal joint  80  (FIG. 6). Also, the axes of pulleys  104  are in the same plane which passes through universal joint  80 . These conditions are required to keep the platform  22  parallel to ring  74 .  
         [0096]    Pulleys  104  guide the cables  98  to their attachment point at the bottom end of center post  110 . Three springs  112  are in series with cables  98 . These three springs  112  are used to provide tension in passive cables  98  and also compensate for small changes in the length of cables  98  when the center post  72  deviates from its vertical position.  
         [0097]    The three passive cables  98  maintain the platform parallel to ring  74  as shown in FIG. 10 for a 2D situation. In an ideal configuration, pulleys  100  and  104  have zero diameters. As seen in the figure, regardless of the angle of  72  BC=EF and DC=DE. Since the overall length of the cables ABCD and GFED are equal, AB=GF all the time. This constitutes a parallelogram which guarantees end effector  22  stays parallel to base platform  24 .  
         [0098]    The embodiment shown at  70  in FIG. 5 is a five degree-of-freedom mechanism that has three translational motions of the moving platform  22  that are provided by actuators  90  and active cables  88 , and the two rotational degrees of freedom are provided by actuators  82  and  84  to orient moving platform  22 . The translational and rotational motions of the moving platform are independent which result in simple kinematics of the mechanism. Mechanism  70  can be converted into a three degree of freedom mechanism by removing rings  74  and  76  and connecting pulleys  100  and their frames directly to base  24 . In this configuration platform  22  is always parallel to the base and its location can be changed by active cables  88  and motors  90 . Alternatively, a three degree of freedom mechanism can be obtained by locking rings  74  and  76  with respect to base  24 .  
         [0099]    5. Alternative Three-to-Five DOF Parallel Mechanism Using Active Cables  
         [0100]    Referring to FIG. 11( a ), there is shown generally at  200  a hybrid parallel mechanism using a combination of active and passive cables to provide five degrees of freedom for moving platform  22 , including three translational degrees of freedom and two rotational degrees of freedom. The overall structure of mechanism  200  is very similar to mechanism  70  in FIG. 5 except for the central post  26  and the way passive cables  98  keep the moving platform  22  parallel to ring  74 . The central post in this design is extensible and connected to both moving platform  22  and ring  74  with universal joints. It further applies an active or passive pushing force to the platform and ring via a spring or air cylinder (not shown in the figure) or it could be a linear motor to continuously adjust the force.  
         [0101]    A close-up of the mechanism that keeps platform  22  parallel to ring  74  is shown in FIGS. 11 b  and  12 . Passive cables  98  are guided to a winch mechanism which includes a drum  97  mounted for rotation in a frame  107  and driven by a motor  99 . Frame  107  is attached to ring  74 . Three pulleys  100  are mounted on frames  106  that are connected to ring  74  by revolute joints  103  and spaced  1200  with respect to each other around ring  74 . Two pulleys  101  are mounted on associated frames  105  that are connected directly to ring  74 . These two pulleys  101  receive two of the cables  98  from two of the pulleys  100  which are then wrapped on drum  97 . Cable  98  from the third pulley  100  goes directly to drum  97 , best seem in FIG. 12. The cables  98  are wound on drum  97  by applying a torque generated by passive elements like rotational springs or active elements such as electrical or air motors shown schematically by  99 . As seen in FIG. 12 the lengths of cables  98  between pulleys  100  and drum  97  are independent from the position and orientation of platform  22 . Also, cables  98  are wrapped around one single drum  97  and as a result the change in the lengths of cables  98  between pulleys  100  and platform  22  will be the same in any robot&#39;s configurations. Now, if cables  98  are attached to platform  22  such that their lengths between pulleys  100  and connection points on platform  22  become equal and parallel to the central post  26 , each two cables  98  will make a parallelogram and therefore platform  22  will remain parallel to ring  74  regardless of its position in the workspace.  
         [0102]    [0102]FIG. 13 shows the arrangement of the active cables  88  that are the same as the arrangement of the active cables in mechanism  70  in FIG. 7( a ). Referring again to FIG. 11 a , mechanism  200  is a five degree of freedom mechanism that includes three translational degrees of freedom of the moving platform  22  provided by actuators  90  and active cables  88 , and the two rotational degrees of freedom provided by actuators  82  and  84  to orient moving platform  22  in its workspace. The translational and rotational motions of the moving platform  22  are independent of each other which results in simple kinematics of the mechanism. Mechanism  200  may be converted into a three degree of freedom mechanism by removing rings  74  and  76  and connecting pulleys  100  and their frames directly to base  24 . This way platform  22  is always parallel to the base  24  and its location can be changed by changing the length of active cables  88  using motors  90 .  
         [0103]    In summary, the embodiment shown in FIGS. 11, 12 and  13  is a 5 dof mechanism. In this mechanism the second set of cables are not attached to the bottom end of the post. They are pulled and collected by winch  97 . There are five pulleys mounted on the inner ring in order to guide the three cables to the winch. This winch pulls and collects all three cables simultanously and hence keeps the cable lengths between the inner ring and the end-effector equal. Therefore, the end-effector stays parallel to the inner ring plane. Winch  97  can be connected to a motor or to a rotational spring in order to pull cables and keep them in tension. In this mechanism the post can be as simple as the mechanisms of FIGS.  1  to  5 .  
         [0104]    6. Three-to-five DOF Parallel Mechanism Using Active Cables  
         [0105]    [0105]FIG. 14 shows a hybrid parallel mechanism at  120  using seven active cables that can produce between 3 and 5 degrees of freedom for the moving platform  22 . In this embodiment, the moving platform  22 , base platform  24 , and extensible center post  26  and universal joint  34  are similar to the previous embodiments. Three active cables  122  as shown in FIGS. 14 and 15 are attached at one end to the top of extensible center post  26  and the other ends are attached to winches  124  which are mounted in bracket frames  126  attached to platform  24 . Winches  124 , which control the lengths of cables  122  control the end location of the extensible rod in the space.  
         [0106]    Referring particularly to FIGS. 14 and 16, two pairs of cables  130  and  132  form two parallelograms. The pair of cables  130  are pulled and collected by two pulleys  136  mounted on the ends of shaft  138 . The pair of cables  132  are pulled and collected by two pulleys  140  mounted on the ends of shaft  142 . Both shafts  138  and  140  and the associated pulleys mounted on the ends of the respective shafts form a single body and therefore, the two pulleys rotate simultaneously with the shaft. Shaft  142  rotates inside collar  146 . There is also a source of constant torque acting between shaft  142  and collar  146 . This torque can be applied by a spring which maintains the cables  132  in tension. Similarly, shaft  138  rotates inside a collar  148 . There is also a source of constant torque acting between shaft  138  and collar  148  which may be applied by a spring and this keeps the cables  130  in tension. Maintaining the shafts  138  and  142  parallel to base  24  and platform  22 ′ ensures that the platform  22  is parallel to the base  24 . Collars  146  and  148  are mounted to frame  150  and collar  146  is connected to motor  152  and collar  148  is connected to motor  154 . The motors rotate the collars connected thereto and this rotation is directly transferred to the platform  22  which alters the orientation of the platform  22 .  
         [0107]    Each of the two longitudinal shafts  138  and  142  mounted on the bottom surface of the support plane are responsible for forming a parallelogram. Each of these two shafts has two pulleys rigidly connected at the two ends. The two shafts are initially parallel to the support base plane and normal to each other. In FIG. 16, there are two sleeves shown as  146  and  148 . The two shafts pass through these sleeves and can rotate about their longitudinal axis. There are also rotational springs (not shown in the figure) used to apply a torque between each sleeve and its associated shaft. Therefore, the shafts are under a passive torque so that they pull and collect the cables. As a result, the two pairs of parallel cables remain in tension and build two parallelograms which force the end-effector to be parallel with the two longitudinal shafts. If we rotate sleeves  146 ,  148  about an axis parallel to the support base plane and normal to the longitudinal axes of the shafts using motors  152  and  154 , the rotation will be directly transferred to the end-effector because the end-effector has to stay parallel to the longitudinal axes of the shafts. Therefore, the two motors control the orientation of the end-effector and the mechanism will provide 5 degrees of freedom.  
         [0108]    7. Three DOF Planar Parallel Mechanism Using Active Cables  
         [0109]    A general three degree of freedom planar parallel mechanism using active cables constructed in accordance with the presented invention is shown generally at  170  in FIG. 17. The moving platform,  22  is attached to a base plate  172  by extensible or telescoping central post  174  and three active cables  176 , through a winch assembly. See FIG. 18 for details. The base plate  172  provides a reference for the moving platform  22 , and its function is identical to the base platform  24  of FIG. 1. The central post  174  is connected by revolute joint  180  to the bottom of moving platform  22  having an axis of rotation  179  (see FIG. 18 for details), and base plate  172  by a revolute joint  178  with the pivoting axes  179  of the revolute joints  178  and  180  being perpendicular to the workspace of the robot. The out of plane moment induced on the moving platform  22  is counter-balanced by these revolute joints. A clevis pin type of revolute joint is a reasonable choice for this component. The cables  176  do not need to be coplanar but they must be held in tension. Cables  176  may be attached to platform  22  by revolute joints  183  having axis of rotation parallel to axis  179  of joint  180 . The purpose of the revolute joints  183  is to reduce the amount of bending at the attachment points on the cables  176  to platform  22  which can increase the life span of the cables and joints. Other attachment devices such as eyelets may be used as well to reduce the bending while using the same design. The central post  174  is used to exert a tensile force on the cables  176 .  
         [0110]    Each of the three winch assemblies  188  used in apparatus  170  comprises a drum  190  in a housing  192  with each drum being driven by a motor  194 , with each housing  192  having a pilot hole  196  in its top surface through which the associated cable  176  passes to be wound on drum  190 . This mechanism uses a pair of cables  176  (hence two winch assemblies  188 ) on one side of the central post  174  and at least one cable  176  and its associated winch  188  on the opposite side of post  174 . As the motor  194  turns, the drum  190  takes up or releases its associated cable  176 . The pilot hole  196  is used to position and set a reference point for the cables. The positioning of the moving platform  22  is controlled directly by the amount of cable released by the drum. A computer controlled motor controller systems (not shown) such as computer  35  connected to controller  31  shown in FIG. 1 is used to adjust the length of the active cables.  
         [0111]    In mechanism  170  shown in FIG. 17, the two parallel cables are similar to the parallelograms in the other embodiments and as long as their lengths remain the same the end effector  22  can only move parallel to the base. However, in this design we have considered two motors to be able to change both the orientation and location of the end effector through three actuators.  
         [0112]    8. Two DOF Planar Parallel Mechanism Using Active Cables.  
         [0113]    In mechanism  170  of FIG. 17, the cables  176  from the side of post  174  having the two winches  188  side-by-side have the ability to constraint the orientation of the moving platform  22 . If these cables are equal in length, the cables  176  and the moving platform  22  forms a parallelogram for the same reasoning as the apparatus shown in FIG. 1. Thus, the moving platform  22  will be parallel to the top plane  173  of the base plate  172 . On the other hand, if cables  176  are different in length, the combination of all three cables determines the orientation of the moving platform  22 . Therefore, referring to FIG. 19, a two translational degree of freedom active cable mechanism shown generally at  200  can be constructed by replacing the two adjacent winch assemblies  188  shown on FIG. 17 with a two cable winch assembly  30  shown in FIG. 1. Note that the resulting mechanism requires only two motors  194  and  33  only. In FIG. 19, a design with one drum and motor for the two cables on the same side of post  174  maintains the orientation of end effector  22  is fixed, which is parallel to the base  172  in FIG. 19. One of the two paired cables could be longer or shorter with respect to the other thereby inclining the end effector  22  and as long as the length ratio of the two cables remains fixed the orientation or angle of the end effector  22  will remain constant.  
         [0114]    9. Three DOF Planar Parallel Mechanism Using Passive Cables  
         [0115]    A general three degree of freedom planar parallel mechanism using passive cables in accordance with the present invention is shown generally at  210  in FIG. 20. The moving platform  22  is attached to the base plate  172  by extensible or telescoping central post  174  and three passive cables  212  each connected at one end of the cables to three link-arms  214  and the other ends connected to platform  22 . The connections of the cables  212  and the central post  174  to moving platform  22  is identical to the connections in mechanism  170  shown in FIGS. 17, 18 and  19 . The connection of post  174  to base  172  is also the same as in FIG. 17. Link-arms  214  are pivotally connected to base  172  through revolute joints  218 . Similar to the active cable counterpart mechanism  170  in FIG. 17, passive cable mechanism  210  also requires a pair of the cables  212  on one side of the central post  174  and at least one cable  212  on the opposite side. The side with two cables  212  controls the orientation of the moving platform  22 . If these cables were equal in length and are parallel to each other, the cables and the tips of the link-arms form two parallelograms. Therefore, the orientation of moving platform  22  will be fixed during movement of the end effector  22 , and in the FIG. 20 it will be parallel to ground. On the other hand, if this pair of cables  212  is orientated differently, the combination of all three cables determines the orientation of the moving platform  22 . It should be pointed out that the motion of ends of the cables  212  attached to arms  214  is not necessarily circular provided by arm  214 , and it can be linear or any other complex trajectory generated by linkage mechanisms. This is analogous to the motion of pins  46  in the mechanism  60  illustrated in FIG. 3.  
         [0116]    Referring to FIG. 21, a computer controlled motor controller system such as computer  35  connected to controller  31  shown in FIG. 1 is used to control the motor which drives the link arms  214 . FIG. 21 shows a bottom view of the mechanism  210  with the motors  33  attached to the lower revolute joints  218  of the link-arms  214 . The rigid link arms  214  are offset to maximize the rotation of link arms  214  without any interference with each other. Increasing the rotation of link arms  214  will minimize the size of the robot. This applies to the embodiments shown in FIGS.  17  to  24 . The orientation of the cables  212  is determined by the amount of rotation on the link-arms  214 . Coupled with the passive cables  212 , the position and the orientation of the moving platform  22  are controlled. The operating principal is similar to the mechanism illustrated in FIG. 2.  
         [0117]    9. Two DOF Planar Parallel Mechanism Using Passive Cables  
         [0118]    The mechanism shown in FIG. 20 can be converted to a two degree of freedom planar manipulator by synchronizing the motion of the paired link-arms. A timing belt (or equivalently a chain-sprocket drive) can be used for that purpose. The configuration can be made by attaching a sheave to the revolute joint  218  and rigidly attach them to the link arm  214 . The synchronizing motion can be achieve by connecting the sheave with a timing belt. A synchronized motion of the paired link-arms  214  ensures the parallelism of the paired cables  212  that in turn restricts orientation of the moving platform  22 . As illustrated in FIG. 22, when two link-arms  214  are parallel, the close loops B-C-E-F and A-D-B-C form two parallelograms, which forces line A-D (attached to the moving platform) to be parallel with line E-F (attached to the base plate). Hence, the rotating degree of freedom of the moving platform is eliminated, leaving two translational degrees of freedom to the mechanism only.  
         [0119]    10. Hybrid Two DOF Planar Parallel Mechanism Using Passive Cables for Positioning and Active Cable for Orientation  
         [0120]    [0120]FIG. 23 shows another alternative embodiment of a mechanism shown at  220  to achieve the parallelism of the moving platform  22 . In mechanism  220 , the cables  212  that are attached to the moving platform  22  are connected to a beam  222 , which pivots about the free end of a link-arm  224 . The orientation of the beam  222  is constrained using a winch assembly  226  that includes a pair of cables  228  attached to beam  222 , a drum  230 , and a torsion spring (represented by a torsion load  232 ). Since both cables  228  are connected to the same drum  230 , their lengths are always equal to each other. The torsion spring  232  is attached to the drum  230  to maintain tension in cables  228 . Note that drum  230  is passive and its rotation depends on the orientation of arm  224  orientation. Analogous to the configuration shown in FIG. 22, the drum  230 , the beam  222 , the pairs of cables  228  and  212 , and the moving platform  22  form two parallelograms that ensure the parallelism between the moving platform  22  and the base plate  172 . Hence, the orientation of the moving platform  22  is maintained parallel to the ground.  
         [0121]    11. Hybrid Three DOF Planar Parallel Mechanism Using Passive Cables For Positioning And Active Cable For Orientation  
         [0122]    Referring now to FIG. 24, another embodiment of the mechanism shown in FIG. 20 is shown at  240 . Mechanism  240  is similar to mechanism  220  of FIG. 23 but includes a cam  242  that routes one of the cables  228 . The objective of cam  242  is to create a bias on the length of one of the active cables  228  to provide a new degree of freedom to the robot mechanism of FIG. 23. Adjusting the bias in the cable will allow to control the orientation of the moving platform  22 . The operating principal is similar to a cam-follower mechanism. The linear guide  119  is used to induce a linear motion to cam  242  as shown in FIG. 24.  
         [0123]    When the cam  242  moves towards the center of the mechanism, it routes the inner active cable  228  around the cam face. This effectively shortened the length the routed active cable while leaving the other active cable untouched. The resulting effect is a distortion on the parallelogram formed by the active cables and the beam. The routed cable pulls the beam on one side and forces the beam to tilt towards the routed cable. As a result, the beam  222  will no longer be parallel to ground, but is controlled by this cam  242 . Since the moving platform is parallel to the beam, the orientation of the moving platform is also controlled. The same operation can be performed on the other cable  228 . When the cam  242  moves towards the edge of the robots, it pulls the beam  222  on one side and forces the beam  222  to tilt towards the edge of the robot, which leads to the same rotation on the moving platform  22 .  
         [0124]    As used herein, the terms “comprises”, “comprising”, “including” and “includes” are to be construed as being inclusive and open ended, and not exclusive. Specifically, when used in this specification including claims, the terms “comprises” and “comprising” and variations thereof mean the specified features, steps or components are included. These terms are not to be interpreted to exclude the presence of other features, steps or components.  
         [0125]    The foregoing description of the preferred embodiments of the invention has been presented to illustrate the principles of the invention and not to limit the invention to the particular embodiment illustrated. It is intended that the scope of the invention be defined by all of the embodiments encompassed within the following claims and their equivalents.