Linking apparatus control device

A control device is provided which is operable to change the position of a distal end side link hub by driving each of arms, which are proximal end side links of a plurality of link mechanisms by means of an actuator. When in a series of operations, the position change of the distal end side link hub is mad by an angle greater than a predetermined angle, a relay position setting unit is provided for setting a relay point between a starting point and a terminating point of each of the arms so that the interference of the three axis arms may be relieved. A position change control unit performs a position control so as to pass simultaneously through the relay point so set.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to a control device for a link actuator that is used in equipment such as, for example, medical device or industrial device that requires a precise and wide operating range.

Description of Related Art

One example of working device equipped with a parallel link mechanism is disclosed in the Patent Document 1 listed below. Since the parallel link mechanism used in this working device has a plurality of links each having such a small operating range that the link length need be increased if the operating range of a travelling plate is desired to be expanded. Also, if the link length is increased, reduction in rigidity of the mechanism in its entirety results in. For this reason, there has been recognized such a problem that the weight of a tool mounted on the travelling plate, that is, the weight capacity of the travelling plate is limited to a small one.

In order to alleviate the foregoing problem, a link actuator provided with three or more sets of link mechanisms in quadric crank chain has been suggested (in, for example, the patent documents 2 and 3 listed below). According to the suggested link actuator, the operation within a precise and wide operating range is possible while it is compact in size.

FIGS. 22 and 23of the accompanying drawings illustrate one example of the link actuator provided with three or more link mechanisms in trinodal crank chain. The illustrated link actuator1includes a proximal end side link hub14, a distal end side link hub15, and three link mechanisms11,12and13each connecting those link hubs14and15together. Each of the link mechanisms11,12and13is made up of a proximal side end link member11a,12aor13a, a distal side end link member11b,12bor13band an intermediate link11c,12cor13c, all cooperating to define a corresponding link mechanism in the trinodal crank chain comprised of four revolute pairs. It is to be noted that inFIGS. 22 and 23, the distal side end link member13ais not illustrated for the sake of clarity. Also, the distal side end link members11a,12aand13aare hereinafter referred to as arms11a,12aand13a, respectively.

According to the above described link actuator of the structure discussed above, a proximal end side link hub14, a distal end side link hub15and three set of link mechanisms11,12and13cooperate with each other to form a mechanism of two degree of freedom in which the distal end side link hub15is movable relative to the distal end side link hub14in two axial directions perpendicular to each other. This two degree of freedom mechanism, while compact in size, is capable of providing the distal end side link hub15with a large operating range. By way of example, the maximum bending angle between the center axis QA of the proximal end side link hub14and the center axis QB of the distal end side link hub15is about ±90 degree and the pivot angle φ of the distal end side link hub15relative to the proximal end side link hub14can be set to the range of 0 to 360 degree.

PRIOR ART DOCUMENT

SUMMARY OF THE INVENTION

In the link actuator provided with three sets of link mechanisms11,12and13in trinodal crank chain such as shown inFIGS. 22 and 23, where the link mechanisms11,12and13having two degrees of freedom are to be driven by actuators (not shown) such as, for example, three motors, the position of the distal end side link hub15is determined by means of the bending angle θ and the angle of pivot φ. The bending angle θ is an angle of inclination of a center axis QB of the distal end side link hub15relative to a center axis QA of the proximal end side link hub14and the pivot angle φ is an angle of pivot of the center axis QB of the distal end side link hub15relative to the center axis QA of the proximal end side link hub14. From the bending angle θ and the pivot angle φ, the rotational angle of each of the arms11a,12aand13a(hereinafter referred to as “arm rotational angle”) (β1n, β2nand β3n) is determined and is positioned by the actuator for driving the arm11a,12aand13a.

By way of example, with respect to a certain position A (θa, φa) of the distal end side link hub15and the position B (θb, φb) thereof, each arm rotational angle corresponding to the respective position can be determined, as A (β1a, β2a, β3a), B (β1b, β2b, β3b) from the relational equation of the proximal end side and distal end side link hub14and15and the arm rotational angle. The movement from the position A to the position B is executed as the rotational angle of each of the arms11a,12aand13amoves from β1ato β1b, from β2ato β2band from β3ato β3b.

The relationship between the command value of the arm rotational angle β and the bending angles θ is shown by the dotted line L1to L3inFIG. 24. As shown therein, by way of example, where the position change is to be accomplished by changing the bending angle θ from −60 degree to 60 degrees in a condition while the pivot angle is fixed at 15 degrees, each of the arms11a,12aand13ais controlled from the starting point A to the terminating point B with the three arms11a,12aand13asynchronized with a constant velocity movement in synchronism on the point-to-point control.

However, if the respective arm rotational angle is determined by dividing the bending angle θ for, for example, −60 degree, −45 degree and −30 degree and using the distal end side link hub15and the arm rotational angle from the position of each of the leading side end link hubs15, each position is fixed according to the path following curved lines M1to M3as shown by the solid lines inFIG. 24. As can readily be understood from such figure, the misfit of the path is large in the vicinity of the bending angle 0 degree particularly in the curve L1and the curve M1.

As discussed above, if drive along the path shown by the curves L1to L3is commanded, as compared with the command of driving along the path shown by the curves M1to M3, the positioning command will be issued so that each arm rotational angle β1, β2and β3may pass a position in which the position of each arm11a,12a,13aon in the course except for the starting point and the terminating point, which is greatly different from the relational equation between the link hub and the arm pivot angle.

Since in this condition each arm11a,12aand13ais connected with each other and the relative position of the three arm rotational angles are uniquely fixed by the position of the distal end side link hub15, the relative position of the arm rotational angles breaks and the three arms11a,12aand13acome to interfere excessively. In other words, the three arms11a,12aand13aassume such arm rotational angles that resulted in a deviation relative to the command values towards the respective actuators. For this reason, a further large torque is required in driving the link along the path of the curves L1to L3.

Since this means that, because as the position changing amount is large for each drive, a positioning command, which direct to a position greatly different from the arm rotational angle that is fixed by the relational equation between the proximal end side and distal end side link hubs14and15and the arm rotational angle β in the course of the path, is issued, interference occurs between each arm11a,12a,13aand an excessive torque is needed to drive the link mechanisms11,12and13. A load is imposed in this condition on the link mechanism11,12,13and/or an assembling inconvenience and/or an abnormal friction or the like result in, which leads to a cause of deterioration in positioning accuracy. In order to alleviate them, the need is recognized that each of the arms has to be driven so as to follow the path proximate to the curves M1to M3shown inFIG. 24.

However, it has been found that the control of the rotational angle of each of the arms11a,12aand13ain such a manner as to avoid the occurrence of the interference (that is, deviation with a position determined by the relation of the three link mechanisms11,12and13with the command value) on all of the paths from a position A to a position B of the distal end side link hub15results in such a problem that the moving time may be elongated since a conversion calculating time in to the rotational angle from the position of the distal end side link hub15to each of the arms11a,12aand13ais needed. Also, where the control is done while the coordinates of the entire path has been stored, a problem arises in that a further large storage memory is required.

In view of the foregoing, an object of the present invention is to provide a control device for a link actuator in which, when the position of the distal end side link hub is to be largely changed, the positioning control of the actuator of each of the arms can be accomplished without departing considerably from each of the arm rotational angles that are uniquely fixed by the mutual relationship of a plurality of link mechanisms, in which drive can be achieved without applying an excessive load to each of parts of the link mechanisms, a delay in calculating time can be avoided to accomplish a high speed movement, and in which the capacity of the storage memory for the control may be small.

A control device for a link actuator according to the present invention will be described with the aid of reference numerals used in the accompanying drawings in connection with embodiments of the present invention. The control device1for the link actuator, according to the present invention, controls each of actuators of the link actuator in such a manner as to change position of a distal end side link hub15relative to a proximal end side link hub14from a starting point position A towards a terminating point position B which is commanded. The link actuator includes three or more link mechanisms11to13that connect the distal end side link hub15to the proximal end side link hub14in a position-changeable fashion, in which each link mechanisms11to13includes a proximal side end link member11ato13a, one end of the proximal side end link member11ato13abeing pivotably connected to the proximal end side link hub14; a distal side end link member11bto13b, one end of the distal side end link member11bto13bbeing pivotably connected to the distal end side link hub15; and an intermediate link member11cto13cwith its opposite ends pivotably connected to the other ends of the proximal side end link member11ato13aand the distal side end link member11bto13b, respectively, each of the link mechanisms11to13has such a shape that a geometric model of the link mechanism11to13represented by lines shows symmetry between a proximal end side portion thereof and a distal end side portion thereof with respect to a center portion of the intermediate link member11cto13c, and each link mechanisms11to13are provided with the actuator that arbitrarily changes position of the distal end side link hub15relative to the proximal end side link hub14by rotating the proximal side end link member in the form of the arm11ato13a.

This control device1referred to above includes a position change control unit41to drive each of the actuators in synchronism with each other on a point-to-point basis from a starting point, which is the rotational angle of the arm11ato13awhen the starting point position A is assumed, to a terminating point which is the rotational angle when the terminating point position B is assumed;

a relay position setting unit42configured to compare a position changing amount of the distal end side link hub15in the position change from the starting point position to the terminating point position with a predetermined amount, and configured to, in the event that the position changing amount of the distal end side link hub15is larger than the predetermined amount, set one or more relay position according to a predetermined rule during the course of an position changing path for changing from the starting point position to the terminating point position and to set by determining a rotational angle which corresponds to a relay point of the rotational path of each of the arms11ato13awhen the relay position is assumed. The position change control unit41performs a position control so that each of the arms simultaneously passes through the relay point set by the relay position change setting unit42.

According to the construction of the present invention as described above, by the relay position setting unit42, when the position change amount of the distal end side link hub15is greater than the predetermined amount, the relay position is set and the relay point in the rotational path of each of the arms11ato13a, at which the relay position is assumed, is set. The position change control unit performs the position control so that each of the arms11ato13apasses simultaneously across the relay point so set.

As described above, the relay position of the distal end side link hub15is set and the control is made to cause each of the arms11ato13ato pass simultaneously across the relay point at which the relay position thereof is assumed. For this reason, when the position of the distal end side link hub15changes considerably, without considerably departing from each of the arm rotational angles that are uniquely determined in dependence on the mutual relationship of the plurality of the link mechanisms11to13, the position control of the actuator3of each of the arms11ato13acan be accomplished. Accordingly, drive can be accomplished without imposing an excessive load on various parts of the link mechanisms11to13.

Also, although the calculation to determine the relay point is necessary, basically because of the point-to-point control, unlike the case in which the rotational angle is controlled so as to avoid the interference over the entire path of the position change of the distal end side link hub15, the calculation time required for the control can be small, no delay from the calculation time occurs and the high speed movement can be achieved. Also, unlike the control taking place while the coordinates of the entire path has been stored, the capacity of the storage memory may be small.

It is to be noted that the position change amount and the predetermined amount referred to in the wording “(to) compare the position change amount of the distal end side link hub15with the predetermined amount” may be directly determined n dependence on the bending angle θ and the pivot angle φ, they may be the bending angle θ or the pivot angle φ, in which the maximum torque occurring in the actuator3, when the point-to-point control is performed, or both of the bending angle θ and the pivot angle φ.

In one embodiment of the present invention, the relay position setting unit42may divide the rotational amount of each of the arms11ato13aon the basis of a division number by which the position change amount of the distal end side link hub15from the starting point position to the terminating point position is divided into an amount smaller than a predetermined amount. The term “predetermined amount” referred to above may be the moving amount over which each of the actuators3for driving, for example, the distal end side link hub15can be driven under the point-to-point control at a value smaller than the predetermined value, and this is determined by the geometric dimensions of the link device and the initial preload applied to the link. Also, the predetermined value about the actuator3to be driven represent a value lower than the input torque permissible value of the link device. Where the link device includes a speed reducer in an input part thereof, it represents a value lower than the input torque permissible value of the speed reducer.

With the path for the position change so divided, the interference between arms11ato13afor each axis is relieved and the drive can be accomplished under an actuator torque proper enough to avoid an assembling inconvenience of the link and an abnormal frictional wear of the link. It is recommended that the movement path of the distal end side link hub15from the starting point position to the terminating point position be determined by approximation.

In one embodiment of the present invention, three link members may be provided and the relay position setting unit sets the relay point according to the rule, and the rule may include: selecting two arms out of the three arms11ato13awhich operate during the course of changing the position from the starting point position of the distal end side link hub15to the terminating point position; equally dividing the rotational path of the selected two arms; and setting the position of the remaining one arm at a position uniquely determined according to a relative positional relationship with the other two arms.

In such case, as a criterion for selecting the two arms out of the three arms11ato13a, the arms having large rotational amounts may be selected. Since in this control the two arms, of which rotational amount is large, can move uniformly at the maximum speed of each axis, the movement can be achieved in the shortest movement time. Also, unless the rotational time is considered the selection of the two arms out of the three arms11ato13amay be arbitrarily chosen. It is, however, to be noted that the trajectory of the link distal end in this condition does not warrant the shortest path.

Particularly where the two arms are selected from the three arms11ato13aas hereinabove discussed, the position (θ, φ) of the distal end side link hub15may be determined from the rotational angle of the selected two arms by a transformation equation of forward transformation, and the rotational angle of the remaining one arm is determined by a transformation equation of inverse transformation from the position (θ, φ) of the link hub15. By so doing, the rotational angle of the remaining one arm can be properly determined.

In such case, the position (θ, φ) of the distal end side link hub15may be determined by a convergence calculation with the use of the rotational angle of the two arms out of the three arms11ato13aand a transformation equation. By conducting the convergence calculation, the position (θ, φ) of the distal end side link hub15can be determined easily from the two rotational angles of the arm.

In one embodiment of the present invention, the relay position setting unit42utilizes the predetermined rule for determining the relay point of each of the arm, and in the rule one or more relay positions on a path through which the distal end side link hub15moves in the shortest distance and sets the rotational angle of each of the arms to be the relay point, the rotational angle corresponding to the position (θ, φ) of the distal end side link hub15on the path, which position is any one of the starting point position, the relay position and the terminating point position on the path and the value achieved between the neighboring positions attains a value smaller than a predetermined value. In this case, the rotational angle of each of the arms may be determined from the position (θ, φ) of the link hub15by means of the transformation equation of inverse transformation.

In other words, with respect to the certain starting point position (the bending angle, the pivot angle) A (θa, φa) and the certain terminating position B (θb, φb) of the distal end side link hub15, the position changing path of the distal end side link hub15moving between the positions A and B is determined as small as possible. By performing a proper approximation if required, the time required to determine the path can be reduced. The path from the position A to the position B is divided into a plurality of positions, from the position N (θn, φn) of the distal end side link hub15, the rotational angle N (β1n, β2n, β3n) of the arm axis relative to the position of the distal end side link hub15is obtained. The link position control is carried out so that the position of each of the axis can move simultaneously.

In one embodiment of the present invention, three link mechanisms may be provided, and, from the starting point position A (θa, φa) and the terminating point position B (θb, φb) of the distal end side link hub15, the position (θ1, θ2, . . . θn, φ1, φ2, . . . φn) (wherein n is equal to the division number minus 1) of each of the distal end side link hubs15, in which the moving amount Δθ of the bending angle θ and the moving amount Δφ of the pivot angle Δθ attains a value smaller than a predetermined moving amount, may be determined according to the transformation equation of inverse transformation and the position (θ1, θ2, . . . θn, φ1, φ2, . . . φn) of the distal end side link hub15so determined is set to be the relay position. By dividing the moving amount Δθ of the bending angle θ and the moving amount Δφ of the pivot angle φ into the value smaller than the predetermined amount, the drive can be accomplished with the interference having been further reduced and without an excessive load.

In one embodiment of the present invention, the position change control unit41may perform a positional control from the starting point position A of the distal end side link hub15to the terminating point position B thereof without acceleration and deceleration over the entire zone except for an acceleration zone, in which the position change starts from the starting position, and a deceleration zone in which deceleration takes place immediately before the terminating point position is attained.

According to one embodiment of the present invention, the link actuator may be of such a design that assuming that in the link actuator a connecting end axis of the intermediate link member, which is pivotably connected with the proximal side end link member, and a connecting end axis of the intermediate link member, which is pivotably connected with the distal side end link member cooperate with each other to form an angle γ therebetween, and connecting end axes of the intermediate link member, which are pivotably connected with the proximal end side and distal side end link members, and connecting end axes of the proximal end side link hub and the distal end side link hub, which are pivotably connected with the proximal end side link member and the distal end side link member, respectively, cooperate with each other to form angles α therebetween, respectively, and; that

a rotational angle of the proximal side end link member relative to the proximal end side link hub is expressed by βn (n=1, 2, 3, . . . ); a circumferential separating angle of each of the proximal side end link members relative to the proximal side end link member forming a reference is expressed by δn (n=1, 2, 3, . . . ); a vertical angle at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub is expressed by θ; a horizontal angle at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub is expressed by φ, and also assuming that, where on a circumference through which a revolute pair portion of the proximal side end link member and the intermediate link member passes, a circumference separating angle of each of a revolute pair portions relative to a phase forming a reference is expressed by εn (n=1, 2, 3, . . . ) and a separating angle of the revolute pair portion of the proximal side end link member and the intermediate link member during a condition in which the position of the distal end side link hub relative to the proximal end side link hub is held in the position of origin (θ=0, φ=0) forming a reference is expressed by ε0;

each of the actuators is controlled to determine the rotational angle βn of the proximal side end link member from the position (θ, φ) of the distal end side link hub relative to the proximal end side link hub forming a target and then to set the determined rotational angle βn to be a desired rotational angle by means of the inverse transformation of the following equation 1 so that the relationship expressed by the following relational equations is satisfied:

The applicant of the present invention has suggested, in the patent document 4 listed above, a control method for the link actuator. The suggested control method is defined by four functions including the rotational angle βn of the end link member, the angle γ formed between the connecting end axis of the intermediate link member, which is pivotably connected with the proximal side end link member, and the connecting end axis of the intermediate link member connected pivotably with the distal side end link member, the circumferential separating angle δn of each of the proximal side end link member relative to the proximal side end link member forming the reference, the vertical angle θ at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub, and the horizontal angle φ at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub.

It has, however, been found that since the function of the angle (axis angle of the end link member) a formed between the connecting end axis of the intermediate link member, which is pivotably connected with the end link member, and the connecting end axis of the link hub connected pivotably with the end link member, which is a parameter required to construct the link actuator, is not included, and is hence limited to the case in which the axis angle α of the end link member is 90 degrees. Accordingly, the suggested control method is unable to control any other link actuator than the link actuator in which the axis angle α of the end link member is 90 degrees.

According to the foregoing construction, once the position (θ, φ) of the distal end side link hub, which is targeted, is determined, inverse transformation of the equation 1 makes it possible to determine the rotational angle βn of the end link member. When each of the actuators is controlled so that the rotational angle βn so determined can be attained, the position (θ, φ) of the distal end side link hub relative to the proximal end side link hub can assume the position so targeted. Since the function of the axial angle α of the end link member is included in the equation 1, when the value of α in the equation 1 is rendered to be the axis angle α of the end link member of each of the link actuators, the operation can be controlled even in the link actuator in which the axis angle α of the end link member is other than 90 degrees.

In one embodiment of the present invention, the use may be made of a position calculating device operable to calculate the position (θ, φ) of the distal end side link hub relative to the current proximal end side link hub from the rotational angle βn of the proximal side end link member by forward-transforming the following equation 1:

According to the above described construction, by means of the position calculating device, the position (θ, φ) of the distal end side link hub relative to the current proximal end side link hub can be calculated by inserting into and forward-transforming the rotational angle βn of the current proximal side end link member. Since in the equation 1 the function of the axis angle α of the end link member is included, by rendering the value of α in the equation 1 to be the axis angle α of the end link member of each of the link actuator, the position (θ, φ) of the distal end side link hub relative to the proximal end side link hub can be calculated even in the link actuator.

According to one embodiment of the present invention, the positive or negative on the second line in the left side of the equation 1 and the positive or negative on the right side of the equation 1 may be determined depending on the direction of assembly of the proximal end side end link relative to the proximal end side link hub. The separating angle ε0involves two solutions that are different in dependence on the direction of assembly of the distal side end link member relative to the proximal end side link hub. Accordingly, the positive or negative on the second line in the left side of Table 1 and the positive or negative in the right side of the equation 2 are fixed depending on the direction of assembly of the proximal end side link relative to the proximal end side link hub. By way of example, when the direction of assembly is in the rightward direction, it is “+” whereas when the direction of assembly is in the leftward direction, it is “−” and, by so doing, the equation 1 establishes. Accordingly, the operation can be controlled and the position (θ, φ) of the distal end side link hub relative to the proximal end side link hub can be calculated.

In a yet further embodiment of the present invention, the axis angle α of the end link member may be 90 degrees. When the axis angle α of the end link member is 90 degrees and the connecting end axis of the intermediate link member, which is pivotably connected with the proximal end side and distal side end link members, and the connecting end axis of the proximal end side and distal end side link member, which is connected pivotably with the proximal end side and distal side end link members, lie perpendicular to each other, the processability such as perforating process of the end link member becomes good and the mass-productivity is excellent.

Alternatively, the axis angle α of the end link member is not greater than 90 degrees. If the axis angle α of the end link member is chosen to be not greater than 90 degrees, although in terms of a mechanism the operating range of the link actuator may become small, the structure is such that the interference between the link mechanism will hardly occur. Also, reduction in weight of the end link member and downsizing can be accomplished, and the end link member can be manufactured at a low cost in terms of, for example, the material cost of the end link member. In view of this, the reduction in weight of the link actuator in its entirety and downsizing can be accomplished. Also, the interior space of the link actuator expands and the structure will be obtained in which cables and any other component parts can be disposed within the interior space.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the present invention will be described in detail with particular reference to the accompanying drawings. At the outset, a link actuator which forms a target to be controlled will described with particular reference toFIGS. 1 to 5. As shown inFIGS. 1 and 2, this link actuator1includes a link actuator main body2and a plurality of position control actuators3for actuating the link actuator main body2and those position control actuators3are controlled by a control device4. In the example as shown, the link actuator main body2is disposed suspended from a support member5via a spacer6on a proximal end side of such link actuator main body2. The link actuator main body2has a distal end side on which an end effector8is mounted through a distal end mounting member7.

The link actuator main body2is of a construction basically identical with the link actuator shown inFIG. 22and previously discussed with reference thereto. As shown inFIG. 3, the link actuator main body2is equipped with three link mechanisms11,12and13(hereinafter, designated as “11to13”). It is to be noted that inFIGS. 1 and 2, only one link mechanism is shown regarding the shape of the link mechanism11and inFIG. 1, with respect to the remaining two link mechanisms12and13, they are shown in a block diagram only for the purpose of description. Those three link mechanisms11to13are of the same geometric shape. In other words, each of the link mechanisms11to13is of such a design that the geometric model, in which each of link members11ato13a,11bto13band11cto13cas will be described later is depicted by line is such that a proximal end side portion and a distal end side portion are of a symmetrical shape with respect to an intermediate portion of intermediate link members11cto13c.

Each of the link mechanisms11,12and13is comprised of a proximal side end link member11a,12a,13a(hereinafter, designated by “11ato13a”), a distal side end link member11b,12b,13b(hereinafter, designated by “11bto13b”) and an intermediate link member11c,12c,13c(hereinafter, designated by “11cto13c”) and forms a trinodal structure link mechanism made up of four revolute pairs.

Each of the proximal end side link members11ato13aand the distal side end link members11bto13bhas a shape similar to that of the figure “L” and also has a proximal end pivotably connected with a proximal end side link hub14and a distal end side link hub15. Each of the intermediate link members11cto13cis pivotably connected at its opposite ends with respective distal ends of the proximal end side link members11ato13aand the distal side end link members11bto13b. It is to be noted that the end link members11ato13aare “arms” of the link actuator1and, therefore, in the description that follows, they may occasionally referred to as “arms11ato13a”.

Each of the proximal end side link hub14and the distal end side link hub16has a hexagonal columnar shape and, the proximal end side and distal side end link members11ato13aand11bto13bare pivotably connected respectively with three side faces16of the six side faces16forming an outer surface thereof, which are alternately spaced from each other.

The proximal side end link members11ato13aand the distal side end link members11bto13bof each of the three link mechanisms11to13is of a structure referred to as a spherical link mechanism. In other words, respective spherical link centers PA (shown inFIGS. 1 and 2) of the proximal side end link members11ato13aare matched with each other and respective spherical link centers PB (also shown inFIGS. 1 and 2) of the distal side end link members11bto13bare matched with each other. Also, the distances from the spherical link centers PA to the proximal side end link members11ato13aremain the same and, also, the distances from the spherical link centers PB to the distal side end link members11bto13bremain the same. The respective revolute pairs that form joints between the proximal end side and distal side end link members11ato13aand11bto13band the intermediate link members11cto13cmay have a certain crossed axes angle or, alternatively, may be parallel to each other.

In other words, the three link mechanisms11to13have respective geometric shapes that are identical with each other. The geometricly identical shape so discussed means that the geometric model of each of the link members11ato13a,11bto13b,11cto13cthat are drawn by lines, that is, each of the revolute pairs and the model drawn by line so as to connect between those revolute pairs is such that a proximal end side portion and a distal end side portion with respect to an intermediate portion of the intermediate link members11cto13crepresents a symmetrical shape.FIG. 4is a diagram showing one of the link mechanisms11depicted by line.

The link mechanisms11to13employed in the practice of this embodiment is of a rotation symmetrical type and, hence, the positional relationships between the proximal end side link hub14and the proximal side end link members11ato13aand the distal end side link hub15and the distal side end link members11bto13bare so designed as to assume a rotation symmetry with respect to a center line C of the intermediate link members11cto13c.FIG. 1illustrates a condition in which a center line QA of the proximal end side link hub14and a center axis QB of the distal end side link hub15lie on the same line, andFIG. 2illustrates a condition in which the center axis QB of the distal end side link hub15relative to the center axis QA of the proximal end side link hub14assumes a predetermined operating angle. Even when the position of each of the link mechanisms11to13changes, the distance H between the proximal end side and distal end side spherical link centers PA and PB does not change.

FIG. 5illustrates a sectional view of the joints between the proximal end side link hub14and the proximal side end link members11ato13a. Shaft portions18protrude outwardly from respective side faces16of the proximal end side link hub14, respective inner rings (not shown) of double-row bearings17are mounted externally on the shaft portions18, and respective outer rings (not shown) of the double-row bearings17are mounted internally on shaft portions on proximal end side link hub side of the proximal side end link members11ato13a. In other words, the structure is such that the inner rings are fixed to the proximal end side link hub14and the outer rings are rotatable together with the respective proximal side end link members11ato13a.

Each of the bearings17is in the form of a ball bearing such as, for example, a deep groove ball bearing or an angular contact ball bearing and is fixed by fastening a corresponding nut19while having been applied a predetermined preload amount. For the bearing17, other than the ball bearing arranged in a number of row as is the case as shown, a roller bearing or a slide bearing may be employed. The joints between the distal end side link hub15and the distal side end link members11bto13bare similar in structure to that previously described.

Also, the joints between the proximal side end link members11ato13aand the intermediate link members11cto13care also connected pivotably with each other through respective double-row bearings20. In other words, respective outer rings (not shown) of the bearings20are mounted externally on the proximal side end link members11ato13a, and respective inner rings (not shown) of the bearings are mounted externally on shaft portions21provided in the corresponding intermediate link members11cto13c. Each of the bearings20is a ball bearing such as, for example, a deep groove ball bearing or an angular contact ball bearing and is fixed by fastening a nut22while having been applied a predetermined preload amount. For the bearing20, other than the ball bearing arranged in a number of row as is the case as shown, a roller bearing or a slide bearing may be employed. The joints between the distal side end link members11bto13band the intermediate link members11cto13care also similar in structure to that previously described.

In the previously described link mechanisms11to13, the angles and length of the shaft portions18of the proximal end side and distal side end link members11ato13aand11bto13bare equal to each other and, also, respective geometric shapes of those end link members11ato13aand11bto13bare equal on the proximal end side and the distal end side. Yet, even in the intermediate link members11cto13c, the shapes on the proximal end side and the leading side are equal to each other.

In this condition, the respective angle positional relationships between the intermediate link members11cto13crelative to the plane of symmetry of the intermediate link members11cto13cand the proximal side end link members11ato13aand the distal side end link members11bto13bthat are connected respectively with the proximal end side link hub14and the distal end side link hub15are chosen to be the same as between the proximal end side and the distal end side. By so doing, it will readily be seen that in view of the geometric symmetry, the proximal end side link hub14and the proximal side end link members11ato13aand the distal end side link hub15and the distal end side end kink members11bto13bwill move in the same manner and rotate at a constant velocity with the same angle of rotation on the proximal end side and the distal end side. The plane of symmetry of the intermediate link members11cto13cat the time of constant velocity rotation is referred to as a constant velocity bisector plane.

For this reason, by disposing a plurality of the link mechanisms11to13of the same geometric shapes, which commonly share the proximal end side link hub14and the distal end side link hub15, on the circumference, the intermediate link members11cto13care limited only to the movement in the constant velocity bisector plane as position where the plurality of the link mechanisms11to13can be moved without contradiction. Accordingly, the constant velocity rotation can be obtained even though the proximal end side and the distal end side assume any arbitrary operating angle.

Each of the link mechanisms11to13includes four rotation portions of the revolute pairs. More specifically, they includes a connection part between the proximal end side link hub14and the proximal side end link members11ato13a; a connection part between the distal end side link hub15and the distal side end link members11bto13b; and two connection parts between proximal end side and distal side end link members11ato13aand11bto13band the intermediate link members11cto13c. By rendering those rotation portions of the four revolute pairs to be bearing structures, the rotational resistance can be relieved while the frictional resistances at those connection parts are reduced, a smooth power transmission can be secured and the durability can be increased.

According to this construction of the link actuator main body2, a large movable range of the distal end side link bub15relative to the proximal end side link hub14can be secured. More specifically, by way of example, the to maximum value of the bending angle θ (the maximum bending angle) between the center axis QA of the proximal end side link hub14and the center axis QB of the distal end side link hub15can be set to about ±90 degree. Also, the angle φ of pivot of the distal end side link hub15relative to the proximal end side link hub14can be set to a vale within the range of 0 to 360 degree.

Referring toFIGS. 1 and 2, the plurality of the actuators3are disposed on the support member and are circumferentially spaced an equal distance from each other. The number of the actuators3is three that is equal to the number of the link mechanisms11,12and13. In the embodiment now under discussion, the actuator3is in the form of a motor and a pinion30is provided on an output shaft3athereof. On the other hand, a connecting member31, shown inFIG. 5, is fixedly fitted to the revolute pair with the shaft portion18in the proximal side end link members11ato13a, and a sector gear32capable of being meshed with the pinion30is provided in this connecting member31. A center axis of the sector gear32is matched with the center axis of the shaft portion18shown inFIG. 5. The pinion30and the sector gear32cooperate with each other to define a speed reducing mechanism33.

When each of the actuators3is rotationally driven, the rotation thereof is transmitted to the shaft portion18, shown inFIG. 5, through the speed reducing mechanism33and the angle of the arms11ato13a, which is the proximal side end link member, relative to the proximal end side link hub14, is accordingly changed. Therefore, the position of the distal end side link hub15relative to the proximal end side link hub14is fixed. This position is defined by the bending angle θ, shown inFIG. 3, and the angle φ of pivot shown inFIG. 3. Respective angles β1, β2and β3of the arms11ato13acan be estimated from values detected by a rotational angle detecting unit35and the value of reduction gear ratio of the speed reducing mechanism33.

In the description that follows, the control device4will be discussed with particular reference toFIG. 1. The control device4is a device for controlling each of the actuator3so that the position of the distal end side link hub15relative to the proximal end side link hub14can be changed from the start position, which is the current position, to the terminating position which is given from an external commanding unit40to the control device4. This control device4is of a type numerically controlled by a computer and is mainly made up of a position change control unit41for performing a basic control and a relay position setting unit42relating to a characteristic control.

The position change control unit41drives each of the actuators3on a point-to-point basis from the starting point, which represents the angle of rotation of the arms11ato13awhen the starting point position is assumed, to the terminating point, which is represented by the angle of rotation when the terminating point position is assumed. This position change control unit41has a function of performing such a synchronous control so that the actuators3can start moving simultaneously form the starting point and can arrive at the terminating point simultaneously, and they can pass a relay point simultaneously.

The position change control unit41referred to above is made up of a plurality of individual control sections43for controlling the respective actuators3for the link mechanisms11to13, a command conversion section44, a synchronous control section45and individual command sections48.

Each of the individual control sections43performs a position control on a point-to-point basis from a given starting point to the terminating point and is, for example, operable to perform a trapezoidal speed control of acceleration, constant speed movement and deceleration. The velocity for the constant speed movement for this trapezoidal speed control and the accelerated velocity during acceleration and deceleration are given by the synchronous control section45. The individual control section43is, more specifically, made up of an operating amount converting part (not shown) for converting, for example, the arm rotation angle into an actuator movement amount, an operation command generating part (not shown) and a servo controller part (not shown). The operation command generating part referred to above applied an operation command to the servo controller part by means of a pulse sweep according to a velocity curve of the trapezoidal speed control, and the servo controller part performs a feedback control with the use of the operation command, which has been so given, and a detection value of the rotational angle detecting unit35.

The command conversion section44converts a command B (θb, φb) of the terminating position, which is determined by the bending angle θ and the pivot angle α from the commanding unit40, into the rotational angle β of the arm11ato13aof each of the link mechanisms11to13and the converted rotational angle β comes to represent the corresponding arm rotational angle. The command conversion section44referred to above applies the converted rotational angle β of each of the arms11ato13ato the associated individual command section48as the position of the terminating point. Calculation to determine the rotational angle β of each of the arms11ato13afrom the bending angle θ and the pivot angle φ is accomplished by means of the inverse transformation according to the relational equation (1) as will be described later.

The starting position refers to the current position and the starting point given to each of the individual command section48refers to the current position of each of the arms11ato13a. This starting point is the terminating point during the previous cycle of movement and the current position estimated from the value, which is detected by each of the rotational angle detecting units35, and the reduction gear ratio of the speed reducing mechanism33or a predetermined reference position and others.

The synchronous control section45performs a synchronous control by setting the velocity at the time of the constant speed movement of the trapezoidal velocity control in each of the individual control sections43and the accelerated velocity (or the acceleration and deceleration time constant) during acceleration and deceleration so that each of the arms11ato13astarts rotation synchronously from the starting point and can terminate synchronously at the terminating point. Instead of the velocity, the terminating time of the acceleration and the starting time of the deceleration may be determined. The synchronous control section45referred to above also determines the velocity curve referred to above, so that a position and/or velocity control, in which the arms11ato13acan pass synchronously through the relay point referred to previously.

The relay position setting unit42referred to previously sets one or more relay positions according to a predetermined rule during the process of changing an position changing path when such position changing amount of the distal end side link hub15, when the distal end side link hub15changes its position from the starting point position to the terminating point position, is found to be greater than a predetermined amount as a result such position changing amount of the distal end side link hub15has been compared by a comparing section47with the predetermined amount in a setting section46. This relay position setting unit42sets by determining the rotational angle, which will become a relay point of the rotating path of each of the arms11ato13awhen the relay position is established. It is to be noted that the path for the position change of the distal end side link hub15is rendered to be, for example the path of a center of the link hub15. Also, the distal end side link hub15can have its position changeable on an arbitrary path, but the relay position assumes the relay position when passing along the position change path that is, for example, the shortest path.

In the example under discussion, the relay position setting unit42divides the rotational amount of each of the arms11ato13abased on the division number by which the position changing amount from the starting point position to the terminating point position of the distal end side link hub15have been divided into a value smaller than a predetermined value. The “predetermined rule” may include, for example, selecting two arms from the three arms11ato13awhich operate during the course of changing the position from the starting point position to the terminating point position, and equally dividing the rotating paths of those selected two arms, and positioning the remaining arm to a position that is uniquely determined from the relative positional relationship with the two arms referred to previously. As the criterion with which the two arms are selected out of the three arms11ato13a, the arm which shows the large rotational amount is preferably selected.

The synchronous control section45causes each of the individual control sections43to fix the velocity curve, referred to previously, so that each of the arms11ato13acan pass simultaneously through the relay point of each of the arms11ato13athat is determined by the relay position setting unit42as hereinabove described. Each of the individual control sections43controls the actuator3of the associated arms11ato13aaccording to the velocity curve so determined. Accordingly, the position change control unit41initiates the simultaneous movement of the actuators3from the starting point, causes them to arrive at the terminating point simultaneously and performs a synchronous control so that they can pass the relay point simultaneously.

The operation of the above described construction will now be described. The link actuator1that will become a target to be controlled is of such a design that the bending angle θ and the pivot angle φ and the rotational angle βn (β1, β2, β3) of each of the proximal end side end links11a,12aand13aare in such relationship as expressed by the following equation (A):
Cos(θ/2)·sin βn−sin(θ/2)·sin(φ+δn)·cos βn+sin(γ/2)=0  (A)

In the equation (A) above, the parameter γ represents the angle defined between a connecting end axis of the intermediate link members11c,12cand13cthat are pivotably connected with the arms11a,12aand13a, and a connecting end axis of the intermediate link members11c,12cand13cthat are pivotably connected with the distal side end link members11b,12band13b. The parameter δn (δ1, δ2, δ3) referred to above represents the separating angle defined by each of the proximal side end link members11a,12aand13ain the circumferential direction relative to the arm11athat forms a reference. Where the number of the link mechanisms11,12and13is three sets and each of the link mechanisms11,12and13are circumferentially equidistantly spaced, the separating angles δ1, δ2and δ3of each of the arms11a,12aand13awill be 0 degree, 120 degrees and 240 degrees, respectively.

From the foregoing relationship, regarding a certain starting point position (the bending angle and the pivot angle) A (θa, φa) and a certain terminating point position B (θb, φb) of the distal end side link hub15, the arm rotational angle corresponding to those positions A and B establish the relationship as respective rotational angle A1(β1a, β2a, β3a) and rotational angle B1(β1b, β2b, β3b) from the foregoing relational equation (A) between the proximal end side link hub14and the distal end side link hub15and the arm rotational angle.

In this condition, the relay position setting unit42determines the amount of movement of the distal end side link hub15from the starting point position A to the terminating point position B and, in the event that the amount of movement so determined is larger than a predetermined amount of movement, divides the interval from the starting position A to the terminating point position B into a plurality of positions so that the amount of movement so determined may become smaller than the predetermined amount of movement. The term “predetermined amount of movement” referred to above is to be understood as meaning the amount of movement in which the motor torque of each of the actuators3comprised of motors can be driven at the value smaller than a predetermined value. This amount of movement referred to above is determined by the geometric dimensions of the link actuator1and the initial preload applied to the link. Also, the predetermined value in connection with the motor torque to be driven represents a value smaller than an input torque permissible value of, for example, the previously described speed reducing mechanism33which forms an input part of the link actuator1.

By dividing the path at the time of the position change in the manner described above and controlling the relay point, which is a dividing part thereof, so that the arms11ato11cof each axis can pass simultaneously, interference between the arms11ato11cof each axis is relieved and they can be driven at a proper motor torque without any assembling inconvenience of the links and abnormal friction or the like being applied. The term “interference” referred to above means the occurrence of the arm rotational angle that results in a deviation relative to the command value to the actuator3as hereinbefore described. The path of movement of the distal end side link hub15from the starting point position A to the terminating position B is determined by approximation.

Also, calculation to determine the relay point is necessary, but basically because of the point-to-point control, unlike the control of the rotational angle so that no interference occur over the entire path of the position change of the distal end side link hub15, the length of time to accomplish the calculation necessitated for the control can be reduced and a high speed movement can be accomplished with no delay brought about by the calculating time. Also, unlike the control that is accomplished by allowing coordinates of the entire path to be stored, the capacity of a storage memory may be small.

For the method of dividing to determine the relay point by means of the relay position setting unit42, the following first to third examples can be employed. In the first place, the first example of the dividing method is shown in Table 1 below:

In connection with the movement from the starting point position A to the terminating point position B, determination is made of the rotational angles of the arm axes β1, β2and β3and then selection is made of two arms which have exhibited a large amount of movement. Assuming that the arm axes exhibiting the large amount of movement are expressed by β1and β2, the respective amounts of movement of the arms β1and β2are equally divided by a division number n which has been previously determined, and then respective rotational angle position of each of the arms11to13so divided is determined. In this condition, the division number n is such that the amount of movement of the distal end side link hub15from the starting point position A to the terminating point position B is expressed by L, the predetermined amount of movement is expressed by d, and L/d=m (quotient) . . . a (remainder), and the division number n is rendered to be n=m+1.

Regarding the rotational angle of the arm axis β3, with the use of the position (θn, φn) of the distal end side link hub15determined by the rotational angles of the biaxial arm axes β1and β2and the power rectifying algorithm, the arm rotational angle of β3is obtained by means of the inverse transformation. With respect to the inverse transformation, the four angles of β1a, β2a, θ and φ satisfy the following equations (B) and (C) in view of the arm rotational angle of the link hub and the previously discussed relational equation (A):
f: cos θ·sin β1a−sin θ·sin φ·cos β1a+sin γ=0≡f(θ,φ)  (B)
g: cos θ·sin β2a−sin θ·sin(φ+σ)·cos β2a+sin γ=0≡g(θ,φ)  (C)

Since those equations (B) and (C) are nonlinear equations of the respective parameters θ and φ, solution is determined numerically. The calculation of determining the position (θn, φn) of the distal end side link hub15with the use of a forward transformation equation from the rotational angles of the biaxial arm axes β1and β2is carried out by means of, for example, the convergence calculation. Here, the parameter γ represents the axis angle determined depending on the designed structure of the link and σ represents the phase angle determined by respective arrangement positions of the three arms. Also, with respect to the inverse transformation, from the previously described relational equation (A) of the link hubs and the arm rotational angle, the arm rotational angles of β1, β2and β3at a certain link hub position (θ, φ) are uniquely determined. Table 2 below illustrates positions at which the rotational angle moving amount of three shafts are divided.

The link position control is carried out in such a manner that the rotational angle position of each of the shafts shown in Table 2 is moved in synchronism with the control performed by the synchronous control section45.

Since according to this control the two arms11aand11b, which have the large amounts of movement, can move at a uniform speed at the maximum velocity of each of the axis, it can be driven in the shortest moving time. Also, unless the moving time is taken into consideration, selection of the two arms out of β1, β2, and β3may be arbitrarily chosen. It is, however, to be noted that it does not warrant that the trace of the link distal end in this condition passes the shortest path.

The second dividing method is now shown. In the practice of this second method, one or more relay positions are taken on the path through which the distal end side link hub15moves in the shortest distance and, of the position on the path, which may be one of the starting point position, the relay position and the terminating point position, the rotational angle of each of the arms11ato13acorresponding to the position (θ, φ) of the link hub15, in which the quantity such as, for example, the distance established between the neighboring positions assumes a value smaller than the predetermined quantity, is rendered to be the relay point. In this case, the rotational angle of each of the arms11ato13amay be determined from the above discussed position (θ, φ) of the link hub15according to the transformation equation of the inverse transformation.

The second dividing method is to determine, specifically with respect to the starting position (the bending angle and the pivot angle) A (θa, φa), and the terminating position B (θb, φb), the path of the distal end side link hub15which moves between the positions A and B may become the shortest distance as small as possible. In this condition, the time required to determine the path can be shortened when a proper approximation is made if so required. By dividing the path from the starting point position A to the terminating point position B into a plurality of positions, the rotational angle N (β1n, β2nand β3n) of the arm axis corresponding to each of the link hubs is obtained by means of the inverse transformation algorithm from the position N(θn, φn) of each of the distal end side link hubs15.

The inverse transformation algorithm referred to above is, for example, a transformation to calculate the rotational angle βn from the bending angle θ and the pivot angle φ according to the previously discussed relational equation (A). The link position control is carried out so as to move the position of the actuator3of each axis simultaneously under the control of the synchronous control section45.

The third dividing method is hereinafter shown. In the practice of this third method, from the certain starting point position A (θa, φa) and the terminating point position B (θb, φb) of the distal end side link hub15, the position (θ1, θ2, . . . θn, φ1, φ2, . . . φn) of each of the distal end side link hubs5, which have been so divided so that the moving amount delta Δθ of the bending angle θ and the moving amount Δφ of the pivot angle φ may attain respective values smaller than the predetermined moving amounts, is determined according to the transformation equation of the inverse transformation and the position (θ1, θ2, . . . θn, φ1, φ2, . . . φn) so determined is set to be the relay position. In this instance, n is equal to (dividing number −1).

The foregoing third dividing method is to determine, the bending angle moving amount Δθ and the pivot angle moving amount Δφ are individually equally divided specifically between the certain starting position (the bending angle and the pivot angle) A (θa, φa) and the terminating position B (θ1, φb) of the distal end side link hub15, followed by determination of a plurality of positions of the distal end side link hub15. The moving amount so divided at that time is rendered to be a value smaller than the predetermined moving angle. Thereafter, from each of the positions N (θa+n×Δθ/M, φa+n×Δφ/M) of the distal end side link hub15, the rotational angle N (β1n, β2n, β3n) of the arm axis is obtained according to the inverse transformation algorithm. In this instance, N and n represent the serial number N (or n) and M represents the dividing number.

The link position control is carried out in such a manner as to achieve a synchronous movement of each of the shafts under the control of the synchronous control section45. In this way, by equally dividing so as to render the moving amount Δθ of the bending angle θ and the moving amount Δφ of the pivot angle φ to attain respective values smaller than the predetermined moving amounts, the drive can be accomplished with a further minimized interference and with no excessive load imposed.

In any one of the first, second and third dividing methods discussed hereinabove, the synchronous control section45of the position change control unit41is preferably so designed that with respect to the path of movement from the certain starting point position A (θa, φa) to the certain terminating point position B (θb, φb) of the distal end side link hub15in the practice of the relevant dividing method, the control towards each of the rotational angle βA (β1a, β2a, β3a) of the arm axes β1to β3and the rotational angle βB (β1b, β2b, β3b) is preferably accomplished by means of a position control without acceleration and deceleration through the relay point on the course as shown inFIG. 7.

In such case, the rotational angle position of each of the shafts shown in Table 3 below is carried out so as to move synchronously under the control of the synchronous control section45. In other words, with respect to the axes β1to β3of all of the arms11ato13a, the time (timing (1) to (2)), during which the acceleration in the trapezoidal velocity control takes place, and the time (timing (4) to (5)), during which the deceleration takes place, are aligned with each other and the control is made to allow each of the relay points to be passed during a period (timing (2) to (4)) such as, for example, the timing (3), in which the constant velocity operation such as takes place.

By performing the positioning control without accelerating or decelerating the relay point in the manner described above, a smooth drove at a constant velocity can be accomplished from the starting point position A point to the terminating point position B.

According to any one of the foregoing embodiments, where the link actuator1is desired to be changed in position in a wide angle, the relative positional relationship of each of the arm rotational angles being then driven can accomplish a positioning control without being diverted considerably from the position at which the equation (A), which is uniquely defined by the mutual relationship between the plurality of the link mechanisms, and accordingly with no excessive load imposed on the link and the high speed movement is enabled.

A second embodiment of the present invention will now be described with particular reference toFIGS. 8 to 13. Parts, which are shown in those figures, but similar to those shown and described in connection with the first embodiment of the present invention, are indicated by like reference numerals and the details thereof are not reiterated for the sake of brevity.FIG. 8is a diagram in which an explanatory diagram descriptive of angles in various circumferential directions is shown is added to a front elevational view showing, with a portion thereof removed, the link actuator. As shown inFIG. 8, the illustrated link actuator1includes a link actuator main body2, a base bench52for supporting the link actuator main body2, a plurality of actuators3for actuating the link actuator main body2, a control device4for controlling those actuators3, and a position calculating device59. In this example, the control device4and the position calculating device59are provided within a control unit54, but the control device4and the position calculating device59may be provided separate from the control unit54.

The proximal end side link hub14and the distal end side link hub15are each formed with a throughhole10extending through a center part thereof in an axial direction and is of a ring shape with its exterior shape represented by a spherical shape. The center of the throughhole10is aligned with respective center axes QA and QB of the proximal end side and distal end side link bubs14and15.

The bending angle θ represents a vertical angle for which the center axis QB of the distal end side link hub15is inclined relative to the center axis QA of the proximal end side link hub14, and the pivot angle φ represents a horizontal angle in which the center axis QB of the distal end side link hub15is inclined relative to the center axis QA of the proximal end side link hub14. It is to be noted that the pivot angle φ has a positive direction which is a counterclockwise direction as viewed from the side of the distal end side link hub15.

FIG. 13is a sectional view showing the proximal end side link hub14, the proximal side end link members11ato13aand the intermediate link members11cto13cin a deployed form. The proximal end side link hub2is formed at three circumferential locations with a radially extending shaft holes111that communicates between a throughhole10in the axial direction and an outer peripheral side thereof, and a shaft member113is rotatably supported by two bearings112provided within the respective shaft holes111. In the example as shown, each of the shaft members113are positioned in circumferentially equally spaced relation, but this is not limited thereto. The shaft member113has an outer side end portion protruding from the proximal end side link hub14, the proximal side end link members11ato13ais connected with its protruding threaded portion113aand is fixedly fastened with a nut114. In the example as shown, the axis angle α of the end link member is chosen to be 90 degrees, but this is not necessarily limited thereto.

The bearing112referred to above is a rolling bearing in the form of, for example, a deep groove ball bearing, its outer ring (not shown) being mounted on an inner periphery of the shaft hole11while its inner ring (also not shown) is mounted on an outer periphery of the shaft member113. The outer ring is non-detachably retained by a stop ring115. Also, a spacer116is interposed between the inner ring and the proximal side end link members11ato13a, and a fastening force of the nut114is transmitted to the inner ring through the proximal side end link members11ato13aand the spacer116to thereby apply a predetermined preload to the bearing112.

The circumferential phase of each of the proximal side end link members11ato13ain the circumferential direction is indicated in the following manner. Specifically, one of the link mechanisms11to13, which forms a reference, is fixed as a link mechanism11forming the reference, and the circumferential phase of a connecting end axis (indicative of a revolute pair center axis S3) of the proximal side end link member11ain the link mechanism11forming the reference is indicated by δ1(for example, δ1=0°). Then, circumferential separating angles of connecting end axes S4and S5of the other two proximal side end link members12aand13arelative to the connecting end axis S3of this proximal side end link member11aare indicated by δ2and δ3, respectively. The separating angle δn (n=1, 2, 3) has a positive direction defined in a counterclockwise direction when viewed from the side of the distal end side link hub15.

Also, with respect to the revolute pair portions T1to T3of the proximal side end link members11ato13aand the intermediate link members11cto13c, such a structure is employed that two bearings119are provided in respective communicating holes118at opposite ends of the intermediate link members11cto13cand, by means of those bearings119, a shaft portion120at a distal end of the proximal side end link members11ato13ais rotatably supported. The bearings119are fixedly fastened by respective nuts122through corresponding spacers121.

The bearing referred to above is a rolling bearing such as, for example, a deep groove ball bearing with its outer ring (not shown) mounted on an inner periphery of the communicating hole118whereas its outer inner ring (also not shown) is mounted on an outer periphery of the shaft portion120. A fastening force of the nut122treaded onto a distal end threaded area120aof the shaft portion120is transmitted to the inner ring through a spacer121with a predetermined preload applied to the bearing119.

InFIG. 13, the revolute pair portion T1of the proximal side end link members11ato13aand the intermediate link members11cto13cis shown at a center position in an axial direction of the two bearings119on its revolute pair center axis S1. In place thereof, the revolute pair portion T1may be expressed by a position on the revolute pair center axis S1and where in all of the three link mechanisms11to13the distances from a spherical surface center PA of the proximal end side link hub14is the same. Where the revolute pair portion T1is expressed by the position of the single point in this way, as shown inFIG. 8, the revolute pair portion T1of each of the link mechanisms11to13remains positioned on the same circumference E.

The circumferential phase of the revolute pair portion T1of each of the link mechanisms11to13is shown as follows. Specifically, the separating angle of the revolute pair portion T1of the rink mechanism11, which forms the reference, in a circumferential direction relative to the connecting end axis S3of the proximal side end link member11ais expressed by ε1. And, the separating angles of the other two revolute pair portions T1in the circumferential direction relative to the revolute pair portion T1of the link mechanism11which forms the reference are expressed by ε2and ε3(not shown), respectively. Even in the separating angle εn (n=1, 2, 3) the counterclockwise direction as viewed from the side of the distal end side link hub15is rendered to be a positive direction. Also, as shown inFIG. 8, the circumferential phase of the revolute pair portion T1of the link mechanism11, which forms the reference, in a condition in which the position of the leading side link hub15lies at the position of origin (θ=0, φ=0) is rendered to be ε0.

Although the connecting structure between the proximal end side link hub14and the proximal side end link members11ato13aand the connecting structure between the proximal side end link members11ato13aand the intermediate link members11cto13chave been described with particular reference toFIG. 13, the connecting structure between the distal end side link hub15and the distal side end link members11bto13band the connecting structure between the distal side end link members11bto13band the intermediate link members11cto13care understood as having the same structures as those described above.

As described above, the use of the structure in which bearings112and119are provided in the four revolute pair portions T1to T4in each of the link mechanisms11to13is effective to relieve the rotational resistance while the frictional resistance occurring in each of the revolute pair portions T1to T4is suppressed and, therefore, not only can a smooth power transmission be secured, but also the durability is increased.

In the structure in which the bearings112and119are provided, application of the preloads to the respective bearings112and119is effective to suppress the saccadic movement of the revolute pair portion T1to T4with the radial gap and the thrust gap having been eliminated, and also effective to eliminate the rotational phase difference between the proximal end side link hub14side and the distal end side link hub15side to allow the constant velocity property to be maintained and also to suppress an undesirable generation of vibrations and abnormal sounds. In particular, by rendering the bearing gap in the bearings112and119to be a negative gap, the backlash occurring between input and output can be minimized.

Because the bearing112is provided in the form as embedded in the proximal end side link hub14and the distal end side link hub15, the exterior shape of the proximal end side link hub14and the distal end side link hub15can be increased without the exterior shape of the link actuator main body2in its entirety being increased. For this reason, a mounting space can be easily secured for the proximal end side link hub14and the distal end side link hub15to be fitted to any other member.

Referring now toFIG. 8, the base bench52referred to previously is a vertically long member, and the proximal end side link hub14of the link actuator main body2is fixed on a top surface thereof. At an outer periphery of a top portion of the base bench52, a collar shaped actuator mounting stand55is provided, and the actuator3referred to previously is fitted to this actuator mounting stand55in a dependent form. The number of the actuators3is three which is the same as the number of the link mechanisms11to13. The actuator3is in the form of a rotary actuator and a bevel gear56mounted on an output shaft thereof and a sector shaped bevel gear57mounted on a shaft member113of the proximal end side link hub14are meshed with each other.

This link actuator1actuates the link actuator main body2when each of the actuators3is rotationally driven by manipulating an operating tool (not shown) provided in the control unit54. Specifically, when the actuator3is rotationally driven, the rotation thereof is transmitted to the shaft member113through the pair of the bevel gears56and57and the angle of the proximal side end link members11ato13arelative to the proximal end side link hub14changes. Accordingly, the position of the distal end side link hub15relative to the proximal end side link hub14is determined. Although in the instance now under discussion the angle of the proximal side end link members11ato13ahas been changed with the use of the bevel gears56and57, any other mechanism such as, for example, spur gears or warm gears may be employed.

The control unit54includes the control device4for controlling each of the actuators3and the position calculating device59for calculating the position (θ, φ) of the distal end side link hub15. The control device4and the position calculating device59are of a numerically controlled system by means of a computer. In the instance now under discussion, the control device4and the position calculating device59has been described as devices separate from each other, those devices58and59may be brought together to provide a single device.

The control device4referred to above, when the position of the distal end side link hub15is commanded from the operating tool, determined the rotational angle βn (n=1, 2, 3) of each of the proximal side end link members11ato13ain dependence on the position of the distal end side link hub15so commanded and then controls each of the actuator3so as to assume the rotational angle βn so determined. The rotational angle βn is a rotational angle of each of the proximal side end link members11ato13awhich corresponds to the position of the distal end side link hub15so commanded and is rendered to be, for example, an angle from a horizontal plane as shown inFIG. 8.

The rotational angle βn corresponding to the commanded distal end side link hub15is determined by means of the inverse transformation of the equation 1 so that the relationship expressed by the equation 1 is satisfied. The inverse transformation referred to above is defined as a transformation to calculate the rotational angle βn of the proximal side end link members11ato13afrom the bending angle θ and the pivot angle φ (FIG. 11). The bending angle θ and the pivot angle φ are in mutual relationship with the rotational angle βn, and it is possible to derive from one value to the other value.

(cos⁢⁢(γ/2)⁢cos⁢⁢ɛ⁢⁢0±sin⁢⁢α⁢⁢cos⁢⁢β⁢⁢nsin⁢⁢α⁢⁢sin⁢⁢β⁢⁢n)=(cos⁡(ϕ-δ⁢⁢n)-sin⁢⁢(ϕ-δ⁢⁢n)0sin⁡(ϕ-δ⁢⁢n)cos⁡(ϕ-δ⁢⁢n)0001)⁢(cos⁡(θ/2)0sin⁡(θ/2)010-sin⁡(θ/2)0cos⁡(θ/2))⁢(cos⁡(ϕ-δ⁢⁢n)sin⁡(ϕ-δ⁢⁢n)0-sin⁡(ϕ-δ⁢⁢n)cos⁡(ϕ-δ⁢⁢n)0001)⁢(cos⁡(γ/2)⁢cos⁢⁢ɛ⁢⁢ncos⁡(γ/2)⁢sin⁢⁢ɛ⁢⁢nsin⁡(γ/2))Equation⁢⁢1⁢ɛ0=±sin-1(sin2⁢α-sin2⁡(γ/2)cos2⁡(γ/2)).Equation⁢⁢2
It is to be noted that the 3×3 matrix on the right side of the equation 1 is a transformation matrix according Euler angle of (φ−δn), θ, −(φ−δn).

The circumferential phase ε0of the revolute pair portion T1of the link mechanism11forming the reference has two mutually different solutions depending on the direction of assemblage of the proximal side end link members11ato13arelative to the proximal end side link hub14. Accordingly, the positive or negative on the second line in the left side of the equation 1 and the positive or negative in the right side of the equation 2 are to be determined depending on the direction of assemblage of the proximal end side end links11ato13arelative to the proximal end side link hub14. When the direction of assemblage is rightward direction, “+” is assigned, and when the direction of assemblage is leftward direction, “−” is assigned. By way of example, if the proximal side end link members11ato13aare assembled in the leftward direction as is the case with the second embodiment shown inFIG. 8, the equations 1 and the equation 2 are defined as the following equations 3 and 4, respectively.

By controlling each of the actuators3so that the rotational angle βn so determined as hereinabove described can establish, the position (θ, φ) of the leading side link hub15attains the targeted position. Since in the equation 3 above, the function of the axis angle α of the end link member is not contained, if the axis angle α of the end link member of the link actuator1is substituted for the parameter α in the equation 3, the operation can be controlled even with the link actuator in which the axis angle α of the end link member is other than 90 degrees.

Also, when by means of the position calculating device59, the rotational angle βn of the current proximal side end link members11ato13ais inserted in the equation 3 above and the forward transformation is then performed, the position (θ, φ) of the current distal end side link hub15is calculated. Since the equation 3 above contains a function of the axis angle α of the end link member, substitution of the axis angle α of the end link member of the link actuator1for the parameter α in the equation 3 makes it possible to calculate the position (θ, φ) of the distal end side link hub15in the link actuator1in which the axis angle α of the end link member is other than 90 degrees.

FIG. 14illustrates a third embodiment which is directed to the system in which the link mechanisms11to13of the link actuator main body2are in a mirror image symmetry. This link actuator1is of such a design that the positional relationship between the proximal end side link hub14and the proximal side end link members11ato13aand the distal end side link hub15and the distal side end link members11bto13bare so positioned as to assume a mirror image symmetry with respect to the center line C of the intermediate link members11cto13c. Other structural features than those described above are identical with those shown inFIG. 8and employed in the practice of the second embodiment. Since even the third embodiment shown inFIG. 14, as is the case with the previously described first embodiment shown inFIG. 8, the proximal side end link members11ato13aare assembled in the leftward direction with respect to the proximal end side link hub14, it is possible to control the actuator3and calculate the position of the distal end side link hub15with the use of the relational equations 3 and 4 referred to hereinbefore.

FIGS. 15 and 16illustrate the link actuator1designed in accordance with a fourth embodiment. This link actuator1is of such a design that each of the link mechanisms11to13of the link actuator main body2is of a rotational symmetrical type and the proximal end side end link11ato13aare assembled in the right direction relative to the proximal end side link hub14. In the case of this link actuator1, the positive or negative on the second line in the left side of the equation 1 and the positive or negative in the right side of the equation 2 represent “+” and are defined by the following equations 5 and 6. Using those equations 5 and 6, it is possible to control the actuator3and calculate the position of the distal end side link hub15.

FIGS. 17 to 19illustrate a link actuator according to a fifth embodiment. This link actuator1is of such a design that as shown inFIG. 17, the proximal end side link hub14of the link actuator main body is disposed on a base bench62through a spacer64. The link actuator main body2is of such a design that the proximal side end link members11ato13aare assembled in the leftward direction relative to the proximal end side link hub14. For this reason, using the relational equations 3 and 4 discussed hereinbefore, the control of the actuator70as will be described later and the calculation of the position of the distal end side link hub15can be achieved.

As shown inFIGS. 18 and 19, the link actuator main body2is of such a design that the bearings131for rotatably supporting the end link members11ato13aand11bto13brelative to the proximal end side link hub14and the distal end side link hub15are rendered to be of an outer ring rotating type.

To describe, by way of example, the revolute pair defined by the proximal end side link hub14and the proximal side end link members11ato13a, a shaft portion132is formed at three circumferential locations of the proximal end side link hub14, an inner ring (not shown) of two bearings131are mounted on an outer periphery of the shaft portion132, and an outer ring (not shown) of the bearing131is mounted on an inner periphery of a communicating hole133formed in the proximal side end link members11ato13a. The bearing131is a ball bearing such as, for example, a deep groove ball bearing or an angular contact ball bearing and fixed in a condition with a predetermined preload amount applied by means of fastening of a nut134. The revolute pair defined by the distal end side link hub15and the distal side end link members11bto13bis also constructed identical with the above construction.

Also, a bearing136provided at a connection portion between the proximal side end link members11ato13aand the intermediate link members11cto13chas an outer ring (not shown), which is mounted on an inner periphery of a communicating hole137formed at a distal end of the proximal side end link members11ato13a, and also has an inner ring (not shown) which is mounted on an outer periphery of a shaft portion138that is integral with the intermediate link members11cto13c. This bearing136is a ball bearing such as, for example, a deep groove ball bearing or angular contact ball bearing and is fixed in a condition with a predetermined preload amount applied thereto by means of fastening of a nut139. The revolute pair defined by the distal side end link members11bto13band the intermediate link members11cto13cis also constructed identical with the construction described above.

In all of the three link mechanisms11to13of the link actuator main body2, an actuator70, which is operable to rotate the proximal side end link members11ato13ato change the distal end position arbitrarily, and a speed reducing mechanism71, which is operable to decelerate and transmit the amount of operation of the actuator70to the proximal side end link members11ato13a, are provided. The actuator70is in the form of a rotary actuator, specifically a servo motor equipped with a speed reducer70aand is fixed on the base bench62by means of a motor fixing member72. The speed reducing mechanism71is made up of a speed reducer70afor the actuator70and a gear type speed reducer73. In the description that follows, a spur gear is employed in the speed reducing mechanism71, but any other mechanism such as, for example, a bevel gear and/or a work mechanism may be employed.

The speed reducer73of the gear type is made up of a small gear76, which is connected with an output shaft70bof the actuator70through a coupling75so as to achieve a rotation transmission, and a large gear77, which is fixed to the proximal side end link member5and is meshed with the small gear76. In the example as shown, each of the small gear76and the large gear77is in the form of a spur gear, and the large gear is a sector gear having serrations formed in a peripheral surface of the sector shape. The large gear77has a pitch circle radius (radius of the pitch circle) greater than that of the small gear76, and the rotation of the output shaft70bof the actuator70is, after having been decelerated into rotation about the revolute pair center axis S1between the proximal end side link hub14and the proximal side end link members11ato13a, transmitted to the proximal side end link members11ato13a. The reduction gear ratio thereof is set to a value greater than 10.

The large gear77has the pitch circle radius so chosen as to be ½ of more of the arm length L of the proximal side end link members11ato13a. The arm length L referred to above is the distance from an axial direction center point P1of the revolute pair center axis S3between the proximal end side link hub14and the proximal side end link members11ato13ato a point P3, which is defined by projecting a axial center point P2on a revolute pair central axis S1formed between the proximal side end link members11ato13aand intermediate link members11cto13conto a plane passing across the axial direction center point P1in a direction perpendicular to the revolute pair center axis S3between the proximal end side link hub14and the proximal side end link members11ato13a. In the case of the embodiment now under discussion, the pitch circle radius of the large gear77is greater than the arm length L discussed above. For this reason, it is advantageous to secure a high speed reduction ratio.

The small gear76referred to above has shaft portions76bprotruding respectively from opposite sides of a threaded portion76ameshed with the large gear77, and those opposite shaft portions76bare rotatably supported on a rotary support member79, installed on the base bench62, through two bearings80, respectively. Each of the bearings80is a ball bearing such as, for example, a deep groove ball bearing or an angular contact ball bearing. Other than the ball bearing being arranged in a plurality of rows as shown, a roller bearing or a slide bearing may be used. A shim (not shown) is provided between each outer rings (not shown) of those two bearings80and, by fastening a nut81threaded onto the shaft portion76b, a preload is applied to the bearing80. The outer ring of the bearing80is press fitted into the rotary support member79.

In the case of the above described fifth embodiment, the large gear77is a member separate from the proximal side end link members11ato13aand is removably fitted to the proximal side end link members11ato13aby means of a connecting member82such as, for example, bolt. This large gear77may be integral with the proximal side end link members11ato13a.

The rotational axis center O1of the actuator70and the rotational axis center O2of the small gear76are so positioned as to be coaxial with each other. Those rotational axis centers O1and O2are rendered to be parallel to the revolute pair axis S3between the proximal end side link hub14and the proximal side end link members11ato13aand level with the height above the base bench62.

As shown inFIG. 17, the control unit54of the link actuator1also includes the control device4for controlling each of the actuators70and the position calculating device59for calculating the position (θ, φ) of the distal end side link hub15. The fifth embodiment is basically identical in structure with the previously described second embodiment shown inFIG. 2, although it differs therefrom in respect of the above described structural details, and, yet, in a manner similar to the previously described second embodiment, the proximal side end link members11ato13aare assembled in the left direction relative to the proximal end link hub14. For this reason, by the control device4and the position calculating device59, with the use of the previously discussed relational equations 3 and 4, the control of the actuator70and the calculation of the position of the leading side link hub15can be accomplished.

The foregoing link actuator1is of such a design that because the actuator70and the speed reducing mechanism71are provided in all of the three link mechanisms11to13, control can be accomplished so as to remove saccadic movement occurring in the link actuator main body2and the speed reducing mechanism71and, hence, not only is the positioning accuracy of the distal end side link hub15be improved, but also the high rigidity of the link actuator itself can be realized.

Also, the gear type speed reducer73of the speed reducing mechanism71is comprised of a combination of the small gear76and the large gear77and can obtain a reducing gear ratio equal to or than higher10. If the reducing gear ratio is high, the positioning resolution of the encoder becomes high and, therefore, the positioning resolution of the distal end side link hub increases. Also, a low output actuator70can be used. In this embodiment the actuator70equipped with the speed reducer70ais used, but if the reducing gear ratio of the gear type speed reducer73is high, the actuator70having no speed reducer equipped can be used and the actuator70can therefore be reduced in size.

With the pitch circle radius of the large gear77so chosen as to be ½ or more of the arm length L of the proximal side end link members11ato13a, the bending moment of the proximal side end link members11ato13aresulting from a distal end load becomes small. For this reason, not only is it unnecessary to increase the rigidity of the link actuator to a value higher than necessary, but also the weight of the proximal side end link members11ato13acan be reduced. By way of example, material for the proximal side end link members11ato13acan be changed from stainless steel (SUS) to aluminum. Also, since the pitch circle radius of the large gear77is relatively large, the surface pressure of the threaded portion of the large gear77can be reduced and the rigidity of the link actuator1becomes high.

Also, if the pitch circle radius of the large gear77is greater than ½ of the arm length referred to above, the large gear77comes to have a diameter sufficiently greater than the outer diameter of the bearing131which is installed in the revolute pair defined by the proximal end side link hub14and the proximal side end link members11ato13a, and, therefore, a space is available between the threaded portion of the large gear77and the bearing131and installation of the large gear77comes to be easy.

Particularly in the case of the fifth embodiment, since the pitch circle radius of the large gear77is greater than the arm length L as described above, the pitch circle radius of the large gear77comes to be further large and the previously described functions and effects come to eminently arise. In addition, it becomes possible when the small gear76is installed on an outer diametric side than the link mechanisms11to13. As a result, a space for installation of the small gear76can be easily obtained and the degree of freedom of designing increased. Yet, the interference between the small gear76and any other member will hardly occur and the range of movement of the link actuator1becomes large.

Since each of the small gear76and the large gear77is in the form of a spur gear, the manufacture thereof is easy and the transmission efficiency of rotation is high. Since the small gear76is supported by the bearing80at its axial opposite ends, the support rigidity of the small gear76is high. Accordingly, the angle retentive rigidity of the proximal side end link members11ato13aresulting from the distal end load becomes high, leading to the increase of the rigidity of the link actuator1and the positioning accuracy thereof. Also, since the rotational axis center O1of the actuator70, the rotational axis center O2of the small gear76and the revolute pair center axis S3between the proximal end link hub14and the proximal side end link members11ato13aall lie on the same plane, the overall balance is good and the assemblability is also good.

Since the large gear77is removable relative to the proximal side end link members11ato13a, the specification such as, for example, the reducing gear ratio of the gear type speed reducer73and the operating range of the distal end side link hub15relative to the proximal end side link hub14can be easily changed, resulting in the increase of the productivity of the link actuator1. In other words, the same link actuator1can be made applicable to various applications by merely changing the large gear77, and the maintenance is good. By way of example, in the event of occurrence of any trouble in the gear type speed reducer73, mere replacement of only the speed reducer73is sufficient to accommodate it.

Although in describing any one of the second to fifth embodiments, the axis angle α of the end link member has been shown and described as 90 degrees, the axis angle α of the end link member may be other than 90 degrees. By way of example, the link actuator main body2employed in the practice of a sixth embodiment shown inFIG. 20is of a rotational symmetrical type as is the case with the fifth embodiment shown in and is of a structure in which the proximal side end link member5is assembled in the left direction relative to the proximal end link hub2while the axis angle α of the end link member is rendered to be 45 degrees.

As discussed above, when the axis angle α of the end link member is chosen to be not greater than 90 degrees, the interior space inside each of the link mechanisms11to13can be set large. Accordingly, cables and any other component parts can be installed within the interior space. Also, even though the size of the link actuator is increased, each of the end link members11ato13aand11bto13bbecomes lightweight and a compact structure is accomplished and, hence, the link actuator in its entirety can be downsized.

The proximal end side and distal end side link hubs14and15of this link actuator main body2includes a disc portion92having a throughhole92adefined therein, a support member93fixed at three locations circumferentially of the disc portion92, and a shaft member94extending towards an outer diametric side while extending parallel from each of the support member93to the disc portion92. The support member93is fixed to the disc portion92by means of bolts or the like (not shown). The disc portion92of the proximal end side link hub14serves as a base for this link actuator91and various appliances or the like are fitted to the disc portion92of the leading side link hub15.

FIG. 21Aillustrates a sectional view showing the proximal end side link hub14of the link actuator1provided with the link actuator main body2of the structure shown in and described with particular reference toFIG. 20, the proximal side end link members11ato13aand the intermediate link members11cto13cin deployed form.FIG. 21Bis a fragmentary enlarged diagram ofFIG. 21A.

The shaft member94referred to previously is fixed to the support member93by means of, for example, a press fitting technique. And, one end of the end link members11ato13a(11bto13b) is pivotably connected with the shaft member94through two bearings131. The other end of the end link members11ato13a(11bto13b) is pivotably connected with a shaft member139of the intermediate link members11cto13cthrough two bearings136. The shaft member139is fixed to the intermediate link members11cto13cby means of, for example, a press fitting technique. The intermediate link members11cto13chas the shaft member139on its opposite ends, and the shaft member136on one end thereof is connected with the proximal side end link members11ato13awhile the shaft member139on other end thereof is connected with the distal side end link members11bto13b. The bearings131and136both referred to above are of an outer ring rotating type.

As shown inFIG. 21B, an inner ring (not shown) of the bearing131is mounted on the outer periphery of the shaft member94of the link hub14(15) and two spacers95and96disposed on this inner ring and on both sides thereof are fastened to a flange portion94aof the shaft member94by means of a nut97. Accordingly, in a condition in which the preload is applied to the bearing131, the end link members11ato13a(11bto13b) are pivotably connected with the intermediate link members11cto13c.

Also, an inner ring (not shown) of the bearing136is mounted on an outer periphery of the shaft member139of the intermediate link members11cto13c, and two spacers98and99disposed this inner ring and on opposite sides thereof are fastened to a flange portion139aof the shaft member139by means of a nut100. Accordingly in a condition in which the preload is applied to the bearing136, the end link members11ato13a(11bto13b) is pivotably connected with the intermediate link members11cto13c. Other structural features are the same as those employed in the fifth embodiment shown in and described with particular reference toFIGS. 17 to 19.

Regarding any one of the second to sixth embodiments of the present invention shown in and described with particular reference toFIG. 8toFIGS. 21A and 21b, the following is available which is of a construction that does not necessarily require the use of the “position change control unit” and the “relay position setting unit”.

The link actuator according to Mode 1 is of such a design that the distal end side link hub is connected with the proximal end side link hub through the three link mechanisms for alteration in position; each of the link mechanisms includes the proximal end side and distal side end link members, which are pivotably connected at one end with the proximal end side link hub and the distal end side link hub, respectively, and the intermediate link member having its opposite ends pivotably connected with the other ends of the proximal end side and distal side end link member; the connecting end axis of the intermediate link member, which is pivotably connected with the proximal side end link member, and the connecting end axis of the intermediate link member, which is pivotably connected with the distal side end link member cooperate with each other to form the angle γ therebetween; the connecting end axis of the intermediate link member, which is pivotably connected with the proximal end side and distal side end link members, and the connecting end axis of the proximal end side and distal end side link hubs, which are pivotably connected with the proximal end side and distal end side link members, cooperate with each other to form the angle α therebetween; each of the link mechanisms is of such a design that the geometric model of the link mechanism depicted by line represents such a shape as to form the symmetry between the proximal end side part and the distal end side part with respect to the center part of the intermediate link member; the actuator is provided in the two of the three link mechanisms for arbitrarily changing the position of the distal end side link hub relative to the proximal end side link hub; and the control device for controlling those actuators is provided.

The link actuator according to Mode 1 is of such a design that in the basic construction described above, assuming that the rotational angle of the proximal side end link member relative to the proximal end side link hub is expressed by βn (n=1, 2, 3, . . . ); the circumferential separating angle of each of the proximal side end link members relative to the proximal side end link member forming the reference is expressed by δn (n=1, 2, 3, . . . ); the vertical angle at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub is expressed by θ; the horizontal angle at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub is expressed by φ; the circumferential separating angle of each of the revolute pairs relative to the phase forming the reference in the circumference through which the revolute pair defined by the proximal side end link member and the intermediate link member passes is expressed by εn (n=1, 2, 3, . . . ); and the separating angle of the revolute pair, defined by the proximal side end link member forming the reference and the intermediate link member, during a condition in which the position of the distal end side link hub relative to the proximal end side link hub lies in the position of origin (θ=0, φ=0), is expressed by ε0, the control device is operable, so as to satisfy the following equations 1 and 2, to determine the desired rotational angle βn of the proximal side end link member from the targeted position (θ, φ) of the distal end side link hub relative to the proximal end side link hub by means of the inverse transformation of the equation 1 and, then, to control each of the actuators to satisfy the rotational angle βn so determined:

In Mode 1 discussed above, with respect to at least two of the three sets or more of the link mechanisms, if the rotational angle βn of the proximal side end link member is fixed, the position of the distal end side link hub relative to the proximal end side link hub is fixed correspondingly. Accordingly, when the actuator is provided in two or more sets of the three sets or more sets of the link mechanisms and those actuators are properly controlled, the position (θ, φ) of the distal end side link hub relative to the proximal end side link hub can be arbitrarily changed.

The link actuator according to Mode 2 is of such a design that in the basic construction described above, assuming that the rotational angle of the proximal side end link member relative to the proximal end side link hub is expressed by βn (n=1, 2, 3, . . . ); the circumferential separating angle of each of the proximal side end link members relative to the proximal side end link member forming the reference is expressed by δn (n=1, 2, 3, . . . ); the vertical angle at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub is expressed by θ; the horizontal angle at which the center axis of the distal end side link hub is inclined relative to the center axis of the proximal end side link hub is expressed by φ; the circumferential separating angle of each of the revolute pairs relative to the phase forming the reference in the circumference through which the revolute pair defined by the proximal side end link member and the intermediate link member passes is expressed by δn (n=1, 2, 3, . . . ); and the separating angle of the revolute pair, defined by the proximal side end link member forming the reference and the intermediate link member, while the position of the distal end side link hub relative to the proximal end side link hub lies in the position of origin (θ=0, φ=0) is expressed by ε0, the provision is made of the position calculating device for determining the position (θ, φ) of the distal end side link hub relative to the current proximal end side link hub from the rotational angle βn of the proximal side end link member by means of the inverse transformation of the equation 1:

In Mode 1 or Mode 2, the positive or negative on the second line in the left side of the equation 1 above and the positive or negative in the right side of the equation 2 above are recommended to fix depending on the direction of assembly of the proximal end side end link relative to the proximal end side link hub.

In Mode 1 or Mode 2, the axis angle α of the end link member is preferably chosen to be 90 degrees.

In Mode 1 or Mode 2, the axis angle α of the end link member may be not greater than 90 degrees.

REFERENCE NUMERALS