FIELD

The invention relates to kinematic structures suitable for being used in motion platforms, and in particular, to kinematic structures suitable for being used in motion platforms for simulating motions of an animal, such as a horse.

BACKGROUND

There is a long history of human-made mechanisms trying to replicate motions of an animal. Such mechanisms may be used for educational, recreational, or other purposes. Emulation of movements by a mechanism can be useful when a living animal cannot be used or use of a living animal would be ineffective, e.g. in a long working process in which living animal would be exhausted or a process where an animal could be put in danger. Practical examples are film making, using fake animal in a performance, or using the mechanism in simulator. For example, a mechanism emulating motions of a horse may be used as a part of the horse-riding simulator.

While it may be desirable to produce as realistic motion as possible, replicating all features of motion of an animal with a mechanical structure may be a very challenging task (or may be impossible in practice). Realistic simulation of motions of an animal may require high transient power (or large accelerations), for example. Therefore, some types of movements are typically simplified or omitted altogether. Thus, existing solutions typically do not produce motion that captures the movements of an animal in an authentic manner.

BRIEF DISCLOSURE An object of the present disclosure is to provide a kinematic structure and a motion platform utilizing the kinematic structure so as to alleviate the above disadvantages. The object of the disclosure is achieved by the kinematic structure which is characterized by what is stated in the independent claim. The preferred embodiments of the disclosure are disclosed in the dependent claims. In a kinematic structure according to the present disclosure, an end effector is positioned between upper ends of two opposing limb elements. The upper ends are connected to the end effector via spherical joints that define a roll axis for the end effector. Lower ends of said limb elements are provided with joints that limit translational motion of the end effector essentially to a vertical plane. The kinematic structure is further provided with a third limb element that dominates roll and pitch of the end effector. The upper end of the third limb element is connected to the end effector via a revolute joint while the lower end is connected to a slider controlling motion of the lower end. The revolute joint is arranged such that the motion of the lower end translates into rotational motion pitching the end effector. Alternatively, the spherical joint may be at the upper end and the revolute joint at the lower end. The kinematic structure is further provided with means for adjusting the roll of the end effector about the roll axis.

With the translational motion of the end effector in the vertical plane and with the pitch and roll of the end effector, the kinematic structure effectively has four degrees of freedom.

The kinematic structure allows implementations that can produce large accelerations and high velocities of the end effector. This can be crucial in achieving realistic simulation of motion. Further, the kinematic structure can be robustly implemented in an elongated form resembling form of a back of an animal, for example. BRIEF DESCRIPTION OF THE DRAWINGS

In the following the invention will be described in greater detail by means of preferred embodiments with reference to the attached drawings, in which

Figures la and lb show a simplified example of an idealized embodiment of a kinematic structure according to the present disclosure;

Figures 2a and 2b show an exemplary embodiment of a kinematic structure according to the present disclosure where the first and second motion planes are not coplanar;

Figure 3 shows an exemplary embodiment of a kinematic structure according to the present disclosure where the structure comprises a fifth limb element;

Figure 4a and 4b show embodiments with three limb elements where one limb provides combined functionalities; and

Figures 5a and 5b show aspects of an exemplary embodiment of a motion platform according to the present disclosure.

DETAILED DISCLOSURE

The present disclosure describes a kinematic structure for a 4D0F (four degrees of freedom) motion platform. The kinematic structure may be used to provide translational motion in a plane and rotational motions about two axes (a roll axis and a pitch axis). The kinematic structure comprises an end effector, a frame, and at least a first limb element, a second limb element, and a third limb element. In a motion platform, the kinematic structure may be oriented such that the end effector is positioned on top and is configured to receive a weight to be carried (e.g. the weight of a person), for example. The translational motion may be configured to occur in a vertical plane and the roll and pitch axes may be essentially horizontal.

In the kinematic structure, the first limb element and the second limb element are positioned on opposite sides of the end effector. Figures la and lb show a simplified example of an idealized embodiment of a kinematic structure according to the present disclosure. In the context of the present disclosure, the term “idealized” is intended to be understood as something that is in a form intended for achieving maximum efficiency. Figure la shows an isotropic view of the structure while Figure lb shows a top view of the same structure. Functionalities of the kinematic structure of Figures la and lb are discussed in relation to a global reference frame xyz on a ground plane on which the kinematic structure is fixed. In Figure la, the direction of the x axis points from a centre of a revolute joint 11.2 at the lower end of a first limb element 11 to a centre of a revolute joint 12.2 at the lower end of a first limb element 12. The z axis points upwards vertically while they axis is determined through the right-hand rule. The kinetic structure provides four DOF motions for the end effector, which are the two translational motions along x and z axes and two orientation (rotational) motions along x and y axes, respectively. The four DOF motions of end effector are independent to each other and can be realized (controlled) through the inverse kinematics of kinematic structure. In a kinematic structure according to the present disclosure, first ends of the first and second limb elements are connected to the end effector via joint elements that implement kinematic functionalities of spherical joints and define a roll axis for the end effector. In all examples described in the present disclosure, the end effector is positioned on top of the kinematic structure. In this kind of embodiments, the first ends are also the upper ends of the first and second limb elements. However, the use of a kinematic structure according to the present disclosure is not limited to specific orientations of the end effector. A kinematic structure according to the present disclosure may be used in any orientation. Therefore, terms like “upper end” and “lower end” should not be considered as something defining absolute relations e.g. in view of direction of gravity. Thus, term “upper end” can be replaced with a more generic term “first end” and term “lower end” replaced with “second end” in the context all embodiments of the kinematic structure according to the present disclosure. The second ends of the first and second limb elements are provided with joint elements implementing the functionalities of revolute joints that restrict motions of the first ends of the first and second limb elements to a first motion plane and a second motion plane. The planes are preferably parallel (or even coplanar). In the examples of the present disclosure, the planes are vertical and the second ends of the first and second limb elements are the lower ends of the said limb elements.

In Figure la, the first limb element 11 and the second limb element 12 are represented as simple constructs of cylinders. The first limb element 11 is connected to the frame through the revolute joint 11.2 and to the end effector 10 through a spherical joint 11.1. The second limb element 12 has an identical configuration to limb element 11. It is connected to the ground through the revolute joint 12.2 and to the end effector 10 through a spherical joint 12.1. The spherical joints 11.1 and 12.1 at the upper ends of the first and second limb elements 11 and 12 define a roll axis R for the end effector 10. Lengths of the first and second limb elements may be adjustable or positions of their second ends may be adjustable with respect to the frame. For example, in the embodiment of Figures la and lb, lengths of limbs 11 and 12 are adjustable. Limb 11 comprises a prismatic joint 11.3 allowing limb 11 to extend and contract along its length. Similarly, limb 12 can extend and contract actively because of a prismatic joint 12.3. Alternatively, positions of the revolute joints 11.2 and 12.2 atthe lower ends oflimbs 11 and 12 maybe adjustable. The revolute joints 11.2 and 12.2 may be connected to prismatic joint elements that allow their positions to be adjusted with respect to the frame in the direction of the roll axis R, for example. In this kind of approach, the first and second limb elements 11 and 12 may have nonadjustable lengths.

In a kinematic structure according to the present disclosure, a first end of the third limb element may be connected to the end effector via a joint element implementing kinematic functionalities of a revolute joint that dominates the roll and pitch of end effector 10. In Figures la and lb, the first end of limb 13is connected to the end effector 10 through a revolute joint 13.1.

In the context of the present disclosure, the term “dominating” means that the joint element at the first end of the third limb element has a major role in determining the roll and pitch of end effector.

On one hand, the angle between a revolute axis of the revolute joint 13.1 and the ground plane dominates the pitch of end effector 10. For this purpose, the position of the second end of the third limb element is adjustable with respect to the frame. The adjustment of the position of the second may occur in any direction, but the most useful and efficient adjustment is along the roll axis. Direction of the revolute axis of the revolute joint 13.1 at the first end of the third limb element 13 may be manipulated by moving the second end of the third limb element 13 and, as a result, the pitch of end effector changes. In Figures la and lb, the second end of the third limb 13 is connected to a slider arrangement comprising a guide 16 fixed to the ground and a prismatic joint in the form of a slider 16.1 that can move along the guide 16. The second end is connected to the prismatic joint 16.1 via a spherical joint 13.2 in the embodiment of Figures la and lb. As a result, the third limb 13 connects the slider arrangement to the end effector 10.

On the other hand, the (translational) position of the revolute joint 13.1 at the first end of the third limb element also has a major role in determining the roll of the end effector 10. For this purpose, length of the third limb element is adjustable. In Figures 1 and lb, the revolute joint 13.1 dominates the roll of the end effector 10 about the roll axis R. The third limb element 13 itself can extend and contract passively through a prismatic joint 13.3. The kinematic structure in Figures la and lb is further provided with a fourth limb element 14. The lower end of the fourth limb element 14 may be connected to the ground through a universal joint 14.2 and the upper end may be connected to the end effector 10 through a spherical joint 14.1. The fourth limb 14 can extend and contract through a prismatic joint 14.3. Limb element 14 may further comprise actuating means configured to actively extend or contract the prismatic joint 14.3. This causes the prismatic joint 13.3 of the third limb element 13 to also extend or contract. When the revolute joint 13.1 at the upper end of the third limb element 13 ascends or descends as a result of the extending or extracting of the prismatic joint 13.3, the roll of end effector 10 changes.

In Figures la and lb, the first motion plane of the first limb element and the second motion plane of the second limb element are essentially vertical planes during use and their normals are perpendicular to the roll axis, and the revolute axis Xi of the revolute joint 13.1 is parallel to the roll axis. The motion planes of the limb elements 11 and 12 lie in the same plane XZ in Figure la. Centre points of all joints of limb elements 11 and 12 are positioned on this plane. Revolute axes Yi and Y2 of revolute joints 11.2 and 12.2 are parallel and perpendicular to the roll axis R. The revolute axis Xi of revolute joint 13.1 is parallel to the guide 16 and to the roll axis R. With this kind of setup, a kinematic structure with high power efficiency can be achieved.

Although the embodiment presented in Figures la and lb has idealized parameters, a kinematic structure according to the present disclosure is not limited only to such parameters. Dimensions (or joint parameters) of a kinematic structure according to the present disclosure may vary due to the manufacturing, assembly and cost-effective considerations, and still produce desired motion features for a horse-riding simulator, for example. Axes of the revolute joints (11.2 and 12.2 in Figures la and lb) at the lower ends of the first and second limb elements do not have to be parallel with respect to each other and they do not have to be perpendicular to the roll axis. The first and second limb elements (or their joints) do not have to be in the same plane.

In theory, a kinematic structure according to the present disclosure can be implemented as long as a first motion plane and a second motion plane that have normals extending at least partially in a direction perpendicular to the roll axis (i.e. the normal has a nonzero component in the direction perpendicular to the roll axis). However, orientation of the motion planes with respect to the roll axis influences power efficiency. Thus, the first and second planes preferably have normals extending mostly in a direction perpendicular to the roll axis (i.e. for, each normal, the component of the normal in the direction perpendicular to the roll axis being larger than any other component of the normal). For example, the first and second motion planes may be essentially vertical planes during use and their normals maybe at angle of 75 to 105 degrees with respect to the roll axis and may have an angle of less than 30 degrees between each other. At the same time, the revolute axis of the joint element at the first end of the third limb element preferably extends mostly in the direction of the of the roll axis. For example, the revolute axis of said joint element and the roll axis preferably have an angle of less than 30 degrees therebetween.

Figures 2a and 2b show an exemplary embodiment of a kinematic structure according to the present disclosure where the first and second motion planes are not coplanar. Figure 2a shows an isotropic view of the structure while Figure 2b shows a top view of the same structure. The kinematic structure in Figures 2a and 2b comprises an end effector 20, a first limb element 21, a second limb element 22, a third limb element 23, and a fourth limb element 24 which may be similar to the corresponding limb elements in the example of Figures la and lb. However, as Figure 2b shows, the first and second limb elements 21 and 22 are not in the same plane.

In this embodiment, the end effector 20 does not only provide four independent DOF motions as the idealized mode does, but also generates two more parasitic DOF of motions, of which one being a slight rotation around z axis, and the other being a slight translation along y axis. However, in some horse gaits, these two DOF motions also present, which means this variant makes the platform motions even closer to a realistic horse-riding motion.

A kinematic structure according to the present disclosure is not limited to four limb elements as discussed in the embodiments of Figures la and lb and Figures 2a and 2b. For example, in some embodiments, additional, redundant limb elements may be used. The kinematic structure may further comprise a fifth limb element connected to the end effector via a joint element acting as a spherical joint and to the frame via a universal joint, for example. Figure 3 shows an exemplary embodiment of a kinematic structure according to the present disclosure where the structure comprises a fifth limb element. In Figure 3, the kinematic structure comprises a first limb element 31, a second limb element 32, a third limb element 33, and a fourth limb element 34 which may be similar to the corresponding limb elements in the earlier examples. In addition, the kinematic structure comprises a fifth limb element 35. The fifth limb element 35 may be identical to the fourth limb element 34 regarding its joints and connections. Both limbs 34 and 35 may comprise means for adjusting their lengths and they both may thus contribute to the same DOF motion but provide more power to the simulator in this way. The third limb element 33 and a slider assembly 36 at its second end may be positioned in the centre of the kinematic structure between the fourth and fifth limb elements.

Alternatively, in other embodiments, functionalities of separate limb elements may be produced in one limb element. Figure 4a and 4b show embodiments with three limb elements where one limb provides combined functionalities. In Figure 4a, the kinematic structure comprises an end effector 40, a first limb element 41a, a second limb element 42a, a third limb element 43, and a prismatic joint assembly 46 for adjusting the position of the second end of the third limb element 43. A fourth limb element as presented in the previous examples is not needed because the third limb element 43 comprises means for actively adjusting its length. Thus, the third limb element 43 incorporates the function of the fourth limb element in the previous examples.

The embodiment of Figure 4b is similar to the embodiment of Figure 4a. For example, the end effector 40, the third limb element 43 and the prismatic joint assembly 46 may be similar to or (the same as) the corresponding limb elements in Figure 4a. However, instead of having the second ends of the first and second limb element fixed a frame via revolute joints and adjusting the lengths of the first and second limb element, the positions of the second ends of the first and second limb elements 41b and 42b are adjusted in Figure 4b. For this purpose, the kinematic structure may be provided with prismatic joint assemblies 47 and 48 that allow positions of the second ends of the first and second limb elements 41b and 42b to be adjusted in a horizontal direction (along an x axis defined in the same manner as in Figure la and lb). The second ends of limb elements 41b and 42b may connect to the prismatic joint assemblies 47 and 48 via the revolute joints at the second ends. In a further variant of the embodiments of Figures 4a and 4b, the kinematic structure may further comprise a fourth limb element that acts as a redundant actuator providing extra force. In contrast to the embodiment of Figures la and lb, the third and fourth limb element both may comprise actuator means for adjusting their lengths. Thus, from the control point of view, this variant of the kinematic structure differs from the embodiment of Figures la and lb since both of said limb elements take part in performing the same function.

In addition to the variations discussed in relation to the embodiments above, the kinematic structure according to the present disclosure also allows many other variations. For example, the revolute axis of the revolute joint (13.1 in Figures la and lb) at the upper end of the third limb element and a length axis of the guide (16 in Figures la and lb) do not have to be parallel. It is also not necessary for the guide 16 to be parallel to the ground. In some embodiment, the centre of the revolute joint (13.2 in Figures la and lb) at the second end of the third limb element may coincide with the centre of the prismatic joint (13.3 in Figures la and lb) of the guide. As regards the joints (joints 11.2, 12.2, 13.2, and 14.2 in Figures la and lb) at the second ends of the limb elements of a kinematic structure according to the present disclosure, it is not necessary that they are positioned on the same plane. They can be on the locations that are at different height with respect to the ground plane. Further, embodiments of the kinematic structure according to the present disclosure are not limited only to the exemplary joint elements as described in the embodiments above. The mechanical implementation of each joint element may vary depending on application. For example, all the spherical joints in the invention can be realized through the combination of a universal joint with an extra revolute joint. In addition, it is not necessary for the shape of the end effector shape to be symmetric or quadrilateral.

The locations of the joint elements at the upper ends of the third limb element and possible further limb elements may also be freely selected, as long as the limb element (or elements) intended to cause the end effector to roll is connected to the end effector at a (non-zero) distance from the roll axis. In variants with like presented in Figures 4a and 4b, this means that the third limb 43 is connected to the end effector 40 at a distance from the roll axis R. In variants with more than three legs, such as in Figures la and lb, the fourth limb element 14 (and fifth limb element, if present) may be connected to the end effector 10 at a distance from the roll axis R.

So far, a kinematic structure according to the present disclosure has been discussed mostly in view of configurations of its limbs and joints. In the following, however, the kinematic structure is discussed in relation to 4D0F motion platforms utilizing said kinematic structure. A 4D0F motion platform according to the present disclosure comprises a kinematic structure according to present disclosure. Further, the motion platform comprises means for actuating the limb elements. These means may take the form of prismatic actuators, for example. In the motion platforms, the prismatic actuators may be used for adjusting the length of a limb element or for adjusting the position of the second end of a limb element.

In some embodiments, the revolute joints at the lower ends of the first and second limb elements are fixed to the frame and the lengths of the first and second limb elements are adjustable, and the motion platform comprises a first prismatic actuator and a second prismatic actuator configured to adjust the lengths of the first and second limb elements. A third prismatic actuator may be configured to extend in a direction crossing the roll axis, at a distance from the roll axis. In order to maximize efficiency, the third prismatic actuator is preferably configured to extend mostly or only in a direction perpendicular to the roll axis during use. For example, the third prismatic actuator may be configured to adjust the length of the third limb element, thereby causing the end effector to roll about the roll axis. A fourth prismatic actuator may be configured to adjust the position of the second end of the third limb element, thereby causing the end effector to pitch about an axis perpendicular to the roll axis.

Figures 5a and 5b show an exemplary embodiment of this kind of motion platform. In Figure 5a, the motion platform comprises and end effector 50, a first limb element 51, a second limb element 52, and a third limb element 53, a horizontal slider arrangement 56, and a frame 59. The kinematic structure may be similar to the embodiment of Figure 4a, for example.

Joint elements 51.1 and 52.1 implement functionalities of spherical joints atthe upper ends of limb elements 51 and 52 connect said limb elements to the end effector 50. The joint elements 51.1 and 52.1 define a roll axis R for the end effector 50.

The motion platform further comprises joint elements 51.2 and 52.2 implementing functionalities of revolute joints atthe lower ends of the of the first and second limb elements 51 and 52. In Figure 5a, the joints 51.2 and 52.2 are fixed to the frame 59 and the lengths of the first and second limb elements 51 and 52 may be adjustable.

The first and second limb elements 51 and 52 further comprise prismatic joints 51.3 and 52.3 allowing the limb elements to extract and contract lengthwise. Each limb may comprise one or more sliders implementing the functionality of a prismatic joint, for example. In Figure 5a, an arrangement of a pair of parallel slider rail assemblies act as a prismatic joint. Further, a first and second prismatic actuators 51.4 and 52.4 are configured to adjust the lengths of the first and second limb elements 51 and 52. Prismatic actuators may be very vulnerable to side loads and it may therefore be preferable to avoid such loads. In theory, the prismatic joint or joints may take all the side load. However, the prismatic joints are not completely rigid in practice. They may bend under the load, and thus some side force could be induced to the actuator. As a result, it may be preferable to take further steps to avoid the side loads. This may be accomplished with a joint arrangement as described in Figure 5b, for example.

In Figure 5b, a prismatic actuator 51.4 is coupled with at least one prismatic joint 51.3 via a spherical joint 51.5 and a universal joint 51.6. One part of the prismatic joint 51.4 may be connected to one end of the actuator 51.4 via the spherical joint 51.5 (that has three rotational DOF). Another part of the prismatic joint 51.3 may be connected to the other end of the prismatic actuator 51.4 via the universal joint 51.6 (that has two rotational DOF). It does not matter from which end of the actuator spherical joint and universal joints are connected.

In the above-discussed joint arrangement, the prismatic joint or joints 51.3, together with the spherical joint 51.5 and the universal joint 51.6, encapsulate prismatic actuator 51.4. The actuator 51.4 can move freely sideways without taking any side loads.

The arrangement of Figure 5b may used for any prismatic actuator of a motion platform according to the present disclosure. For example, in Figure 5a, limbs 51, 52, and 53 have this kind of encapsulation. While the joint arrangement has been discussed mainly in relation to the embodiment of Figures 5a and 5b, it can also be applied to any other variant of a kinematic structure and a motion platform according to the present disclosure. In Figure 5, a third limb element 53 is provided with prismatic joints in the form of sliders. The third limb element 53 further comprises a third prismatic actuator 53.4 configured to adjust the length of the third limb element 53 in a direction perpendicular to the roll axis R. Because the third limb element 53 is connected at a distance from the roll axis R, the extension or contraction of the third limb element 53 caused by the third actuator 53.4 results in the end effector 50 to roll about the roll axis R. In addition, the motion platform in Figure 5a comprises a fourth prismatic actuator assembly 56 that is configured to adjust the position of the second end of the third limb element 53, thereby causing the end effector 50 to pitch about an axis perpendicular to the roll axis R. A separate fourth limb as a presented in the idealized model of Figures la and lb is not needed, since the horizontal prismatic actuator assembly 56 and the prismatic actuator 53.4 in the third limb element 53 dominate the pitch and roll of the end effector.

While the embodiment of Figure 5 describes a variant of a motion platform having actuators adjusting the lengths of the first and second limb elements and a third limb element with combined functionalities, motion platforms with adjustable-length first and second limb elements can also be based on all other above-discussed embodiments of a kinematic structure according to the present disclosure.

For example, the motion platform may further comprise a fourth limb element (corresponding to the limb element 14 in Figures la and lb, limb element 24 in Figures 2a and 2b, or limb element 34 in Figures 3a and 3b, for example). The fourth limb element may be connected to the end effector via a joint element acting as a spherical joint and to the frame via a universal joint, and the third prismatic actuator may be configured to adjust the length of the fourth limb element.

Further, the kinematic structure may even comprise a redundant fifth limb element (corresponding to the fifth limb element 35 in Figure 3, for example). This fifth limb element may be connected to the end effector via a joint element acting as a spherical joint and to the frame via a universal joint. The motion platform may further comprise a fifth prismatic actuator that is configured to adjust the length of the fifth limb element. Thus, the fourth and fifth prismatic actuator may be configured to adjust the lengths of the fourth and fifth limb element. In this manner, the third and fifth limb element both contribute to the same DOF motion (roll of the end effector) but provides more power to the simulator in this way.

Alternatively, in other embodiments of a motion platform according to the present disclosure, the joint elements at the lower ends of the first and second limb elements may be connected to prismatic joint elements allowing the positions of their second of the first and second limb elements to be adjusted with respect to the frame in the direction parallel to the roll axis. The kinematic structure of the motion platform may be similar to that presented in Figure 4b, for example. The motion platform may comprise a first and second prismatic actuators configured to adjust the positions of the second ends of the first and second limb elements. A third prismatic actuator connected to the end effector at a (non-zero) distance from the roll axis, the third prismatic actuator being configured to extend in a direction perpendicular to the roll axis, thereby causing the end effector to roll about the roll axis. A fourth prismatic actuator may be configured to adjust the position of the second end of the third limb element, thereby causing the end effector to pitch about an axis perpendicular to the roll axis. While adjustment of positions of the first and second limb element has been discussed in relation of the exemplary kinematic structure of Figure 4b, this functionality can be used in all variations of the kinematic structure and the motion platform according to the present disclosure.

While the above embodiments discuss the third limb element having a revolute joint at its first end and a spherical joint at its second end, the kinematic structure and the motion platform according to the present disclosure can alternatively be implemented with the third limb element having a spherical joint at its first end and a revolute joint at its second end. In other words, the spherical joint and the revolute joint may switch places at the ends of the third limb element. For example, in the embodiment of Figures la and lb, the joint 13.1 at the first end of the third member 13 may be a spherical joint and the joint 13.2 may be a revolute joint. The revolute joint may have a revolute axis parallel to the roll axis R of the end effector 10 (and to the x axis) in Figures la and lb. The third limb element 13 dominates roll and pitch of the end effector also in this alternative configuration of the joints of the third limb element. Because joint 13.2 at the second end of the third limb element 13 is a revolute joint in the alternative configuration, the third limb element 13 remains always perpendicular to the direction of translation of the slider 16.1 along the guide 16. When the slider 16.1 is moved, both ends of the third limb element 13 move by the same amount along the x axis because of the revolute joint at the second end restricts the motion of the first end. As a result, the end effector 10 also moves along the x axis when the slider 16.1 moves, causing the end effector 10 to pitch as it bucks against one of the first and second limb elements while at the same time pulling away from the other. In the alternative configuration, the angle between the roll axis R of the end effector 10 and the third prismatic actuator (that causes the end effector 10 to roll about the roll axis R ) can change during use. The kinematic structure may be configured to keep the third prismatic actuator extending in a direction crossing the roll axis R at any point during use. In order to maximize efficiency, the third prismatic actuator is preferably configured to extend mostly in a direction perpendicular to the roll axis R during use.

While the above discussion on the alternative configuration describes a revolute joint that is parallel to the roll axis, other implementations are also possible. For example, a revolute axis of the joint element at the second end of acting as the revolute joint in the third limb element and the roll axis may have an angle of less than 30 degrees therebetween. Further, while the alternative configuration of the joints of the third limb element has been explained in relation to the embodiment of Figures la and lb, it can be applied to all above-discussed embodiments of the kinematic structure and motion platform according to the present disclosure, including the embodiments of Figures 2a to 5b.

The above-discussed kinematic structure and motion platform and their variants can be used for various purposes. A motion platform according to the present disclosure can be implemented as a compact structure making it easily utilizable in various simulation applications. For example, a motion platform utilizing the kinematic structure may be used to form a horse-riding simulator platform that gives the equestrian (or the rider) the same riding experience compared to a real horse but without any environmental and horse physical limitations. The simulator platform may comprise a 4D0F motion platform according to the present disclosure, a cover structure covering the kinematic structure of the motion platform, wherein the cover structure emulates the shape of a back of a horse, and a saddle attached to the cover structure and/or the end effector, for example. This kind of simulator platform can be used to output the realistic saddle movement of a horse (or the kind of four-legged mammals). Regarding the different horse gaits, the invention outputs the same riding features

(or experience) of that gait by generating the same accelerations of the saddle.

The specific kinematic design makes the output motion of the invented platform programmable with respect to the required motions, which means the application of the invention is not only limited to certain motion patterns of a specific horse but can be used to replicate any back motions of a horse. The special parallel robotic design allows the platform to output the transient power (or accelerations) close to a real horse does, which is critical to a realistic experience (or the fidelity) of a horse-riding simulator and is not achieved by any horse-back riding simulator in the market yet. With a motion platform according to the present disclosure, accelerations up to 10 g can be achieved, for example. The use of motion platforms according to the present disclosure is not limited only to simulation of saddle movements of a horse (or the kind of four legged mammals). The platforms may be used for simulating other things, such as motions of motorcycle, for example. A simulator platform may comprise a 4D0F motion platform according to the present disclosure, a cover structure covering the kinematic structure of the motion platform, wherein the cover structure emulates the shape of a motorcycle, and a saddle attached to the cover structure and/or the end effector.

It is obvious to a person skilled in the art that the kinematic structure and the motion platform can be implemented in various ways. The invention and its embodiments are not limited to the examples described above but may vary within the scope of the claims.