An actuator based on magnetic shape memory material

Abstract

An actuator comprises a toothed rack (101) and a body element (102) such that the toothed rack and the body element are moveable with respect to each other The actuator comprises tooth plates (104-107) moveably supported with respect to the body element. Each tooth plate is moveable back and forth towards and away from the toothed rack. The actuator comprises magnetic shape memory elements (108-111) between the body element and the tooth plates, and coils (112-115) for directing a magnetic field to each magnetic shape memory element to change its length (L108). The toothed rack and / or the tooth plates have oblique tooth surfaces so that forces directed by the tooth plates to the toothed rack cause forces for moving the toothed rack and the body element with respect to each other. A motion range of the actuator is not limited by properties of the magnetic shape memory elements.

Description

[0001] An actuator based on magnetic shape memory material

[0002] Field

[0003] The invention relates to an actuator based on magnetic shape memory “MSM” material. The actuator can be a rotary actuator or a linear actuator having a straight or curved motion path.

[0004] Background

[0005] The exceptional properties of magnetic shape memory “MSM” materials have driven interest in their application for actuators. MSM materials exhibit high theoretical acceleration, strain ranging from 6 to 12 percent, high power density, and other beneficial characteristics. These features enable the use of MSM material in miniature devices, including micro-positioning systems and robotic applications.

[0006] At present, numerous actuators utilizing MSM exploit the linear deformation of MSM elements. In these designs, the MSM elements are firmly attached to the endeffectors of the actuators. Various enhancements to this approach have been proposed over the years. For example, the publication J.Y. Gauthier, A. Hubert, J. Abadie, C. Lexcellent, and N. Chaillet, Multistable actuator based on magnetic shape memory alloy, in Proc. 10thInt. Conf. New Actuators, vol. 1 , Jun. 2006, pp.787-790 introduced a push-push design and a multi-stability feature.

[0007] An inherent challenge related to actuators where MSM elements are rigidly connected to end-effectors of the actuators is that a motion range of the end-effector is typically very short, often just a few millimeters or even less than one millimeter. Furthermore, an external force reduces the available motion range; and the magnetic field-induced stress in MSM materials is relatively low, what results in actuators’ limited force output. Moreover, the majority of MSM actuators primarily produce linear motion, although, there is a demand for rotary actuators too. Publication US20070289301 describes torque actuators based on MSM materials. The torque actuator described in US20070289301 has however a limited motion range and does not allow to make a full turn. Summary

[0008] The following presents a simplified summary to provide basic understanding of some aspects of various invention embodiments. The summary is not an extensive overview of the invention. It is neither intended to identify key or critical elements of the invention nor to delineate the scope of the invention. The following summary merely presents some concepts of the invention in a simplified form as a prelude to a more detailed description of exemplifying embodiments.

[0009] In this document, the word “geometric” when used as a prefix means a geometric concept that is not necessarily a part of any physical object. The geometric concept can be for example a geometric point, a straight or curved geometric line, a geometric plane, a non-planar geometric surface, a geometric space, or any other geometric entity that is zero, one, two, or three dimensional.

[0010] In accordance with the invention, there is provided a new actuator based on magnetic shape memory “MSM” material. The actuator can be a rotary actuator or a linear actuator having a straight or curved motion path.

[0011] An actuator according to the invention comprises:

[0012] - a toothed rack, and

[0013] - a body element mechanically supported with respect to the toothed rack so that the toothed rack and the body element are moveable with respect to each other,

[0014] - tooth plates moveably supported with respect to the body element so that each of the tooth plates is moveable back and forth towards the toothed rack and away from the toothed rack,

[0015] - magnetic shape memory elements whose first ends are attached to the body element and second ends are attached to the tooth plates, and

[0016] - coils configured to direct a magnetic field to each of the magnetic shape memory elements to change a length between the first and second ends of the magnetic shape memory element and thereby to move the tooth plate attached to the magnetic shape memory element.

[0017] The toothed rack and / or the tooth plates has / have oblique tooth surfaces so that a force directed by each tooth plate to the toothed rack, when the tooth plate has a mechanical contact with the toothed rack and is being moved towards the toothed rack, causes a force in a direction in which teeth of the toothed rack are consecutive to each other to move the toothed rack and the body element with respect to each other.

[0018] In a case of a linear actuator, a motion range of an actuator according to an exemplifying and non-limiting embodiment is limited by the length of the toothed rack but not by a motion range of the MSM elements. In a case of a rotary actuator, the number of rotations in an actuator according to an exemplifying and non-limiting embodiment is unlimited.

[0019] A force transfer ratio between each MSM element and the toothed rack can be adapted by selecting the obliqueness of the tooth surfaces of the toothed rack and / or the tooth plates in a suitable way - this is analogous to selecting a thread pitch of a threaded rod to adjust a relationship between a linear force and a torque. The total force producible by an actuator according to an exemplifying and non-limiting embodiment can be increased by increasing the number of the MSM elements and the respective tooth plates.

[0020] Exemplifying and non-limiting embodiments are described in accompanied dependent claims.

[0021] Various exemplifying and non-limiting embodiments both as to constructions and to methods of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific exemplifying and nonlimiting embodiments when read in conjunction with the accompanying drawings.

[0022] The verbs “to comprise” and “to include” are used in this document as open limitations that neither exclude nor require the existence of unrecited features. The features recited in dependent claims are mutually freely combinable unless otherwise explicitly stated.

[0023] Furthermore, it is to be understood that the use of “a” or “an”, i.e. a singular form, throughout this document does not exclude a plurality.

[0024] Brief description of the figures

[0025] Exemplifying and non-limiting embodiments and their advantages are explained in greater detail below in the sense of examples and with reference to the accompanying drawings, in which: figures 1 a, 1 b, and 1 c illustrate a linear actuator according to an exemplifying and non-limiting embodiment, figures 2a, 2b, and 2c illustrate rotary actuators according to exemplifying and nonlimiting embodiments, figure 3 illustrates a linear actuator according to an exemplifying and non-limiting embodiment, figure 4 illustrates a linear actuator according to an exemplifying and non-limiting embodiment, figure 5 illustrates a linear actuator according to an exemplifying and non-limiting embodiment, and figure 6 illustrates details of an actuator according to an exemplifying and nonlimiting embodiment.

[0026] Description of exemplifying and non-limiting embodiments

[0027] The specific examples provided in the description below should not be construed as limiting the scope and / or the applicability of the invention. Lists and groups of examples provided in the description are not exhaustive unless otherwise explicitly stated. Figure 1a illustrates schematically an actuator according to an exemplifying and non-limiting embodiment. The actuator comprises a body element 102 and a toothed rack 101 that is mechanically supported with respect to the body element 102 so that the toothed rack 101 and the body element 102 are moveable with respect to each other. In this exemplifying case, the actuator is a linear actuator so that the toothed rack 101 and the body element 102 are moveable with respect to each other in the positive and negative x-directions of a coordinate system 199 and teeth of the toothed rack 101 are consecutive to each other in the x-direction of the coordinate system 199. Mechanical structures for supporting the toothed rack 101 and the body element 102 with respect to each other are not shown in figure 1 a. In an exemplifying case, the body element 102 can be attached to fixed structures and the toothed rack 101 can be attached to a moveable part that is linearly moved by the actuator.

[0028] The actuator comprises tooth plates 104, 105, 106, and 107 each of which is moveably supported with respect to the body element 102 so that each of the tooth plates is moveable back and forth towards the toothed rack 101 and away from the toothed rack 101 , i.e. each of the tooth plates is moveable back and forth in the positive and negative z-directions of the coordinate system 199. In this exemplifying case, each of the tooth plates 104-107 has six teeth so that a tooth-pitch of each tooth plate is the same as a tooth-pitch of the toothed rack 101 . The number of teeth in each tooth plate can be as well 1 , 2, 3, 4, 5, or greater than 6.

[0029] The actuator comprises magnetic shape memory “MSM” elements 108, 109, 110, and 111 whose first ends are attached to the body element 102 and second ends are attached to the tooth plates 104-107. The MSM elements may comprise for example alloy of nickel, manganese, and gallium Ni-Mn-Ga, or some other suitable MSM material. The actuator comprises coils 112, 1 13, 114, and 1 15 configured to direct a magnetic field to each of the magnetic shape memory elements 108-111 to change a length between the first and second ends of the magnetic shape memory element and thereby to move the respective tooth plate attached to the magnetic shape memory element. In figure 1 a, the length between the first and second ends of the magnetic shape memory element 108 is denoted as L s. Figure 1 b shows details of the toothed rack 101 and the tooth plate 104 in an exemplifying situation where the tooth plate 104 has a mechanical contact with the toothed rack 101 and is being moved towards the toothed rack 101 in the positive z-direction of the coordinate system 199. In this exemplifying case, both the toothed rack 101 and the tooth plate 104 have oblique tooth surfaces so that a force Fin directed by the tooth plate 104 to the toothed rack 101 in the positive z-direction of the coordinate system 199 causes a force Fout directed to the toothed rack 101 in the negative x-direction of the coordinate system 199 to move the toothed rack 101 in the negative x-direction of the coordinate system 199. The force Fout can be estimated based on the force Fin and an angle cp using e.g. the virtual work balancing principle. The work done by the force Fin on a displacement of Az of the tooth plate 104 is FinAz, and correspondingly the work done by the force Fout on a displacement of Ax of the toothed rack 101 is F0UtAx. Thus, Fout = Fin Az / Ax = Fin I tan(cp) = Fin cot(cp). Thus, the force transfer ratio Fout / Finbetween each MSM element and the toothed rack 101 can be adapted by selecting the obliqueness of the tooth surfaces of the toothed rack 101 and / or of the tooth plates 104-107 in a suitable way, i.e. by selecting the angle cp in a suitable way.

[0030] In the exemplifying actuator illustrated in figures 1 a and 1 b, the teeth of the toothed rack 101 and the teeth of the tooth plates 104-107 have a trapezoidal profile with rounded corners. The trapezoidal tooth profile is also shown in figure 1 c, where the radius of curvature of the rounding is denoted as R. This tooth profile maintains a substantially constant force transfer ratio Fout / Fin and is easy to manufacture. It is however also possible to use different tooth profiles. Figure 6 illustrates details of an actuator according to an exemplifying and non-limiting embodiment where teeth of a toothed rack 601 and teeth of a tooth plate 604 have a triangular profile. Thus, the invention is not limited to any specific tooth profiles.

[0031] In the exemplifying actuator illustrated in figures 1a and 1 b, the number of the MSM elements is four and correspondingly the number of the tooth plates is four, too. Since the number of MSM elements installed on a single actuator does not have an upper limit, it is possible that several tooth plates can be engaged with the toothed rack at the same time. The forces generated by the engaged tooth plates is summed up into the total output force. The number of simultaneously engaged tooth plates, which will be called as contact ratio CR, can be found in the following way with reference to figure 1 c, where tb is a projected length of the tooth oblique surface, tais a projected length of the tooth flat surface, and h is a tooth height such that tb = h x tan(cp). The tooth height h depends on the maximum MSM element extension and the tooth height h must be less that the maximum MSM extension, otherwise the teeth will block the motion of the toothed rack. Typically, h = MSM max extension - a safety margin. The above-mentioned contact ratio CR, i.e. the number of simultaneously engaged tooth plates, is:

[0032] CR = N / (2ta / tb+ 2), (1 ) where N is the number of the MSM elements i.e. the number of the tooth plates. To maximize the contact ratio CR and thereby the force output, tais advantageously close to zero. In this exemplifying case, the maximum possible contact ratio is N / 2. To obtain motion, the contact ratio CR value is advantageously greater than 1 . Thus, the number of MSM elements for this type of actuators is advantageously at least 3.

[0033] In the exemplifying situation shown in figure 1 a, the coils 112-115 of the actuator are connected to a driver 116 configured to supply electric currents to the coils in accordance with control signals generated by a controller 117. In the exemplifying actuator illustrated in figure 1 a, a motion of the toothed rack 101 in the negative x- direction of the coordinate system 199 can be achieved by moving the tooth plates 104-107 towards the toothed rack 101 and then back in the following order: tooth plate 104 - tooth plate 107 - tooth plate 106 - tooth plate 105, and then repeating this cycle as long as the toothed rack 101 is wanted to be moved in the negative x- direction of the coordinate system 199. Motion in the reverse direction, i.e. the positive x-direction of the coordinate system 199, can be achieved by reversing the actuation order of the tooth plates 104-107. During one cycle of successive actuations of the tooth plates 104-107, the toothed rack 101 passes typically a distance equal to one tooth-pitch. Therefore, a single engaged tooth plate will push the toothed rack 101 by a distance P / N, where P is the tooth-pitch N is the number of tooth plates in the actuator. A distance D between two successively actuated tooth plates can be described by the following formula: D = P / N + nP, (2) where n is an integer.

[0034] An average speed v of the toothed rack 101 with respect to the body element 102 can be expressed as: v = f P, (3) where is f the operating frequency of the tooth plates, i.e. the operating frequency of the MSM elements.

[0035] The controller 117 shown in figure 1a can be implemented with one or more processor circuits, each of which can be a programmable processor circuit provided with appropriate software, a dedicated hardware processor such as an application specific integrated circuit “ASIC”, or a configurable hardware processor such as a field programmable gate array “FPGA”. Furthermore, the controller 117 may comprise one or more memory devices such as one or more random-access memory “RAM” devices.

[0036] Figures 2a, 2b, and 2c illustrate actuators according to exemplifying and non-limiting embodiments. The exemplifying actuators illustrated in figures 2a-2c are rotary actuators where the toothed rack constitutes a ring and a geometric axis of rotation is a geometric center axis of the ring. In figures 2a-2c, the geometric center axes are parallel to the z-axes of coordinate systems 299a, 299b, and 299c, respectively. For the sake of illustration clarity, the body elements supporting the tooth plates and the MSM elements are not shown in figures 2a-2c. Furthermore, the coils for directing magnetic fields to the MSM elements and mechanical structures for supporting the toothed racks and the body elements rotatably with respect to each other are not shown in figures 2a-2c.

[0037] In the exemplifying actuator illustrated in figure 2a, the teeth of the toothed rack 201 a are on an outer race of the ring, and the tooth plates and the MSM elements are outside the ring so that the tooth plates are radially moveable with respect to the ring. In figure 2a, one of the tooth plates is denoted with a reference 204a and one of the MSM elements is denoted with a reference 208a. In this exemplifying case, each of the tooth plates has only one tooth.

[0038] In the exemplifying actuator illustrated in figure 2b, the teeth of the toothed rack 201 b are on an inner race of the ring, and the tooth plates and the MSM elements are surrounded by the ring so that the tooth plates are radially moveable with respect to the ring. In figure 2b, one of the tooth plates is denoted with a reference 204b and one of the MSM elements is denoted with a reference 208b. In this exemplifying case, each of the tooth plates has only one tooth.

[0039] In the exemplifying actuator illustrated in figure 2c, the teeth of the toothed rack 201 c are on a side-surface of the ring, and the tooth plates and the MSM elements are positioned with respect to the ring so that the tooth plates are axially moveable with respect to the ring in parallel with the geometric center axis of the ring, i.e. in parallel with the z-axis of the coordinate system 299c. In figure 2c, one of the tooth plates is denoted with a reference 204c and one of the MSM elements is denoted with a reference 208c. In the exemplifying case shown in figure 2c, the whole circumference of the ring is not populated by the tooth plates and the MSM elements. It is however also possible that the whole circumference of the ring is populated by the tooth plates and the MSM elements in the same way as in the actuators illustrated in figures 2a and 2b. In conjunction with the actuators illustrated in figures 2a and 2b, it is also possible that the whole circumference of the ring is not populated by the tooth plates and the MSM elements.

[0040] In actuators where the toothed rack constitutes a ring, an angular distance 0 between two successively actuated tooth plates can be described by the following formula:

[0041] 0 = P / (rN) + nP / r, (3) where N is the number of the tooth plates i.e. the number of the MSM elements, r is the radius of the ring, P is the tooth-pitch, and n is an integer.

[0042] Figure 3 illustrates an actuator according to an exemplifying and non-limiting embodiment. The actuator comprises springs configured to return each of the tooth plates to a position from which the MSM element attached to the tooth plate is configured to move away the tooth plate. In figure 3, one of the tooth plates is denoted with a reference 304, one of the MSM elements is denoted with a reference 308, and the spring connected to the tooth plate 304 is denoted with a reference 318. In an actuator according to one exemplifying and non-limiting embodiment, each of the MSM elements is configured to push the tooth plate attached to the MSM element towards the toothed rack 301 in response to a magnetic field directed to the MSM element, and each of the springs is configured move the tooth plate attached to the spring away from the toothed rack 301. In this exemplifying case, each MSM element can be such that the length of the MSM elements extends under a magnetic field. In an actuator according to another exemplifying and non-limiting embodiment, each of the springs is configured push the tooth plate attached to the spring towards the toothed rack, and each of the MSM elements is configured move the tooth plate attached to the MSM element away from the toothed rack in response to a magnetic field directed to the MSM element. In this exemplifying case, each MSM element can be such that the length of the MSM elements contracts under a magnetic field. As the springs push the tooth plates towards the toothed rack, the toothed rack 301 is blocked from moving in a power loss situation. This is an advantageous property in cases where free motion of the toothed rack 301 is unacceptable e.g. in power loss situations.

[0043] Figure 4 illustrates an actuator according to an exemplifying and non-limiting embodiment. The actuator comprises swing elements pivoted to the body element 402, and each of the swing elements is connected to two of the tooth plates so that reciprocal movements of these two tooth plates connected to the swing element are in opposite phases with respect to each other. In figure 4, one of the swing elements is denoted with a reference 419, the tooth plates connected to the swing element 419 are denoted with references 404 and 406, and the MSM elements connected to the tooth plates 404 and 406 are denoted with references 408 and 410. In this exemplifying case, each MSM element can be such that the length of the MSM elements extends under a magnetic field or such that the length of the MSM elements contracts under a magnetic field. When the MSM element 408 extends under a magnetic field and pushes the tooth plate 404 towards the toothed rack 401 , the swing element 419 pulls the tooth plate 406 away from the toothed rack 401. Correspondingly, when the MSM element 410 extends under a magnetic field and pushes the tooth plate 406 towards the toothed rack 401 , the swing element 419 pulls the tooth plate 404 away from the toothed rack 401 . An actuator according to an exemplifying and non-limiting embodiment further comprises springs connected to the swing elements, and each of the springs is configured to turn the swing element connected to the spring away from a middle position of the swing element in response to a situation in which the swing element is deviated from the middle position. In figure 4, the spring connected to the swing element 419 is denoted with a reference 420. The spring 420 stores energy when the tooth plate 404, or 406, is detached from the toothed rack 401 and the swing element 419 is turning towards its middle position, and the spring 420 releases the energy when the tooth plate 406, or 404, is being engaged with the toothed rack 401 and the swing element 194 is turning away from its middle position after the swing element 419 has passed the middle position. As the toothed rack 401 is moved when the tooth plate 406, or 404, is being engaged with the toothed rack 401 , the energy released by the spring 420 intensifies the force directed to the toothed rack 401 and thus increases a force output. As the spring 420 tends to move the swing element 419 away from its middle position, one of the tooth plates 406 and 404 is engaged with the toothed rack 401 in a power loss situation. This is an advantageous property in cases where free motion of the toothed rack 401 is unacceptable e.g. in power situations.

[0044] Figure 5 illustrates an actuator according to an exemplifying and non-limiting embodiment. In this exemplifying actuator, tooth plates and corresponding MSM elements whose reciprocal movements are in opposite phases with respect to each other are arranged to be adjacent to each other. Thus, the swing elements are connected to adjacent ones of the tooth plates and therefore the swing elements do not need to overlap with each other. In figure 5, one of the swing elements is denoted with a reference 519, the tooth plates connected to the swing element 519 are denoted with references 504 and 505, and the MSM elements connected to the tooth plates 504 and 505 are denoted with references 508 and 509. In this exemplifying case, each MSM element can be such that the length of the MSM elements extends under a magnetic field or such that the length of the MSM elements contracts under a magnetic field. The spring 520 operates in the same way as the spring 420 in the actuator illustrated in figure 4.

[0045] The specific examples provided in the description given above should not be construed as limiting the scope and / or the applicability of the invention. Lists and groups of examples provided in the description given above are not exhaustive unless otherwise explicitly stated.

Claims

What is claimed is:1 . An actuator comprising:- a toothed rack (101 , 201 a-201 c, 301 , 401 ), and- a body element (102) mechanically supported with respect to the toothed rack so that the toothed rack and the body element are moveable with respect to each other, characterized in that the actuator comprises:- tooth plates (104-107, 204a-204c, 304, 404, 406, 504, 505) moveably supported with respect to the body element so that each of the tooth plates is moveable back and forth towards the toothed rack and away from the toothed rack,- magnetic shape memory elements (108-111 , 208a-208c, 308, 408, 410, 508, 509) whose first ends are attached to the body element and second ends are attached to the tooth plates, and- coils (112-115) configured to direct a magnetic field to each of the magnetic shape memory elements to change a length between (L s) the first and second ends of the magnetic shape memory element and thereby to move the tooth plate attached to the magnetic shape memory element, wherein at least one of the toothed rack and the tooth plates has / have oblique tooth surfaces so that a force (Fin) directed by each tooth plate to the toothed rack, when the tooth plate has a mechanical contact with the toothed rack and is being moved towards the toothed rack, causes a force (Fout) in a direction (x) in which teeth of the toothed rack are consecutive to each other to move the toothed rack and the body element with respect to each other.

2. An actuator according to claim 1 , wherein the tooth plates (104-107) are consecutive to each other in the direction (x) in which the teeth of the toothed rack are consecutive to each other.

3. An actuator according to claim 1 or 2, wherein each of the tooth plates (104- 107, 204c, 304) has at least two teeth and a tooth-pitch of the teeth of the tooth plates is a same as a tooth-pitch of the teeth of the toothed rack (101 , 201 c, 301 ).

4. An actuator according to any one of claims 1 -3, wherein the toothed rack (201 a-201 c) constitutes a ring, and the toothed rack and the body element are rotatable with respect to each other so that a geometric axis of rotation is a geometric center axis of the ring.

5. An actuator according to claim 4, wherein the teeth of the toothed rack (201 a) are on an outer race of the ring, and the tooth plates (204a) and the magnetic shape memory elements (208a) are outside the ring so that the tooth plates are radially moveable with respect to the ring.

6. An actuator according to claim 4, wherein the teeth of the toothed rack (201 b) are on an inner race of the ring, and the tooth plates (204b) and the magnetic shape memory elements (208b) are surrounded by the ring so that the tooth plates are radially moveable with respect to the ring.

7. An actuator according to claim 4, wherein the teeth of the toothed rack (201 c) are on a side-surface of the ring, and the tooth plates (204c) and the magnetic shape memory elements (208c) are positioned with respect to the ring so that the tooth plates are moveable with respect to the ring in parallel with the geometric center axis of the ring.

8. An actuator according to any one of claims 1 -3, wherein the toothed rack (101 ) is straight, and the toothed rack (101 ) and the body element (102) are linearly moveable with respect to each other in the direction (x) in which the teeth of the toothed rack are consecutive to each other.

9. An actuator according to any one of claims 1 -8, wherein the actuator comprises springs (318) configured to return each of the tooth plates to a position from which the magnetic shape memory element attached to the tooth plate is configured to move away the tooth plate.

10. An actuator according to claim 9, wherein each of the magnetic shape memory elements is configured to push the tooth plate attached to the magnetic shape memory element towards the toothed rack in response to the magnetic field directed to the magnetic shape memory element, and each of the springs is configured move the tooth plate attached to the spring away from the toothed rack.

11. An actuator according to claim 9, wherein each of the springs is configured push the tooth plate attached to the spring towards the toothed rack, and each of the magnetic shape memory elements is configured move the tooth plate attached to the magnetic shape memory element away from the toothed rack in response to the magnetic field directed to the magnetic shape memory element.

12. An actuator according to any one of claims 1 -8, wherein the actuator comprises swing elements (419, 519) pivoted to the body element, and each of the swing elements is connected to two of the tooth plates (404, 406, 504, 505) so that reciprocal movements of the two tooth plates connected to the swing element are in opposite phases with respect to each other.

13. An actuator according to claim 12, wherein the actuator comprises springs (420, 520) connected to the swing elements, and each of the springs is configured to turn the swing element connected to the spring away from a middle position of the swing element in response to a situation in which the swing element is deviated from the middle position.

14. An actuator according to claim 12 or 13, wherein the tooth plates are successively in the direction in which the teeth of the toothed rack are consecutive to each other, and each of the swing elements (519) is connected to adjacent ones of the tooth plates (504, 505).

15. An actuator according to any one of claims 1 -14, wherein the teeth of the toothed rack and the teeth of the tooth plates have i) a trapezoidal profile with rounded corners or ii) a triangular profile.

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