Method and system for calculating section deformation torque of software actuator under equal-width condition
By calculating the dimensional parameters of the soft actuator cross section under equal width conditions, and calculating its torque, bending moment and pressure-angle relationship, the problem of lack of data basis in the existing technology is solved, and the accuracy of soft actuator design and selection efficiency are improved.
Patent Information
- Application Number
- CN202510635667.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-16
- Publication Date
- 2025-09-19
Smart Images

Figure CN120671332A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of soft robots, and in particular relates to a method and system for calculating the cross-sectional deformation torque of a soft actuator under constant width conditions. Background Art
[0002] Common cross-sectional shapes of soft actuators include rectangle, semicircle and circle. A larger cross-sectional area and aspect ratio are conducive to the bending performance of the soft actuator, but the cross-sectional shape with an arc at the top and the cross-sectional shape with an arc have lower internal impedance.
[0003] The current calculation method generally considers retaining the arc line of the upper half of the cross-section and supplementing the lower half into a rectangle to fit the contact surface, setting it as a combination of a semicircle and a rectangle or a circle and a triangle at any angle; however, there is no suitable method to calculate the cross-sectional deformation moment for actuators with a combination of multiple cross-sectional shapes, and there is a lack of effective methods to describe the unilateral influence of the cross-sectional shape on the bending of the soft actuator. As a result, there is a lack of favorable data basis when designing and selecting the actuator, which is not conducive to the development and application of soft robots. Summary of the Invention
[0004] The technical problem of the present invention is: the present invention proposes a method for calculating the cross-sectional deformation moment of a soft actuator under equal-width conditions. According to the ratio of the longitudinal height to the transverse length of the cross-section, the height of the rectangle, the radius of the circular part, the height of the semi-rectangular part of the semi-cut circle, the radius of the circular part of any cut circle, and the bisection angle of the central angle corresponding to the cut circle at any angle and other dimensional parameters, the torque of the bottom rectangular shape of the actuator cross-section, the passive bending moment and the pressure-angle relationship of the cross-section during the equal-distance process are calculated. Through the appropriate cross-sectional deformation moment calculation method and the pressure-angle relationship, the unilateral influence of the cross-sectional shape on the bending of the soft actuator is effectively described, providing a favorable data basis for actuator design and selection.
[0005] The purpose of the present invention is to provide a method and system for calculating the cross-sectional deformation torque of a soft actuator under constant width conditions to solve the above problems.
[0006] This object is achieved by the subject matter of the independent technical solutions. Among other aspects, a method, a computer-readable storage medium, an electronic device, and a computer program product are provided. Advantageous improvements are provided in the dependent technical solutions. Various aspects are explained with reference to the method, while the remaining aspects are explained with reference to the device. Accordingly, these aspects are interchangeable.
[0007] According to a first aspect, a method for calculating the cross-sectional deformation moment of a soft actuator under constant width conditions is provided, comprising: Obtaining dimensional parameters related to the actuator cross section; the dimensional parameters include cross section width, actuator wall thickness, ratio of longitudinal height to transverse length of the cross section, rectangle height, radius of the circular portion, height of the lower semi-rectangular portion of the semi-circular cut, radius of the circular portion of any cut circle, and bisection angle of the central angle corresponding to the cut circle at any angle; The torque of the bottom rectangular shape of the actuator cross section, the passive bending moment and the pressure-angle relationship of the cross section during the isometric process are calculated based on the dimensional parameters.
[0008] Furthermore, the bottom rectangular shape of the actuator cross section The calculation formula for torque is: ; Where, AV Indicates the height of the rectangle; a Indicates the width of the section; t represents the wall thickness of the actuator; v It represents the ratio of the longitudinal height to the transverse length of the cross section; x represents the input pressure of the gas at the distance from the bottom layer to the actuator tip cross section; P in Indicates pressure.
[0009] Preferably, for a cross section containing a circular portion, the angle is used as the integral variable in the integral calculation.
[0010] Furthermore, the moment generated at the bottom of the cross section is the passive bending moment. In the process of calculating the passive bending moment, each cross-sectional shape is split into different regular shape blocks along the height direction, and then the integral of each shape block is defined in the form of infinitesimal elements.
[0011] Preferably, the passive bending moment The calculation formula is: ; ; Where, Indicates the overall stretch angle; x represents the input pressure of the gas at the distance from the bottom layer to the actuator tip cross section; l k Indicates the width of the microelement; l h Indicates the height of the microelement; s 1 represents the width stress of the microelement; l Indicates the height of the microelement from the bottom; α represents the middle angle; β represents the integral variable; r represents the radius of the circular portion; and t represents the wall thickness of the actuator.
[0012] Preferably, the calculation formula for the pressure-angle relationship of the cross section during the isometric process is: ; Where, k c represents a constant coefficient; F ( θ ) represents the expression of the passive bending moment integral with respect to the overall bending angle after numerical integration; k z Represents a rectangular cross section.
[0013] According to a second aspect, a system for calculating the cross-sectional deformation torque of a soft actuator under constant width conditions is provided, comprising: A data acquisition module is used to obtain dimensional parameters related to the actuator cross section; the dimensional parameters include cross section width, actuator wall thickness, ratio of longitudinal height to transverse length of the cross section, rectangle height, radius of the circular portion, height of the lower semi-rectangular portion of the semi-circular cut, radius of the circular portion of any cut circle, and bisection angle of the central angle corresponding to the cut circle at any angle; A calculation module is used to calculate the torque, passive bending moment and pressure-angle relationship of the bottom rectangular shape of the actuator cross section during the isometric process based on the dimensional parameters.
[0014] According to a third aspect, a computer-readable storage medium is provided, comprising a computer program soft actuator cross-sectional deformation moment calculation system, for storing a computer program and calculating the soft actuator cross-sectional deformation moment under equal width conditions.
[0015] According to the fourth aspect, an electronic device is provided, comprising a memory, a processor and a computer program stored in the memory, a soft actuator cross-sectional deformation moment calculation system, for implementing the steps of a soft actuator cross-sectional deformation moment calculation method under equal width conditions.
[0016] According to a fifth aspect, a computer program product is provided, comprising a computer program, which, when executed by a processor, performs the steps of a method for calculating the cross-sectional deformation moment of a soft actuator under conditions of equal width.
[0017] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for calculating the cross-sectional deformation moment of a soft actuator under equal-width conditions. According to the ratio of the longitudinal height to the transverse length of the cross-section, the height of the rectangle, the radius of the circular part, the height of the semi-rectangular part of the semi-cut circle, the radius of the circular part of any cut circle, and the bisecting angle size parameters of the central angle corresponding to the cut circle at any angle, the torque of the bottom rectangular shape of the actuator cross-section, the passive bending moment, and the pressure-angle relationship of the cross-section during the equal-distance process are calculated. This method effectively describes the unilateral influence of the cross-sectional shape on the bending of the soft actuator, and can provide favorable data basis for actuator design and selection. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The present invention will be further described below with reference to the accompanying drawings and examples.
[0019] Picture 1 Schematic diagram of the shapes of various cross sections of the brake according to an embodiment of the present invention.
[0020] Picture 2 Schematic diagram of the splitting method of the cross-sectional shape of an embodiment of the present invention.
[0021] Picture 3 Schematic diagram of the width of the annular element according to an embodiment of the present invention.
[0022] Picture 4 Schematic diagram of the pressure-angle relationship of rectangular cross-sections with different height ratios according to an embodiment of the present invention.
[0023] Picture 5 Schematic diagram of the pressure-angle relationship of circular cross-sections with different aspect ratios according to an embodiment of the present invention. DETAILED DESCRIPTION
[0024] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
[0025] Example 1: A method for calculating the cross-sectional deformation moment of a soft actuator under constant width conditions includes: Obtaining dimensional parameters related to the actuator cross section; the dimensional parameters include cross section width, actuator wall thickness, ratio of longitudinal height to transverse length of the cross section, rectangle height, radius of the circular portion, height of the lower semi-rectangular portion of the semi-circular cut, radius of the circular portion of any cut circle, and bisection angle of the central angle corresponding to the cut circle at any angle; The torque of the bottom rectangular shape of the actuator cross section, the passive bending moment and the pressure-angle relationship of the cross section during the isometric process are calculated based on the dimensional parameters.
[0026] Based on the dimensional parameters such as the ratio of the longitudinal height to the transverse length of the cross-section, the height of the rectangle, the radius of the circular part, the height of the semi-rectangular part of the semi-cut circle, the radius of the circular part of any cut circle, and the bisection angle of the central angle corresponding to the cut circle at any angle, the torque of the bottom rectangular shape of the actuator cross-section, the passive bending moment and the pressure-angle relationship of the cross-section during the isometric process are directly calculated, and the cross-section deformation moment and pressure-angle relationship are calculated through appropriate methods. The following steps are involved: S1. Calculate the active tensile torque.
[0027] Based on the air cavity cross-section under constant width conditions, the total active torque acting on the actuator front end under the influence of the inlet pressure can be used to approximately measure the impact of different cross-sectional shapes on actuator performance, thereby selecting the optimal cross-sectional shape for a specific selection. Common cross-sectional shapes for soft actuators include rectangular, semicircular, and circular.
[0028] On the basis of retaining the arc of the upper half of the cross section, the lower half is supplemented into a rectangle, and two other circular cross-sectional shapes are added. The combination of semicircle and rectangle is recorded as semicircle, and the combination of arbitrary angle circular and triangle is recorded as arbitrary circular. Considering that the actuator is fixed on the finger, its overall cross-sectional shape in the sagittal plane should be close to square rather than rectangular. The width of all cross sections is proposed here. a , and the wall thickness of the actuator is t = a / 5, and note the ratio of the longitudinal height to the transverse length of the cross section v is the aspect ratio. Under these conditions, the specific dimensions of each section can be calculated. The height of the rectangle is AV , the radius of the circular part of the semicircular, full circle and half-circular cross-section r = a / 2, the height of the semi-rectangular part of the semi-circle is r , width is 2 r , the radius of the circular part of any tangent circle R = a / 2sin θ , among which θ The angle that bisects the central angle of a circle tangent to any angle.
[0029] The cross-sectional shapes are as follows Picture 1 As shown: For rectangular shapes, the input pressure of the gas is the distance from the bottom layer to the actuator tip cross section. x The force generated on the horizontal line f RS , the calculation formula is: f RS =a Pin d x ; Where x represents the distance between the actuator tip and the bottom layer, a Indicates the width of the section, P in Indicates pressure.
[0030] Actuator cross-section bottom rectangular shape The calculation formula for torque is: ; Where, AV Indicates the height of the rectangle; a Indicates the width of the section; t represents the wall thickness of the actuator; v It represents the ratio of the longitudinal height to the transverse length of the cross section; x represents the input pressure of the gas at the distance from the bottom layer to the actuator tip cross section; P in Indicates pressure.
[0031] For cross sections containing circular parts, the angle is used in the integral calculation. β As the integration variable, replace the integration variable x Then calculate. t and the corresponding radius r and R Substitute the active tensile moment calculation results of the above cross-sectional shapes into the calculation results, and then extract a 3 P in After that, a purely numerical result can be obtained. This is used to measure the magnitude of the active torque generated by the air pressure at each section, which is called the active torque coefficient, as shown in Table 1. The active torque coefficients of rectangular sections and sections cut into circles at any angle still contain the aspect ratio of the rectangular section. v and the bisector of the central angle of the tangent circle θ .
[0032] Table 1
[0033] As shown in Table 1, compared with the full circle cross section, when the aspect ratio is 1, the rectangular cross section Kz =0.7, compared with the semicircular cross section, when the aspect ratio is 0.5, the rectangular cross section Kz=0.225. When the aspect ratio is 0.5 for cutting a circle at any angle, the cross-sectional shape is also a semicircular cross-sectional shape, and the active torque coefficient is also 0.1619; when the aspect ratio is 1, the corresponding active torque coefficient is 0.6497. The rectangular cross-section is more advantageous in terms of active torque. Under the premise of the same width and the same aspect ratio, the rectangular cross-sectional area is larger. A single active torque coefficient cannot fully describe the characteristics of the actuator during bending, because the material of the actuator itself will also generate internal tensile torque to resist deformation during bending and stretching. Therefore, only by comparing the active torque generated by air pressure and the tensile torque generated by the material of the same cross-section at the same time can the advantages and disadvantages of each cross-sectional shape be compared.
[0034] S2. Calculate the passive bending moment.
[0035] Considering that rubber or other soft materials will generate rebound resistance to resist elastic deformation when deformed, the passive bending moment generated at the bottom of the cross section is taken into account. Using the Simpson numerical integration method, each cross-sectional shape can be split into different regular shape blocks according to the height direction, and then the integral of each shape block is defined in the form of microelement. The splitting method is as follows: Picture 2 shown.
[0036] The splitting method of the semi-tangential circle and the arbitrary angle tangential circle is similar. They are combined sections, and the calculation formula for the passive bending moment is: ; Where, l k represents the width of the microelement, l h represents the height of the microelement, s 1 represents the stress of the infinitesimal element, l Indicates the height of the microelement from the bottom.
[0037] For cross sections containing circular portions, the angle is used as the integral variable in the integral calculation.
[0038] For normally cut circular blocks and rectangular blocks, the height and width of their infinitesimal elements are consistent with the calculation in the active torque.
[0039] For annular blocks, the moment generated at the bottom of the cross section is the passive bending moment. In the process of calculating the passive bending moment, each cross section shape is split into different regular shape blocks according to the height direction, and then the integral of each shape block is defined in the form of infinitesimal elements. The width of the annular block infinitesimal element is defined as follows: Picture 3 shown.
[0040] The dotted line in the figure represents the annular block formed by the wall thickness of the soft actuator. At the same height, the calculation formula of the infinitesimal width lk with respect to the integral variable β is obtained by the intermediate angle α: ; Where, Indicates the overall stretch angle; x represents the input pressure of the gas at the distance from the bottom layer to the actuator tip cross section; l k Indicates the width of the microelement; l h Indicates the height of the microelement; s 1 represents the width stress of the microelement; l Indicates the height of the microelement from the bottom; α represents the middle angle; β represents the integral variable; r represents the radius of the circular portion; and t represents the wall thickness of the actuator.
[0041] For each cross-section shape block, according to its length and width, the passive bending moment expression of each cross-section shape for the bottom is obtained according to the calculation formula. From the calculation formula, the passive bending moment of the rectangular cross section is obtained. M b Rs ( ϕ , v ) After calculation, the integral is stretched by two variables as a whole ϕ and aspect ratio v The passive bending moment of the circle at any angle is composed of ϕ Bisect the angle with the center of the tangent circle θ The calculation formula for other sections is only composed of the overall tensile angle θ As the independent variable. For rectangular cross-section, v ∈[0.5,1.0], the value is taken every 0.1; for the circular section, at the bisection angle θ ∈[15°,90°], take special values θ =[90, 56.442, 45.584, 38.682, 33.749, 30], corresponding to the aspect ratio of the cut circle section v =[0.5, 0.6, 0.7, 0.8, 0.9, 1.0]. The above analysis shows that the passive bending moment of the semicircular cross-section is much smaller than that of other cross-sections due to its aspect ratio of 0.5. The passive bending moment of the rectangular cross-section is positively correlated with the aspect ratio, while the passive bending moment of the circular cross-section at any angle is negatively correlated with the aspect ratio.
[0042] S3. Pressure-angle relationship.
[0043] The active moment coefficient and passive bending moment describe the unilateral influence of the cross-sectional shape on the bending of the soft actuator from a single perspective. By comprehensively considering the bending performance of the cross-sectional shape, the pressure-angle relationship of the cross-sectional shape during the isometric process is obtained. In the final static bending state of the soft actuator, the active tensile moment and the passive bending moment remain equal at the top of the actuator. The pressure-angle relationship of the cross-sectional shape during the isometric process is calculated as: ; Where, k c represents a constant coefficient; F ( θ ) represents the expression of the passive bending moment integral with respect to the overall bending angle after numerical integration; k z Represents a rectangular cross section.
[0044] like Picture 4 and Picture 5 As shown, when the aspect ratio is within the range of [0.5, 1], the rectangular cross-section performs worse than the other three cross-sections containing a top curve, with a significant difference in bending angle at the same pressure. Unlike the results under active tensile torque, the full-circular cross-section outperforms the semicircular cross-section in terms of pressure-angle. This significant advantage in active tensile torque offsets the difference in passive bending moment. However, after compressive deformation, the full-circular cross-section weakens and approaches that of the semicircular cross-section.
[0045] For sections with circular sections at any angle, as the bisection angle gradually increases from [15°, 90°], the bottom curve and the semicircle tangent coincide, indirectly proving the accuracy of the section shape segmentation and calculation. Furthermore, as the angle increases, the intake pressure requirement also increases. Thanks to its smallest aspect ratio, the semicircular section also becomes the section with the lowest intake pressure at equal bending angles. The semicircular section achieves the best performance in terms of the pressure-angle relationship, and its impact on bending performance becomes increasingly apparent as the bending angle increases. At θ of 270°, the intake pressure requirements for the full circle and semicircular sections are reduced by 5.17% and 13.75%, respectively. Compared to rectangular and circular sections with the same aspect ratio of 1, the intake pressure requirements are reduced by an average of approximately 15%.
[0046] According to a second aspect, a system for calculating the cross-sectional deformation torque of a soft actuator under constant width conditions is provided, comprising: A data acquisition module is used to obtain dimensional parameters related to the actuator cross section; the dimensional parameters include the cross section width, the actuator wall thickness, the ratio of the longitudinal height to the transverse length of the cross section, the height of the rectangle, the radius of the circular portion, the height of the semi-rectangular portion of the semi-circular portion, the radius of the circular portion of any tangent circle, and the angle bisecting the central angle of the tangent circle at any angle; A calculation module is used to calculate the torque, passive bending moment and pressure-angle relationship of the bottom rectangular shape of the actuator cross section during the isometric process based on the dimensional parameters.
[0047] According to a third aspect, a computer-readable storage medium is provided, comprising a computer program and a system for calculating the cross-sectional deformation moment of a soft actuator as described in claim 7, for storing the computer program and calculating the cross-sectional deformation moment of the soft actuator under equal width conditions.
[0048] According to the fourth aspect, an electronic device is provided, comprising a memory, a processor, a computer program stored on the memory, and a soft actuator cross-sectional deformation moment calculation system as described in claim 7, for implementing the steps of a soft actuator cross-sectional deformation moment calculation method under equal width conditions.
[0049] According to a fifth aspect, a computer program product is provided, comprising a computer program, which, when executed by a processor, performs the steps of a method for calculating the cross-sectional deformation moment of a soft actuator under conditions of equal width.
[0050] Example 2: An embodiment of the present invention provides a system for calculating the cross-sectional deformation torque of a soft actuator under constant width conditions, comprising: A data acquisition module is used to obtain dimensional parameters related to the actuator cross section; the dimensional parameters include the cross section width, the actuator wall thickness, the ratio of the longitudinal height to the transverse length of the cross section, the height of the rectangle, the radius of the circular portion, the height of the semi-rectangular portion of the semi-circular portion, the radius of the circular portion of any tangent circle, and the angle bisecting the central angle of the tangent circle at any angle; A calculation module is used to calculate the torque, passive bending moment and pressure-angle relationship of the bottom rectangular shape of the actuator cross section during the isometric process based on the dimensional parameters.
[0051] Example 3: An embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon for storing the computer program and calculating the cross-sectional deformation torque of the soft actuator under equal width conditions, so that a computer device, including a personal computer, a server or a network device, executes the method steps in the embodiment.
[0052] Example 4: An embodiment of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory, for implementing the steps of the method for calculating the cross-sectional deformation moment of a soft actuator under the condition of equal width in the embodiment.
[0053] Example 5: An embodiment of the present invention provides a computer program product, including a computer program for implementing the steps of calculating the cross-sectional deformation moment of a soft actuator under the condition of equal width in the embodiment.
[0054] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions recited in the claims, including equivalent alternatives to the technical features of the technical solutions recited in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.
Claims
1. A method for calculating the cross-sectional deformation moment of a soft actuator under constant width conditions, characterized in that: include: Obtaining dimensional parameters related to the actuator cross section; The size parameters include the cross-sectional width, the actuator wall thickness, the ratio of the longitudinal height to the transverse length of the cross-sectional area, the height of the rectangle, the radius of the circular portion, the height of the semi-rectangular portion of the semi-circular portion, the radius of the circular portion of any tangent circle, and the bisection angle of the central angle of the tangent circle corresponding to any angle; The torque of the bottom rectangular shape of the actuator cross section, the passive bending moment and the pressure-angle relationship of the cross section during the isometric process are calculated based on the dimensional parameters.
2. The method for calculating the cross-sectional deformation moment of a soft actuator under the condition of constant width according to claim 1, characterized in that: The actuator cross-section bottom rectangular shape The calculation formula for torque is: ; Where, av Indicates the height of the rectangle; a Indicates the width of the section; t represents the wall thickness of the actuator; v It represents the ratio of the longitudinal height to the transverse length of the cross section; x represents the input pressure of the gas at the distance from the bottom layer to the actuator tip cross section; P in Indicates pressure.
3. The method for calculating the cross-sectional deformation moment of a soft actuator under the condition of constant width according to claim 1, characterized in that: For the cross section containing a circular portion, the angle is used as the integral variable in the integral calculation.
4. The method for calculating the cross-sectional deformation moment of a soft actuator under constant width conditions according to claim 1, characterized in that: The moment generated at the bottom of the cross section is the passive bending moment. During the calculation of the passive bending moment, each cross-sectional shape is split into different regular shape blocks along the height direction, and then the integral of each shape block is defined in a microelement manner.
5. The method for calculating the cross-sectional deformation moment of a soft actuator under the condition of constant width according to claim 1, characterized in that: The passive bending moment The calculation formula for the width of the ring block element is: ; ; Where, Indicates the overall stretch angle; x represents the input pressure of the gas at the distance from the bottom layer to the actuator tip cross section; l k Indicates the width of the microelement; l h Indicates the height of the microelement; s 1 represents the width stress of the microelement; l Indicates the height of the microelement from the bottom; α represents the middle angle; β represents the integral variable; r represents the radius of the circular portion; and t represents the wall thickness of the actuator.
6. The method for calculating the cross-sectional deformation moment of a soft actuator under the condition of constant width according to claim 1, characterized in that: The calculation formula of the pressure-angle relationship of the cross section during the isometric process is: ; Where, k c represents a constant coefficient; F ( θ ) represents the expression of the passive bending moment integral with respect to the overall bending angle after numerical integration; k z Represents a rectangular cross section, and Pin represents pressure.
7. A system for calculating cross-sectional deformation torque of a soft actuator under constant width conditions as described in claims 1-6, characterized in that: include: A data acquisition module is used to obtain dimensional parameters related to the actuator cross section; the dimensional parameters include the cross section width, the actuator wall thickness, the ratio of the longitudinal height to the transverse length of the cross section, the height of the rectangle, the radius of the circular portion, the height of the semi-rectangular portion of the semi-circular portion, the radius of the circular portion of any tangent circle, and the angle bisecting the central angle of the tangent circle at any angle; A calculation module is used to calculate the torque, passive bending moment and pressure-angle relationship of the bottom rectangular shape of the actuator cross section during the isometric process based on the dimensional parameters.
8. A computer-readable storage medium, characterized in that It comprises a computer program and a system for calculating the cross-sectional deformation moment of a soft actuator as claimed in claim 7, and is used for storing the computer program and calculating the cross-sectional deformation moment of the soft actuator under the condition of equal width.
9. An electronic device, characterized in that: It includes a memory, a processor, a computer program stored in the memory, and a soft actuator cross-sectional deformation moment calculation system as described in claim 7, which is used to implement the steps of calculating the soft actuator cross-sectional deformation moment under equal width conditions.
10. A computer program product, characterized in that The method comprises a computer program and steps for calculating the cross-sectional deformation moment of a soft actuator under equal width conditions when the computer program as claimed in any one of claims 7 is executed by a processor.