Flapping-rotor aircraft that achieves multi-mode motion based on servo motors

Abstract

This invention discloses a flapping rotor aircraft based on servo motors for multi-mode motion, belonging to the field of micro-aircraft. The multi-mode motion includes flapping wing mode and flapping rotor mode. The invention comprises a central shaft component, fuselage component, flapping component, torsion component, and wing component. Control signals from the main control board control the servo motor's motion angle and rotation speed, enabling the servo motor to control flapping wing motion parameters such as flapping angle and torsion angle, completing the flapping wing rotation and achieving the transition between flapping wing and flapping rotor modes. The torsional motion of the flapping wing is described by combining the characteristics of step functions and harmonic functions, overcoming the shortcomings of using step functions to describe the torsion angle in ADAMS simulation and servo control, such as simulation calculation divergence, large inertial forces, and reduced servo motor lifespan. This invention exhibits superior aerodynamic performance, combining the vertical takeoff and landing and hovering performance of rotor flight mode with the cruise forward flight performance of flapping wing flight mode, meeting different flight requirements and possessing better environmental adaptability.

Description

Technical Field

[0001] The flapping rotor aircraft disclosed in this invention, which achieves multi-mode motion based on servo motors, belongs to the field of micro aircraft. Background Technology

[0002] Since its inception in the 1990s, the concept of micro-aircraft has attracted considerable attention from scholars. Compared to fixed-wing and rotorcraft micro-aircraft, flapping-wing micro-aircraft possess superior aerodynamic efficiency and maneuverability, enabling vertical takeoff and landing and hovering. However, their mechanical structure is complex. To improve the flight performance of flapping-wing micro-aircraft, some scholars have proposed a flapping-rotor aircraft concept that combines rotor and flapping-wing flight modes. This involves installing a pair of centrally symmetrical flapping wings on the aircraft. The flapping wings, while flapping up and down, generate a couple of forces on the two wing surfaces, enabling the flapping wings to spin. Therefore, the aircraft does not require additional balancing devices. Compared to rotorcraft, flapping-rotor aircraft have a simpler structure, while flapping-wing aircraft are more efficient during takeoff and hovering. Combining the advantages of both, they possess a high aerodynamic lift coefficient and aerodynamic efficiency.

[0003] While micro flapping rotorcraft possess unique advantages, their flight mode remains that of a rotorcraft, significantly limiting their forward flight efficiency and speed. In contrast, flapping rotorcraft capable of multi-mode motion can flexibly switch between rotor-based and symmetrical longitudinal flapping flight modes to meet diverse flight requirements and exhibit better environmental adaptability. Summary of the Invention

[0004] The purpose of this invention is to provide a flapping rotor aircraft that achieves multi-mode motion based on servo motors. This aircraft can control flapping motion parameters such as flapping angle, twist angle, and frequency through servo motors to achieve flapping wing rotation and complete the conversion between flapping rotor and flapping wing flight modes.

[0005] This invention is achieved through the following technical solution:

[0006] The present invention discloses a flapping rotor aircraft based on servo motors to achieve multi-mode motion, comprising a central shaft component, a fuselage component, a flapping component, a torsion component, and a wing component.

[0007] The central shaft component consists of a central shaft and a bearing. The central shaft is fixed to the ground. The central shaft is inserted into the bearing for a fixed connection.

[0008] The fuselage component comprises a fuselage frame, a main control board, a battery, a voltage regulator module, a first servo, and a second servo. A bearing is installed between the fuselage frame and the central shaft. In flapping rotor mode, the fuselage frame rotates around the central shaft under aerodynamic torque. The bearing is fixedly connected to the junction of the fuselage frame and the central shaft to eliminate friction between the bearing and the fuselage frame, and between the bearing and the central shaft, during rotational motion. The main control board is mounted to the fuselage frame with screws, receives control signals, and transmits them to six servos: the first, second, third, fourth, fifth, and sixth servos. Each servo corresponds to a set of servo blades and a servo frame. The battery is located on the top of the fuselage frame and supplies power to the main control board and the aforementioned six servos. The voltage regulator module adjusts the input voltage supplied to the main control board by the battery. The first and second servos are fixed to both sides of the fuselage frame and are used to adjust the flapping angle of attack and the flapping rotation motion during mode transitions. The fuselage components rotate around the central shaft component via bearings.

[0009] The flapping component comprises a first rudder blade, a second rudder blade, a third rudder frame, a fourth rudder frame, a third rudder, and a fourth rudder. The first rudder blade is connected to the first rudder, and the second rudder blade is connected to the second rudder. The flapping component is connected to the first and second rudders in the fuselage component, and the first and second rudders control the flapping component to rotate to a fixed angle or flip. The first and second rudders in the fuselage component are located on the left and right sides of the fuselage, respectively.

[0010] The torsion component comprises a third rudder blade, a fourth rudder blade, a fifth rudder mechanism frame, a sixth rudder mechanism frame, a fifth rudder, and a sixth rudder. The third rudder blade is connected to the third rudder, and the fourth rudder blade is connected to the fourth rudder. The torsion component is connected to the third and fourth rudders in the flapping component, and the flapping motion of the wing is controlled by the third and fourth rudders. The third and fourth rudders are located on the left and right sides of the fuselage, respectively.

[0011] The wing components consist of a fifth rudder blade, a sixth rudder blade, and flapping wings. The fifth rudder blade is connected to a fifth servo, and the sixth rudder blade is connected to a sixth servo. There are two flapping wings, symmetrically mounted on both sides of the fuselage. Each wing includes a main sparsity, two secondary spars, and a wing membrane. The main and secondary spars together form the wing frame, and the wing membrane is bonded to each spars. The wing components are respectively connected to the fifth and sixth servos in the torsion mechanism, and the fifth and sixth servos control the torsional movement of the flapping wings. The fifth and sixth servos are located on the left and right sides of the fuselage, respectively.

[0012] To facilitate the installation and removal of components, it is preferable that the bearing is fixed with hot melt adhesive during installation, and the rudder plate, servo motor and servo motor frame are all fixed with screws.

[0013] The central shaft and fuselage frame are subjected to relatively small forces and torques; therefore, considering manufacturing costs, white resin material is preferred for 3D printing. The servo frame and servo blades are subjected to larger torques, requiring a high-strength material; therefore, black nylon material is preferred for 3D printing.

[0014] To meet the strength and stiffness requirements of the flapping wing and reduce the wing mass, the main and secondary spars are preferably made of carbon fiber reinforced composite materials. To meet the toughness and elasticity requirements of the flapping wing, the wing membrane is preferably made of polyimide.

[0015] The operating method of the flapping rotor aircraft based on servo motors for multi-mode motion disclosed in this invention is as follows: The multi-mode motion includes a flapping wing mode and a flapping rotor mode. The flapping wing mode refers to two flapping wings symmetrically distributed, generating vertical lift and forward thrust during vertical flapping. The flapping rotor mode refers to two flapping wings centrally symmetrically distributed, generating vertical lift and two opposing thrusts during vertical flapping, thus creating a force couple centered on the wing's symmetry point, causing the flapping wings to rotate around the central axis under the action of the force couple. The aircraft achieves the transition between flapping wing and flapping rotor modes by controlling six servo motors to rotate the flapping rotor. The transition states between flapping wing and flapping rotor modes include a minimum flapping angle (downward flapping to the lowest point) and a maximum flapping angle (upward flapping to the highest point).

[0016] The flapping motion of a flapping rotor aircraft can be decomposed into flapping, torsional, and rotational motions. Rotational motion is passive; therefore, two servos are installed on each of the left and right flapping wings to control the active flapping and torsional motions respectively. The flapping wing mode and flapping rotor mode have the same preset maximum and minimum flapping angles. Preferably, the maximum upper flapping angle... Both are 50°, maximum downward angle. All angles are -30°. In flapping wing mode, preferably, the upward flapping twist angle is 90° and the downward flapping twist angle is 0°. In rotor mode, the upward flapping twist angle is 40° and the downward flapping twist angle is 0°. Since the servo has a maximum control angle, an additional servo is added to each side to control the flapping wing rotation during mode transitions. These additional servos are designated as the first servo and the second servo. The main control board sends motion parameters to the aforementioned six servos. Upon receiving the instructions from the main control board, the six servos perform periodic rotational movements according to the set function, thereby controlling the flapping wing rotation.

[0017] To avoid problems such as computational divergence, large inertial forces, and reduced servo lifespan in simulation and servo control, and to preferably use a function that more closely resembles real torsional motion to describe it, a combination of step and harmonic functions is used to describe the torsional motion of the flapping wing. The flapping angle is shown in both rotor and flapping wing modes. The twist angle α and the rotation angle ψ are expressed as functions of equation (1):

[0018]

[0019] In the formula, To make the angle of the shot, if... Indicates the maximum top angle. Indicates the maximum bottom angle, then α is the torsion angle, ψ is the rotation angle, n represents the ratio of rotational speed to beat frequency, and f represents the beat frequency. Represents dimensionless time. It indicates the beginning of a periodic motion. It indicates the end of a cycle of motion.

[0020] The switching between flapping wing mode and flapping rotor mode must be performed when the flapping angle is at its minimum or maximum.

[0021] When the flapping angle is at its minimum, the method for switching from flapping wing mode to flapping rotor mode is as follows: before the mode switch... The flapping wings are in flapping mode, with the two flapping wings symmetrically mounted. The third servo drives the third servo blade, and the fourth servo drives the fourth servo blade, both rotating around their respective output shafts. This rotation of the third and fourth servo blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing movement, effectively acting as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode switch is required, a mode switch transition phase begins. When the flapping wings reach near the lowest point The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side remains unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original symmetrical flapping wing mode is transformed into a centrally symmetrical flapping rotor motion mode. Simultaneously, the control angle settings of the fifth and sixth servos, which control the flapping wing's torsional motion, will change from 0° to 90° to 140° (40° on the other side) to 140° (0° to 140° on the other side) to complete the transition from flapping wing to flapping rotor mode. Subsequently, another torsional transition process occurs within the transition cycle. Continue transitioning from 140° (40° on one side) to 180° (0° on the other side) using the twist angle setting in flapping rotor mode. After that time... The flapping wing moves in a flapping rotor mode.

[0022] When the flapping angle is at its minimum, the method for switching from flapping rotor mode to flapping wing mode is as follows: before the mode switch... The flapping wings are in flapping rotor mode, with the two flapping wings installed in a centrally symmetrical configuration. The third servo drives the third rudder blade, and the fourth servo drives the fourth rudder blade, both rotating around their respective output shafts. This rotation of the third and fourth rudder blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. During this vertical flapping motion, the flapping wings generate vertical lift and two opposing thrusts, creating a torque centered on the wing's symmetry point. This torque causes the flapping wings to rotate around their central axis. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing's movement and can be considered as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode transition is required, a transition phase begins. When the flapping wings reach near the lowest point The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side will remain unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original centrally symmetrical flapping rotor mode is transformed into a symmetrical flapping wing motion mode. Simultaneously, the control angle settings for the fifth and sixth servos, which control the flapping wing's torsional motion, will change from 0° to 40° to 0° to 90° torsional motion in the flapping rotor mode. Subsequently, another torsional transition process occurs within the conversion cycle. Continue transitioning from 90° to 180° (0° on the other side) with the twist angle set in flapping wing mode. During this time... The flapping wings move in a flapping wing pattern.

[0023] When the flapping angle is at its maximum, the method to switch from flapping wing mode to flapping rotor mode is as follows: before the mode switch... The flapping wings are in flapping mode, with the two flapping wings symmetrically mounted. The third servo drives the third servo blade, and the fourth servo drives the fourth servo blade, both rotating around their respective output shafts. This rotation of the third and fourth servo blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing movement, effectively acting as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode switch is required, a mode switch transition phase begins. First flap the wings to the vicinity of the lowest point. The flapping wing transitions from 0° to 90° using the twisting transition process characteristic of flapping wing mode, then enters the upward flapping phase, before flapping to near its highest point. The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side remains unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original symmetrical flapping wing mode is transformed into a centrally symmetrical flapping rotor motion mode. Simultaneously, the control angle settings of the fifth and sixth servos, which control the flapping wing's torsional motion, will transition from 90° to 0° in the flapping wing mode, then to 90° to 180°, and finally back to 180° (0° on the other side) in the flapping rotor mode, transitioning to 140° (40° on the other side). After this time... The flapping wing moves in a flapping rotor mode.

[0024] When the flapping angle is at its maximum, the method for switching from flapping rotor mode to flapping wing mode is as follows: before the mode switch... The flapping wings are in flapping rotor mode, with the two flapping wings installed in a centrally symmetrical configuration. The third servo drives the third rudder blade, and the fourth servo drives the fourth rudder blade, both rotating around their respective output shafts. This rotation of the third and fourth rudder blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing movement and can be considered as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode switch is required, a mode switch transition phase begins. First flap the wings to the vicinity of the lowest point. The flapping wing still transitions from 0° to 40° using the twisting transition process of the flapping rotor mode, and then enters the upward flapping phase, before flapping to near the highest point. The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side remains unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original centrally symmetrical flapping rotor mode is transformed into a face-symmetrical flapping wing motion mode. Simultaneously, the control angle settings of the fifth and sixth servos, which control the flapping wing's torsional motion, will transition from a 40° to 0° torsional motion in the flapping rotor mode to a 40° to 180° (0° on the other side), and finally back to a 180° to 90° torsional motion in the flapping wing mode. After this time... The flapping wings move in a flapping wing pattern.

[0025] By controlling six servos to flip the flapping rotor, the aircraft can flexibly switch between flapping wing mode and flapping rotor mode, thus achieving both the cruise forward flight performance of flapping wing mode and the vertical take-off, landing and hovering performance of rotor mode, resulting in superior aerodynamic characteristics.

[0026] As a preferred option, set the maximum upward angle. Both are 50°, maximum downward angle. Both are -30°. In flapping wing mode, as a preferred setting, the upper flapping twist angle is 90° and the lower flapping twist angle is 0°. In rotor flapping mode, the upper flapping twist angle is 40° and the lower flapping twist angle is 0°.

[0027] Beneficial effects:

[0028] 1. The flapping rotor aircraft disclosed in this invention is based on servo motors to achieve multi-mode motion. The main control board sends control signals to control the movement angle and speed of the servo motors, thereby enabling the servo motors to control flapping motion parameters such as flapping angle and twist angle, complete flapping wing flipping, and achieve efficient and flexible switching between flapping wing and flapping rotor modes.

[0029] 2. The flapping rotor aircraft disclosed in this invention, which achieves multi-mode motion based on servo motors, combines the characteristics of step functions and harmonic functions to describe the torsional motion of the flapping wing. This overcomes the shortcomings of using step functions to describe the torsion angle, such as simulation calculation divergence, large inertial force, and reduced servo motor life in ADAMS simulation and servo motor control.

[0030] 3. The flapping rotor aircraft flipping based on servo motors disclosed in this invention achieves multi-mode motion. On the basis of achieving the beneficial effects 1 and 2, the flapping flipping model of this invention has better aerodynamic performance than single rotor and flapping wing flight modes. It combines the vertical take-off and landing and hovering performance of rotor flight mode with the cruise forward flight performance of flapping wing flight mode, which can meet different flight requirements and has better environmental adaptability. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the overall structure of the present invention;

[0032] Figure 2 This is a schematic diagram illustrating the mode conversion implementation of the present invention;

[0033] Figure 3 This is a schematic diagram of the shaft component in this invention;

[0034] Figure 4 This is a schematic diagram of the structure of the fuselage component of the present invention;

[0035] Figure 5 This is a schematic diagram of the structure of the flapping component of the present invention;

[0036] Figure 6 This is a schematic diagram of the structure of the torsion component of the present invention;

[0037] Figure 7 This is a schematic diagram of the structure of the wing component of the present invention;

[0038] Figure 8 This is a transition curve diagram showing the conversion from flapping wing mode to flapping rotor mode in the state of minimum flapping angle according to the present invention;

[0039] Figure 9 This is a transition curve diagram showing the transition from flapping rotor mode to flapping wing mode in the state of minimum flapping angle according to the present invention;

[0040] Figure 10 This is a transition curve diagram showing the conversion from flapping wing mode to flapping rotor mode when the flapping angle is at its maximum.

[0041] Figure 11 This is a transition curve diagram showing the transition from flapping rotor mode to flapping wing mode when the flapping angle is at its maximum.

[0042] Among them: 1—Central shaft component, 2—Fuselage component, 3—Flapping component, 4—Torsion component, 5—Wing component; 1.1—Central shaft, 1.2—Bearing; 2.1—Fuselage frame, 2.2—Main control board, 2.3—Battery, 2.5—First servo, 2.6—Second servo; 3.1—First rudder blade, 3.3—Third servo servo frame, 3.5—Third servo; 4.1—Third rudder blade, 4.3—Fifth servo servo frame, 4.5—Fifth servo; 5.1—Fifth rudder blade, 5.3—Main beam, 5.4—Secondary beam, 5.5—Wing membrane. Detailed Implementation

[0043] To better implement this invention and clarify its key points, the invention will be described in detail below with reference to the accompanying drawings and examples.

[0044] like Figure 1 As shown, this embodiment discloses a flapping rotor aircraft that achieves multi-mode motion based on servo motors. It consists of six servo motors, combined with a servo motor frame, battery, main control board, fuselage frame, central shaft, flapping wings, etc. The total mass of the entire aircraft after assembly is 341.0 grams.

[0045] like Figure 2 The diagram shown is a schematic representation of the flapping wing changes during mode switching in the flapping rotor aircraft that achieves multi-mode motion based on servo motors disclosed in this embodiment. The difference between the flapping rotor mode and the flapping wing mode lies in whether the flapping wings on both sides are arranged symmetrically at the center or symmetrically at the surface. Therefore, the key to realizing the switching between flapping rotor and flapping wing modes is to flip one side of the flapping wing, so that the flapping wing in the flapping rotor mode is arranged symmetrically at the center and the flapping wing in the flapping wing mode can be switched between each other.

[0046] like Figure 3 As shown, this embodiment discloses a pivot component for a flapping rotor aircraft that achieves multi-mode motion based on servo motors. The pivot component includes a pivot rod and bearings, and is fixed to the ground. The bearing 1.2 is sealed with an iron cap and installed between the fuselage frame and the pivot rod. The bearing is fixed with hot melt adhesive at the junction with the fuselage frame and the pivot rod to eliminate friction during rotational motion.

[0047] like Figure 4The diagram shows the fuselage component of a flapping rotor aircraft based on servo motors for multi-mode motion, as disclosed in this embodiment. The fuselage component comprises a fuselage frame, a main control board, a battery, a voltage regulator module, a first servo motor, and a second servo motor. A bearing is installed between the fuselage frame and the central axis. In flapping rotor mode, the fuselage frame rotates around the central axis under aerodynamic torque. The bearing is fixedly connected to the junction of the fuselage frame and the central axis to eliminate friction between the bearing and the fuselage frame, and between the bearing and the central axis, during rotational motion. The main control board is mounted to the fuselage frame with screws, receives control signals, and transmits them to six servo motors: the first, second, third, fourth, fifth, and sixth servo motors. Each servo motor corresponds to a set of servo blades and a servo motor frame. The battery is located on the top of the fuselage frame and supplies power to the main control board and the aforementioned six servo motors. The battery supply voltage is 7.4V, and the main control board input voltage should be below 6V. Therefore, a voltage regulator module is used to adjust the input voltage supplied to the main control board by the battery. By rotating the voltage regulator module's voltage knob, the input voltage of the main control board is adjusted to 6V. The voltage regulator module, used to adjust the input voltage supplied to the main control board by the battery, has an interface and is connected between the battery and the main control board via wires. The first and second servos are respectively fixed to both sides of the fuselage frame and are used to adjust the flapping wing angle of attack and the flapping wing roll motion during mode transitions. The fuselage components rotate around the central shaft component via bearings.

[0048] like Figure 5 The diagram shows the flapping component of a flapping rotor aircraft that achieves multi-mode motion based on servos, as disclosed in this embodiment. The flapping component comprises a first servo blade, a second servo blade, a third servo frame, a fourth servo frame, a third servo, and a fourth servo. The first servo blade is connected to the aforementioned first servo, and the second servo blade is connected to the aforementioned second servo. The flapping component is respectively connected to the first and second servos in the aforementioned fuselage components, and the first and second servos control the flapping component to rotate to a fixed angle or flip.

[0049] like Figure 6 The diagram shows the torsion component of a flapping rotor aircraft, which utilizes servos to achieve multi-mode motion according to this embodiment. The torsion component comprises a third servo plate, a fourth servo plate, a fifth servo frame, a sixth servo frame, a fifth servo, and a sixth servo. The third servo plate is connected to the aforementioned third servo, and the fourth servo plate is connected to the aforementioned fourth servo. The torsion component is connected to the third and fourth servos in the aforementioned flapping component, and the flapping motion is controlled by the third and fourth servos. The third and fourth servos are located on the left and right sides of the fuselage, respectively.

[0050] like Figure 7The diagram shows the wing component of a flapping rotor aircraft based on servo motors for multi-mode motion, as disclosed in this embodiment. The wing component consists of a fifth servo blade, a sixth servo blade, and flapping wings. The fifth servo blade is connected to the aforementioned fifth servo motor, and the sixth servo blade is connected to the aforementioned sixth servo motor. There are two flapping wings, symmetrically mounted on both sides of the fuselage. Each flapping wing includes a main spar, two secondary spars, and a flapping membrane. The main spar and secondary spars together form the flapping wing frame. The flapping membrane is cut to the dimensions of the main spar and the two secondary spars extending chordally to the trailing edge and then bonded to the flapping wing frame. To meet the strength and stiffness requirements of the biomimetic micro flapping rotor aircraft's wing during flapping and to reduce wing mass, the main spar cross-sectional width decreases from 3mm at the wing root to 1mm at the wingtip, and the secondary spar cross-sectional width is 1mm. To meet the elasticity and toughness requirements of the wing membrane and to reduce wing mass, the wing membrane is a 15μm thick polyimide film. The wing components are respectively connected to the fifth and sixth servos in the aforementioned torsion components, and the flapping wing torsion motion is controlled by the fifth and sixth servos. The fifth and sixth servos are located on the left and right sides of the fuselage, respectively.

[0051] like Figure 8 The figure shows the transition curve for the present invention to switch from flapping wing mode to flapping rotor mode when the flapping angle is at its minimum. Before the mode switch... When the aircraft is in flapping-wing mode, it enters a transition cycle when a mode switch is required. When the flapping wings reach near the lowest point The twist angle of the flapping wing transitions from 0° to 90° in the flapping wing mode, then from 0° to 140° (40° on the other side), completing the transition from flapping wing mode to flapping rotor mode. Subsequently, another twisting transition process occurs within the transition cycle. The twist angle continues from 140° (40° on the other side) to 180° (0° on the other side) in flapping rotor mode, after which time... The aircraft moves in a flapping rotor mode.

[0052] like Figure 9 The diagram shows the transition curve for the present invention, which achieves the switch from flapping rotor mode to flapping wing mode at the minimum flapping angle. Before the mode switch... The aircraft is operating in flapping rotor mode. When a mode switch is required, it enters a switching cycle. When the flapping wings reach near the lowest point The twist angle of the flapping wing transitions from 0° to 40° in the flapping rotor mode, then from 0° to 90°, completing the transition from flapping rotor mode to flapping wing mode. Subsequently, another twist transition process occurs within the transition cycle. Continue the transition from 90° to 180° (0° on the other side) with the twist angle setting in flapping wing mode, after which time... The aircraft moves in flapping wing mode

[0053] like Figure 10 The figure shows the transition curve for the present invention when switching from flapping wing mode to flapping rotor mode at the maximum flapping angle. Before the mode switch... When the aircraft is in flapping-wing mode, it enters a transition cycle when a mode switch is required. First flap the wings to the vicinity of the lowest point. The flapping wing transitions from 0° to 90° using the twisting transition process characteristic of flapping wing mode, then enters the upward flapping phase, before flapping to near its highest point. The twist angle of the flapping wing transitions from 90 degrees to 0 degrees in flapping mode, then changes from 90 degrees to 180 degrees (0 degrees on the other side), completing the transition from flapping wing mode to flapping rotor mode, and then time... The aircraft moves in a flapping rotor mode.

[0054] like Figure 11 The figure shows the transition curve for the present invention when switching from flapping rotor mode to flapping wing mode at the maximum flapping angle. Before mode switching... The aircraft is operating in flapping rotor mode. When a mode switch is required, it enters a switching cycle. First flap the wings to the vicinity of the lowest point. The flapping wing still transitions from 0° to 40° using the twisting transition process of the flapping rotor mode, and then enters the upward flapping phase, before flapping to near the highest point. The twist angle of the flapping wing changes from 40° to 0° in flapping mode to a transition from 40° to 180° (0° on the other side), completing the transition from flapping rotor mode to flapping wing mode, and then time... The aircraft moves in flapping-wing mode.

[0055] The detailed working method for mode switching of the flapping rotor aircraft based on servo motors to achieve multi-mode motion, disclosed in this embodiment, is as follows:

[0056] The flapping and twisting motions of a flapping rotorcraft are achieved by controlling servos to perform corresponding rotational movements. The control process is as follows: the PC sends servo motion signals, which are received by the main control board and transmitted to the servos. The servos receive the motion angle information and complete the corresponding rotational motion.

[0057] After burning the code to the main control board using Arduino, power on the flapping rotorcraft and turn on the voltage regulator module and main control board. Adjust the input voltage of the main control board to 6V by rotating the voltage regulator module's voltage knob. At this point, the flapping rotorcraft's servos rotate to the set initial position and remain stationary. Ensure the flapping rotorcraft's main control board and the PC are on the same Wi-Fi network. Set the main control board's IP address in the Simulink signal connection module and run it. Time signals are transmitted to the servo motion function at fixed time steps to calculate and output the servo rotation angle at the corresponding moment. The signal connection module sends the servo motion parameters to the main control board, which then sends commands to the servos. The servos perform periodic rotational movements according to the set function.

[0058] The preferred servo motor is the Weichuang Power DMC810 servo motor. The servo blade and the servo motor are fixed together by screws, allowing the servo motor to drive the servo blade to rotate. The servo blade is provided with a connection hole.

[0059] The main control board is preferably the Py-Apple Controller (integrated version). The main control board has WIFI receiving function and provides a Type-C interface for data transmission.

[0060] To meet the power supply requirements of the flapping rotorcraft, the preferred power source is an 800mAh 2S dual-day lithium battery, which also has advantages such as good heat dissipation, good cycle performance, and higher energy density.

[0061] The switching between flapping wing mode and flapping rotor mode must be performed when the flapping angle is at its minimum or maximum.

[0062] Example 1:

[0063] When the flapping angle is at its minimum, the method for switching from flapping wing mode to flapping rotor mode is as follows: before the mode switch... The flapping wings are in flapping mode, with the two flapping wings symmetrically mounted. The third servo drives the third servo blade, and the fourth servo drives the fourth servo blade, both rotating around their respective output shafts. This rotation of the third and fourth servo blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing movement, effectively acting as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode switch is required, a mode switch transition phase begins. When the flapping wings reach near the lowest point The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side remains unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original symmetrical flapping wing mode is transformed into a centrally symmetrical flapping rotor motion mode. Simultaneously, the control angle settings of the fifth and sixth servos, which control the flapping wing's torsional motion, will change from 0° to 90° to 140° (40° on the other side) to 140° (0° to 140° on the other side) to complete the transition from flapping wing to flapping rotor mode. Subsequently, another torsional transition process occurs within the transition cycle. Continue transitioning from 140° (40° on one side) to 180° (0° on the other side) using the twist angle setting in flapping rotor mode. After that time... The flapping wing moves in a flapping rotor mode.

[0064] When the flapping angle is at its minimum, the method for switching from flapping rotor mode to flapping wing mode is as follows: before the mode switch... The flapping wings are in flapping rotor mode, with the two flapping wings installed in a centrally symmetrical configuration. The third servo drives the third rudder blade, and the fourth servo drives the fourth rudder blade, both rotating around their respective output shafts. This rotation of the third and fourth rudder blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. During this vertical flapping motion, the flapping wings generate vertical lift and two opposing thrusts, creating a torque centered on the wing's symmetry point. This torque causes the flapping wings to rotate around their central axis. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing's movement and can be considered as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode transition is required, a transition phase begins. When the flapping wings reach near the lowest point The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side will remain unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original centrally symmetrical flapping rotor mode is transformed into a symmetrical flapping wing motion mode. Simultaneously, the control angle settings for the fifth and sixth servos, which control the flapping wing's torsional motion, will change from 0° to 40° to 0° to 90° torsional motion in the flapping rotor mode. Subsequently, another torsional transition process occurs within the conversion cycle. Continue transitioning from 90° to 180° (0° on the other side) with the twist angle set in flapping wing mode. During this time... The flapping wings move in a flapping wing pattern.

[0065] The transition curves are expressed in function form. For the motion parameters under the mode conversion used in this embodiment, the transition curve from flapping wing to flapping rotor mode is expressed as Equation (2), and the transition curve from flapping rotor to flapping wing mode is expressed as Equation (3).

[0066]

[0067]

[0068] Example 2:

[0069] When the flapping angle is at its maximum, the method to switch from flapping wing mode to flapping rotor mode is as follows: before the mode switch... The flapping wings are in flapping mode, with the two flapping wings symmetrically mounted. The third servo drives the third servo blade, and the fourth servo drives the fourth servo blade, both rotating around their respective output shafts. This rotation of the third and fourth servo blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing movement, effectively acting as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode switch is required, a mode switch transition phase begins. First flap the wings to the vicinity of the lowest point. The flapping wing transitions from 0° to 90° using the twisting transition process characteristic of flapping wing mode, then enters the upward flapping phase, before flapping to near its highest point. The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side remains unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original symmetrical flapping wing mode is transformed into a centrally symmetrical flapping rotor motion mode. Simultaneously, the control angle settings of the fifth and sixth servos, which control the flapping wing's torsional motion, will transition from 90° to 0° in the flapping wing mode, then to 90° to 180°, and finally back to 180° (0° on the other side) in the flapping rotor mode, transitioning to 140° (40° on the other side). After this time... The flapping wing moves in a flapping rotor mode.

[0070] When the flapping angle is at its maximum, the method for switching from flapping rotor mode to flapping wing mode is as follows: before the mode switch... The flapping wings are in flapping rotor mode, with the two flapping wings installed in a centrally symmetrical configuration. The third servo drives the third rudder blade, and the fourth servo drives the fourth rudder blade, both rotating around their respective output shafts. This rotation of the third and fourth rudder blades drives the two flapping wings, along with the fifth and sixth servos connected to them, in a vertical flapping motion. (It should be noted that the twist angle remains constant during the flapping motion; therefore, the fifth and sixth servos do not yet control the flapping wing movement and can be considered as a single unit with no relative motion to the flapping wings, flapping up and down along with them under the control of the third and fourth servos.) When a mode switch is required, a mode switch transition phase begins. First flap the wings to the vicinity of the lowest point. The flapping wing still transitions from 0° to 40° using the twisting transition process of the flapping rotor mode, and then enters the upward flapping phase, before flapping to near the highest point. The sixth servo will drive the sixth servo blade to rotate 180°. Since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the sixth servo side will also rotate 180°, while the flapping wing on the fifth servo side remains unchanged. Therefore, by rotating only the flapping wing on the sixth servo side, the original centrally symmetrical flapping rotor mode is transformed into a face-symmetrical flapping wing motion mode. Simultaneously, the control angle settings of the fifth and sixth servos, which control the flapping wing's torsional motion, will transition from a 40° to 0° torsional motion in the flapping rotor mode to a 40° to 180° (0° on the other side), and finally back to a 180° to 90° torsional motion in the flapping wing mode. After this time... The flapping wings move in a flapping wing pattern.

[0071] The transition curves are expressed in function form. For the motion parameters under the mode conversion used in this embodiment, the transition curve from flapping wing to flapping rotor mode is expressed as Equation (4), and the transition curve from flapping rotor to flapping wing mode is expressed as Equation (5).

[0072]

[0073]

[0074] The above examples illustrate in detail the purpose, technical solution, and beneficial effects of this invention. It should be noted that these descriptions only represent specific embodiments of this invention and are not limited to the scope of protection of this invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A flapping rotor aircraft that achieves multi-mode motion based on servo motors, characterized in that: It includes the central shaft component (1), the fuselage component (2), the flapping component (3), the torsion component (4), and the wing component (5); The central shaft component (1) consists of a central shaft (1.1) and a bearing (1.2); the central shaft (1.1) is perpendicular to the ground; the central shaft (1.1) is inserted into the bearing (1.2) for fixed connection; The fuselage component (2) consists of a fuselage frame (2.1), a main control board (2.2), a battery (2.3), a voltage regulator module, a first servo motor (2.5), and a second servo motor (2.6). A bearing (1.2) is installed between the fuselage frame (2.1) and the central shaft (1.1). In flapping rotor mode, the fuselage frame (2.1) rotates around the central shaft (1.1) under the action of aerodynamic torque. The bearing (1.2) is fixedly connected to the junction of the fuselage frame (2.1) and the central shaft (1.1) to eliminate the friction between the bearing (1.2) and the fuselage frame (2.1), and between the bearing (1.2) and the central shaft (1.1) during rotation. The main control board (2.2) is installed on the fuselage frame (2.1) with screws and receives control signals. The control signal is transmitted to six servos, namely the first servo (2.5), the second servo (2.6), the third servo (3.5), the fourth servo, the fifth servo (4.5), and the sixth servo. Each servo corresponds to a set of servo blades and servo frames. The battery (2.3) is placed on the top of the fuselage frame (2.1) and is used to power the main control board (2.2) and the aforementioned six servos. The voltage regulator module is used to adjust the input voltage provided to the main control board (2.2) by the battery (2.3). The first servo (2.5) and the second servo (2.6) are respectively fixed on both sides of the fuselage frame (2.1) and are used to adjust the flapping angle of attack and the flapping wing roll motion during mode switching. The fuselage components rotate around the central shaft component through the bearing (1.2). The flapping component (3) consists of a first rudder blade (3.1), a second rudder blade, a third rudder frame (3.3), a fourth rudder frame, a third rudder (3.5), and a fourth rudder. The first rudder blade (3.1) is connected to the first rudder (2.5), and the second rudder blade is connected to the second rudder (2.6). The flapping component is connected to the first rudder (2.5) and the second rudder (2.6) in the fuselage component, and the first rudder (2.5) and the second rudder (2.6) control the flapping component to rotate to a fixed angle or flip. The first rudder (2.5) and the second rudder (2.6) in the fuselage component are located on the left and right sides of the fuselage, respectively. The torsion component (4) is composed of a third rudder blade (4.1), a fourth rudder blade, a fifth rudder frame (4.3), a sixth rudder frame (4.4), a fifth rudder (4.5), and a sixth rudder. The third rudder blade (4.1) is connected to the third rudder (3.5), and the fourth rudder blade is connected to the fourth rudder. The torsion component is connected to the third rudder (3.5) and the fourth rudder in the flapping component, and the flapping motion of the flapping wing is controlled by the third rudder (3.5) and the fourth rudder. The third rudder (3.5) and the fourth rudder are located on the left and right sides of the fuselage, respectively. The wing component (5) consists of a fifth rudder blade (5.1), a sixth rudder blade, and a flapping wing; the fifth rudder blade (5.1) is connected to the fifth servo motor (4.5), and the sixth rudder blade is connected to the sixth servo motor; there are two flapping wings in total, symmetrically installed on both sides of the fuselage; each wing includes a main sparsity (5.3), two secondary sparsity (5.4), and a wing membrane (5.5), the main sparsity (5.3) and the secondary sparsity (5.4) together form the wing frame, and the wing membrane (5.5) is bonded to each sparsity; the wing component is respectively connected to the fifth servo motor (4.5) and the sixth servo motor in the torsion component, and the fifth servo motor (4.5) and the sixth servo motor control the torsion motion of the flapping wing; the fifth servo motor (4.5) and the sixth servo motor are located on the left and right sides of the fuselage respectively; The multi-mode motion includes a flapping wing mode and a flapping rotor mode. The flapping wing mode refers to two flapping wings symmetrically distributed, which generate vertical lift and forward thrust when flapping vertically. The flapping rotor mode refers to two flapping wings centrally symmetrically distributed, which generate vertical lift and two opposing thrusts during vertical flapping, thus creating a couple centered on the wing's symmetry point, causing the flapping wings to rotate around the central axis under the action of the couple. The aircraft switches between flapping wing and flapping rotor modes by controlling six servos to flip the flapping rotor. The states for switching between flapping wing and flapping rotor modes include the minimum flapping angle transition state and the maximum flapping angle transition state.

2. The flapping rotor aircraft based on servo motors to achieve multi-mode motion as described in claim 1, characterized in that: The bearing (1.2) is fixed with hot melt adhesive during installation, and the rudder plate, rudder motor and rudder motor frame are all fixed with screws.

3. The flapping rotor aircraft based on servo motors to achieve multi-mode motion as described in claim 1, characterized in that: The central shaft (1.1) and fuselage frame (2.1) are made of white resin material using 3D printing; the third servo frame (3.3), fourth servo frame, fifth servo frame (4.3), sixth servo frame (4.4), first servo plate (3.1), second servo plate, third servo plate (4.1), fourth servo plate, fifth servo plate (5.1), and sixth servo plate are made of black nylon material using 3D printing.

4. The flapping rotor aircraft based on servo motors to achieve multi-mode motion as described in claim 1, characterized in that: The main beam (5.3) and secondary beam (5.4) are made of carbon fiber reinforced composite material; the wing membrane (5.5) is made of polyimide material.

5. The flapping rotor aircraft based on servo motors to achieve multi-mode motion as described in claim 1, 2, 3 or 4, characterized in that: The flapping motion of a flapping rotor aircraft can be broken down into flapping, torsional, and rotational motions. Rotational motion is passive; therefore, each flapping wing has two servos to control the active flapping and torsional motions respectively. The flapping wing mode and flapping rotor mode have the same preset maximum and minimum flapping angles. The maximum upper flapping angle... Both are 50°, maximum downward angle. All are -30°; in the flapping wing mode, the upper flapping twist angle is set to 90° and the lower flapping twist angle is 0°, while in the rotor flapping mode, the upper flapping twist angle is 40° and the lower flapping twist angle is 0°; since the servo has a maximum control angle, an additional servo is added to each side to control the flapping wing flipping motion during mode switching. The additional servo is the first servo (2.5) and the second servo (2.6); the main control board (2.2) will send the motion parameters of the servo to the aforementioned 6 servo. After receiving the instructions from the main control board (2.2), the 6 servo will perform periodic rotational motion according to the set function, thereby controlling the flapping wing flipping motion; The switching between flapping wing mode and flapping rotor mode must be performed when the flapping angle is at its minimum or maximum. When the flapping angle is at its minimum, the method for switching from flapping wing mode to flapping rotor mode is as follows: Represents dimensionless time, when <1. Before mode switching, the flapping wings are in flapping mode, and the two flapping wings are symmetrically installed. The third servo (3.5) drives the third servo blade (4.1), and the fourth servo drives the fourth servo blade to rotate around their respective output shafts. The rotation of the third servo blade (4.1) and the fourth servo blade drives the two flapping wings on the left and right sides, as well as the fifth servo (4.5) and the sixth servo connected to the two flapping wings, to flap vertically. When mode switching is required, i.e. =1~2, enter the mode conversion transition stage; the sixth servo will drive the sixth servo blade to rotate at an angle of 180°; since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the side of the sixth servo will also rotate at an angle of 180°, while the flapping wing on the side controlled by the fifth servo (4.5) remains in its original state and does not rotate. Therefore, by only rotating the flapping wing on the side controlled by the sixth servo, the original symmetrical flapping wing mode is transformed into a centrally symmetrical flapping rotor motion mode; at the same time, the fifth servo (4.5) and the sixth servo, which control the twisting motion of the flapping wing, will also change the control twisting angle setting from 0° to 90° in the flapping wing mode to 140° (40° on the other side) in the flapping rotor mode. >2, the mode transition phase ends, and the flapping wing then moves in flapping rotor mode; The method for switching from flapping rotor mode to flapping wing mode when the flapping angle is at its minimum is as follows: When <1. Before mode switching, the flapping wings are in flapping rotor mode, and the two flapping wings are in a centrally symmetrical installation state. The third servo (3.5) drives the third rudder (4.1), and the fourth servo drives the fourth rudder to rotate around their respective servo output shafts. The rotation of the third rudder (4.1) and the fourth rudder drives the two flapping wings on the left and right sides, as well as the fifth servo (4.5) and the sixth servo connected to the two flapping wings, to flap vertically. During the vertical flapping process, the flapping wings will generate vertical lift and two opposing thrusts, thus generating a couple centered on the wing's symmetry point, causing the flapping wings to rotate around the central axis under the action of the couple. When mode switching is required, i.e. =1~2, enter the mode conversion transition stage; the sixth servo will drive the sixth servo blade to rotate at an angle of 180°; since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the side of the sixth servo will also rotate at an angle of 180°, while the flapping wing on the side controlled by the fifth servo (4.5) will remain in its original state and will not rotate. Therefore, by rotating only the flapping wing on the side controlled by the sixth servo, the original centrally symmetrical flapping rotor mode will be transformed into a face-symmetrical flapping wing motion mode; at the same time, the control of the twist angle of the fifth servo (4.5) and the sixth servo, which control the twisting motion of the flapping wing, will also change from 0° to 40° twist in the flapping rotor mode to 0° to 90° twist in the flapping wing mode. >2, the mode transition phase ends, and the flapping wings move in flapping wing mode; When the flapping angle is at its maximum, the method for switching from flapping wing mode to flapping rotor mode is as follows: When <1. Before mode switching, the flapping wings are in flapping mode, and the two flapping wings are symmetrically installed. The third servo (3.5) drives the third servo blade (4.1), and the fourth servo drives the fourth servo blade to rotate around their respective output shafts. The rotation of the third servo blade (4.1) and the fourth servo blade drives the two flapping wings on the left and right sides, as well as the fifth servo (4.5) and the sixth servo connected to the two flapping wings, to flap vertically. When mode switching is required, i.e. =1~2, enter the mode conversion transition stage; the sixth servo will drive the sixth servo blade to rotate at an angle of 180°; since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the side of the sixth servo will also rotate at an angle of 180°, while the flapping wing on the side controlled by the fifth servo (4.5) will remain in its original state and will not rotate. Therefore, by only rotating the flapping wing on the side controlled by the sixth servo, the original symmetrical flapping wing mode will be transformed into a centrally symmetrical flapping rotor motion mode; at the same time, the fifth servo (4.5) and the sixth servo, which control the twisting motion of the flapping wing, will also transition from 90° to 0° twisting in the flapping wing mode to 90° to 180° twisting, and then to 180° to 140° twisting in the flapping rotor mode. >2, the mode transition phase ends, and the flapping wing moves in flapping rotor mode; The method for switching from flapping rotor mode to flapping wing mode when the flapping angle is at its maximum is as follows: When <1. Before mode switching, the flapping wings are in flapping rotor mode, and the two flapping wings are in a centrally symmetrical installation state; the third servo (3.5) drives the third rudder (4.1), and the fourth servo drives the fourth rudder to rotate around their respective servo output shafts. The rotation of the third rudder (4.1) and the fourth rudder drives the left and right flapping wings, as well as the fifth servo (4.5) and the sixth servo connected to the two flapping wings, to perform a vertical flapping motion; when mode switching is required, i.e. =1~2, enter the mode conversion transition stage; the sixth servo will drive the sixth servo blade to rotate at an angle of 180°; since the sixth servo blade is connected to both the flapping wing and the sixth servo, the flapping wing on the side of the sixth servo will also rotate at an angle of 180°, while the flapping wing on the side controlled by the fifth servo (4.5) remains in its original state and does not rotate. Therefore, by rotating only the flapping wing on the side controlled by the sixth servo, the original centrally symmetrical flapping rotor mode is transformed into a face-symmetrical flapping wing motion mode; at the same time, the fifth servo (4.5) and the sixth servo, which control the twisting motion of the flapping wing, will also change the control twisting angle setting from 0° to 40° in the flapping rotor mode to 40° to 180°, and finally change to 180° to 90° in the flapping wing mode. >2, the mode transition phase ends, and the flapping wings move in flapping wing mode.

6. The flapping rotor aircraft based on servo motors to achieve multi-mode motion as described in claim 5, characterized in that: The function describes the torsional motion of the flapping wing using a combination of step and harmonic functions; in both flapping rotor and flapping wing modes, the flapping angle... Twist angle and rotation angle The function is expressed as equation (1): (1) In the formula, To make the angle of the shot, if with Indicates the maximum top angle. Indicates the maximum bottom angle, then , , For the twist angle, The rotation angle is... It represents the ratio of rotational speed to beat frequency. Indicates the frequency of the beat. It indicates the beginning of a periodic motion. It indicates the end of a cycle of motion.

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