Arm tremor suppression method based on inerter nonlinear energy trap
By utilizing the energy transfer mechanism of the inertial capacitive nonlinear energy trap, the limitations of existing wearable devices in suppressing arm tremors in terms of effectiveness and adaptability are solved, achieving stable and low-cost tremor suppression and improved comfort.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-29
- Publication Date
- 2026-04-03
AI Technical Summary
Existing wearable devices have shortcomings in terms of quality, structure, and control range, resulting in limited effectiveness and adaptability in suppressing arm tremors. Drug treatment has significant side effects and reduced efficacy, while surgical treatment is costly and risky.
An energy transfer mechanism using an inertial capacitive nonlinear energy trap is employed. By connecting an inertial capacitive element in series with a spring and a damper, an inertial capacitive nonlinear energy trap is constructed. A four-degree-of-freedom arm tremor motion equation is established, and the nonlinear energy transfer and dissipation characteristics are used to suppress arm tremor.
It provides stable and widely adaptable tremor suppression effects for different tremor frequencies, requires no external energy input, has a simple system structure, low maintenance costs, reduces vibration amplitude, and improves comfort and freedom of movement.
Smart Images
Figure CN121789901A_ABST
Abstract
Description
Technical Field
[0001] This patent relates to the field of biomedical engineering, and in particular to a method for suppressing arm tremors based on an inertial capacitive nonlinear energy trap. Background Technology
[0002] Arm tremor is an involuntary tremor that occurs in the upper arm, forearm, and hand while the limb is at rest, primarily found in patients with Parkinson's disease. Although this symptom is generally not life-threatening, it severely impacts patients' daily living abilities, causing difficulty in basic activities such as writing, eating, and dressing, leading to a series of quality-of-life problems. Existing treatments mainly include three categories: drug therapy, physical rehabilitation, and surgical treatment. Drug therapy often has side effects, and its effectiveness diminishes over time; surgical treatment, while effective, is costly and carries associated risks. In contrast, physical rehabilitation, as a non-invasive treatment method, has been widely used in recent years, especially in tremor suppression. Wearable devices, as part of physical rehabilitation, alleviate tremors through external mechanical action or electrical stimulation, and have become an important means of tremor suppression. These devices are easy to wear and use, and can help patients reduce tremors without relying on drugs or surgery. However, existing wearable devices have certain shortcomings in terms of quality, structure, and control range, limiting their effectiveness and adaptability. To address the shortcomings of existing technologies, this invention proposes an arm tremor suppression method based on an inertial capacitive nonlinear energy trap, utilizing the special energy transfer mechanism of a nonlinear energy trap. Summary of the Invention
[0003] The purpose of this invention is to provide a method for suppressing arm tremor based on an inertial capacitive nonlinear energy trap. By introducing an inertial capacitive nonlinear energy trap, the tremor energy is effectively transferred and dissipated, avoiding frequency tuning and adapting to changes in different tremor frequencies, thereby providing a stable and good tremor suppression effect to improve the patient's quality of life.
[0004] An arm tremor suppression method based on an inertial capacitive nonlinear energy trap is proposed. This method constructs an arm tremor model incorporating the inertial capacitive nonlinear energy trap and utilizes the energy transfer mechanism and dissipation characteristics of the nonlinear energy trap to suppress the arm's vibration amplitude. The method includes the following steps:
[0005] Step 1: Based on the biomechanical characteristics of the human body and the mechanism of resting tremor, establish a three-degree-of-freedom motion equation for the human arm considering the nonlinear characteristics of muscles. With the shoulder joint as the origin, the angular displacements of the upper arm, forearm, and hand in the established coordinate system are θ1, θ2, and θ3, respectively. Then, the velocities of the center of mass of each part of the arm, v1, v2, and v3, can be expressed as follows:
[0006] (1)
[0007] The coefficients l1, l2, and l3 mentioned above represent the lengths of the three parts of the arm, and a1, a2, and a3 represent the distances from the joints of each part to the center of mass of the corresponding limb.
[0008] The kinetic energy T of the arm system is
[0009] (2)
[0010] The coefficients m1, m2, and m3 mentioned above represent the masses of the three parts of the arm, and I1, I2, and I3 represent the moments of inertia of the three parts of the arm.
[0011] The potential energy V of the arm system is
[0012] (3)
[0013] The coefficients k1, k2, and k3 mentioned above represent the muscle stiffness of the shoulder, elbow, and wrist joints, respectively. s This indicates the stiffness of the biceps brachii.
[0014] The Rayleigh dissipation function R of the arm system is
[0015] (4)
[0016] The coefficients c1, c2, and c3 mentioned above represent the muscle damping of the shoulder, elbow, and wrist joints, respectively. s This indicates the damping of the biceps brachii.
[0017] The amplitude of vibration exhibited by the human arm during resting tremor is relatively small, therefore it has sinθ. i ≈ θ i cosθ i ≈1 (i = 1, 2, 3), combining equations (1), (2), (3), and (4), we can obtain the three-degree-of-freedom dynamic equation of the arm as follows:
[0018] (5)
[0019] The above coefficient θ s1 θ s2 and θ s3 F1, F2, and F3 represent the angular displacement changes at three points on the arm, respectively. The remaining coefficients have the following meanings:
[0020]
[0021] Step 2: Based on the mechanical properties of the inertial capacitive element, it is used as the mass component of a traditional nonlinear energy trap to construct an inertial capacitive nonlinear energy trap. Its dynamic equation is as follows:
[0022] (6)
[0023] The coefficient 'b' above represents the capacitance coefficient, which can be adjusted as needed. c b k represents the damping of the inertial capacitive nonlinear energy trap. b The stiffness of the capacitive nonlinear energy trap is represented by the inertial element, which is implemented as a ball screw in this model.
[0024] Step 3: Establish the four-DOF arm tremor motion equations including the inertial capacitive nonlinear energy trap. Since the object to be vibration damped is the human arm, the inertial capacitive nonlinear energy trap is installed near the wrist joint to avoid affecting the normal movement of the arm. The influence of mass on the arm's motion behavior is also considered. The final four-DOF arm tremor motion equations including the inertial capacitive nonlinear energy trap are as follows:
[0025] (7)
[0026] The above coefficient l b This represents the distance (m) from the elbow joint to the installation location of the inertial capacitive nonlinear energy trap. b x represents the mass of the capacitive nonlinear energy trap, and x2 represents the displacement of the capacitive nonlinear energy trap in the vertical direction of the forearm.
[0027] Step 4: Based on the arm tremor motion equation established in Step 3, considering the influence of tremor frequency, calculate the dynamic response of each joint at different tremor frequencies; construct a bifurcation diagram of the three joints of the arm with the excitation frequency as the abscissa and the vibration amplitude of each joint as the ordinate, apply bifurcation theory to perform stability analysis on the arm tremor system, identify the stability region of each joint and the possible bifurcation phenomena, analyze the transformation between periodic solutions and chaotic solutions, and then determine the stability boundary of the system and the nonlinear behavior under tremor frequency changes.
[0028] Step 5: Solve for an approximate solution to equation (7) using the harmonic balance method. Introduce the following parameter transformations to equation (7).
[0029] (8)
[0030] The system's equations of motion can then be transformed into,
[0031] (9)
[0032] Since resting arm tremor is a low-frequency, small-amplitude vibration, the first harmonic approximation is sufficient to characterize its main vibrational characteristics. Therefore, only the first harmonic component is retained, and the approximate solution of the equation is assumed to be...
[0033] (10)
[0034] The above coefficient aij and b ij (i, j=1,2,3,4) represents the harmonic coefficients to be determined.
[0035] Substituting the approximate solution into equation (9), and categorizing and rearranging the cosine and sine terms in the equation, we can obtain a set of nonlinear equations concerning the harmonic coefficients and the excitation frequency; among them, the set of equations concerning the cosine terms is as follows:
[0036] (11)
[0037] The system of equations concerning the sine term is as follows:
[0038] (12)
[0039] This allows us to obtain the response amplitudes of each joint and the inertial capacitive nonlinear energy trap in the human arm.
[0040] (13)
[0041] Numerical simulation was used to study steps 4 and 5. By comparing the flutter stability and response amplitude before and after the installation of the capacitive nonlinear energy trap on the arm, the control effect of the capacitive nonlinear energy trap was evaluated, thereby verifying its practical application effect in flutter suppression.
[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0043] (1) In terms of control methods, this invention adopts a passive control method, which requires no external energy input and avoids the problems of high energy consumption, complex control algorithms and adjustment delays in active control systems. Passive control is performed through a nonlinear mechanism, resulting in a simple system structure, high stability and low maintenance cost.
[0044] (2) Regarding the tremor suppression effect, this invention introduces a nonlinear energy trap energy transfer and dissipation mechanism, which can effectively transfer tremor energy to an additional energy dissipation channel, reducing the amplitude of arm tremors. This method does not require frequency tuning, is widely adaptable to different tremor frequencies, and provides better tremor suppression effect and stronger adaptability.
[0045] (3) In terms of arm comfort, the present invention provides additional inertial effect through inertial capacitive elements, effectively reducing the overall mass of the system, reducing interference with normal arm activities, and ensuring that the patient’s natural movement is not affected during tremor suppression, thereby improving comfort and freedom of movement. Attached Figure Description
[0046] Figure 1 This is a simplified system structure diagram of the arm-inertial capacitive nonlinear energy trap of the present invention;
[0047] Figures 2(a) to (c) show the bifurcation comparison of different joints of the present invention before and after the installation of the inertial capacitive nonlinear energy trap. Figures (a) to (c) correspond to the shoulder joint, elbow joint and wrist joint of the arm, respectively.
[0048] Figures 3(a) to (c) are phase diagram comparisons of the different joints of the present invention before and after the installation of the inertial capacitive nonlinear energy trap. Figures (a) to (c) correspond to the shoulder joint, elbow joint and wrist joint of the arm, respectively.
[0049] Figures 4(a) to (c) show the amplitude-frequency response comparison of different joints of the present invention before and after the installation of the inertial capacitive nonlinear energy trap. Figures (a) to (c) correspond to the shoulder joint, elbow joint and wrist joint of the arm, respectively.
[0050] Figure 1 The numbers in the text are explained below:
[0051] 1 represents the shoulder joint, 2 represents the upper arm, 3 represents the elbow joint, 4 represents the forearm, 5 represents the wrist joint, 6 represents the hand, and 7 represents the biceps brachii. Detailed Implementation
[0052] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.
[0053] like Figure 1 As shown, a mechanical model of a human arm with an inertial capacitive nonlinear energy trap is established with the shoulder joint 1 as the origin coordinate. The arm moves in the xy plane. This model mainly consists of the upper arm 2, forearm 4, hand 6, and inertial capacitive nonlinear energy trap, neglecting the relative motion between the fingers and palm. The inertial capacitive nonlinear energy trap is installed on the forearm 4, at a distance l from the elbow joint 3. b .
[0054] This patent provides a method for suppressing arm tremor based on an inertial capacitive nonlinear energy trap, including the motion equation of a four-degree-of-freedom arm with the inertial capacitive nonlinear energy trap installed, stability analysis, and vibration reduction effect study. The specific implementation steps are as follows:
[0055] Step 1: Based on the biomechanical characteristics of the human body and the mechanism of resting tremor, a three-degree-of-freedom motion equation for the human arm is established. The nonlinear characteristics of the biceps brachii are considered, and the mechanical model of the biceps brachii describes its influence on arm movement through nonlinear stiffness and nonlinear damping. For example... Figure 1 As shown, when a human arm trembles, the angular displacements of the upper arm, forearm, and hand in the established coordinate system are θ1, θ2, and θ3, respectively. Therefore, the velocities of the center of mass of each part of the arm, v1, v2, and v3, can be expressed as follows:
[0056] (1)
[0057] The coefficients l1, l2, and l3 mentioned above represent the lengths of the three parts of the arm, and a1, a2, and a3 represent the distances from the joints of each part to the center of mass of the corresponding limb.
[0058] The kinetic energy T of the arm system is
[0059] (2)
[0060] The coefficients m1, m2, and m3 mentioned above represent the masses of the three parts of the arm, and I1, I2, and I3 represent the moments of inertia of the three parts of the arm. The first term in equation (2) represents the kinetic energy of the upper arm, the second term represents the kinetic energy of the forearm, and the third term represents the kinetic energy of the hand.
[0061] The potential energy V of the arm system is
[0062] (3)
[0063] The coefficients k1, k2, and k3 mentioned above represent the muscle stiffness of the shoulder, elbow, and wrist joints, respectively. s The first four terms in equation (3) represent the elastic potential energy of the upper arm, forearm, hand, and biceps brachii, respectively, while the remaining three terms represent the gravitational potential energy of the upper arm, forearm, and hand, respectively.
[0064] The Rayleigh dissipation function R of the arm system is
[0065] (4)
[0066] The coefficients c1, c2, and c3 mentioned above represent the muscle damping of the shoulder, elbow, and wrist joints, respectively. s The four terms in equation (4) represent the damping work done by the upper arm, forearm, hand, and biceps brachii, respectively.
[0067] The amplitude of vibration exhibited by the human arm during resting tremor is relatively small, therefore it has sinθ. i ≈ θ i cosθ i ≈1 (i = 1, 2, 3). Furthermore, the vibration rhythm of the arm is close to a sine wave, therefore the external torques acting on each part of the arm are all represented by sine functions. Combining equations (1), (2), (3), and (4), the three-degree-of-freedom dynamic equations of the arm are established using the Lagrange method.
[0068] (5)
[0069] The above coefficient θ s1 θ s2 and θs3 F1, F2, and F3 represent the angular displacement changes at three points on the arm, respectively. The remaining coefficients have the following meanings:
[0070] Step 2: The inertial capacitive element can generate inertial force equivalent to tens or even hundreds of times its own mass. Utilizing this special property, it is used as the mass component of a traditional nonlinear energy trap, and connected in series with a spring and damper to construct an inertial capacitive nonlinear energy trap. Its dynamic equation is as follows:
[0071] (6)
[0072] The coefficient b above represents the capacitance coefficient, which can be adjusted according to actual needs. b k represents the damping of the inertial capacitive nonlinear energy trap. b This represents the stiffness of the capacitive nonlinear energy trap. In this model, the capacitive element is implemented as a ball screw, therefore...
[0073] (7)
[0074] Equation (6) can also be expressed as
[0075] (8)
[0076] The coefficient N above represents the multiple of the inertial force generated by the inertial capacitive element.
[0077] Step 3: Establish the four-DOF arm tremor motion equations including the inertial capacitive nonlinear energy trap. Since the object to be vibration damped is the human arm, the inertial capacitive nonlinear energy trap is installed near the wrist joint to avoid affecting the normal movement of the arm. The influence of mass on the arm's motion behavior is also considered. The final four-DOF arm tremor motion equations including the inertial capacitive nonlinear energy trap are as follows:
[0078] (9)
[0079] The above coefficient l b This represents the distance (m) from the elbow joint to the installation location of the inertial capacitive nonlinear energy trap. b Let x represent the mass of the capacitive nonlinear energy trap, and x2 represent the displacement of the capacitive nonlinear energy trap in the vertical direction of the forearm. In this system of equations, the fourth and last terms of the first equation represent the coupling between the shoulder joint and the capacitive nonlinear energy trap, the fourth and last terms of the second equation represent the coupling between the elbow joint and the capacitive nonlinear energy trap, and the last two terms of the fourth equation represent the gravitational effect of the capacitive nonlinear energy trap on the arm.
[0080] Step 4: Based on the arm tremor motion equation established in Step 3, considering the influence of tremor frequency, calculate the dynamic response of each joint at different tremor frequencies; construct a bifurcation diagram of the three joints of the arm with the excitation frequency as the abscissa and the vibration amplitude of each joint as the ordinate, apply bifurcation theory to perform stability analysis on the arm tremor system, identify the stability region of each joint and the possible bifurcation phenomena, analyze the transformation between periodic solutions and chaotic solutions, and then determine the stability boundary of the system and the nonlinear behavior under tremor frequency changes.
[0081] In this step, bifurcation diagrams and phase diagrams of each joint of the arm are plotted, and the stability changes and oscillation behavior of the arm with and without control are compared and analyzed to illustrate the tremor suppression performance of the inertial capacitive nonlinear energy trap. This step is completed using numerical methods. Considering the influence of external excitation, the initial conditions of the arm system are set to zero. The purpose of this is to simplify the calculation process, eliminate the interference of the initial state of the system on the tremor behavior, and allow the study to focus on the dynamic response of the system during tremor, thereby more clearly reflecting the impact of the invention on system stability and vibration amplitude.
[0082] Step 5: Since the harmonic balance method has high accuracy in solving the peak amplitude-frequency response of multi-degree-of-freedom nonlinear systems, the approximate solution of the motion equation (9) is obtained by using the harmonic balance method. The following parameter transformation is introduced into the motion equation (9).
[0083] (10)
[0084] The system's equations of motion can then be transformed into,
[0085] (11)
[0086] Since resting arm tremor is a low-frequency, small-amplitude vibration, the first-order harmonic approximation is sufficient to characterize its main vibrational features. By using the first-order harmonic approximation, the model can be simplified, avoiding the complex calculations of higher harmonics, thus more accurately reflecting the key characteristics of the tremor. Therefore, only the first-order harmonic component is retained, and the approximate solution of the equation is assumed to be...
[0087] (12)
[0088] The above coefficient a ij and b ij (i, j=1,2,3,4) represents the harmonic coefficients to be determined.
[0089] Substituting the approximate solution into equation (9), and categorizing and rearranging the cosine and sine terms in the equation, we can obtain a set of nonlinear equations concerning the harmonic coefficients and the excitation frequency; among them, the set of equations concerning the cosine terms is as follows:
[0090] (13)
[0091] The system of equations concerning the sine term is as follows:
[0092] (14)
[0093] This allows us to obtain the response amplitudes of each joint and the inertial capacitive nonlinear energy trap in the human arm.
[0094] (15)
[0095] The first three terms in Equation (15) represent the steady-state response amplitudes of the shoulder joint, elbow joint, and wrist joint, respectively, and the last term represents the steady-state response amplitude of the inertial capacitive nonlinear energy trap.
[0096] By solving equations (13) and (14) using software and substituting the obtained harmonic coefficients into equation (15), the amplitude-frequency response of the arm system can be obtained. It should be noted that when the human arm trembles, the amplitude of the distal joints (such as fingers and wrists) will be higher than that of the proximal joints (such as elbows and shoulders). Therefore, in the subsequent calculations, the excitation amplitude at each joint should conform to the condition F1 < F2 < F3.
[0097] To further illustrate the superiority of the present invention, the following examples are provided.
[0098] The parameters of the arm model are shown in Table 1.
[0099] Table 1 Human Arm Parameters
[0100]
[0101] The parameters of the inertial capacitive nonlinear energy trap are shown in Table 2.
[0102] Table 2 Parameters of the inertial capacitive nonlinear energy trap
[0103]
[0104] Given the excitation amplitudes of each joint as F1=0.05, F2=0.1, and F3=0.2, the initial conditions of the arm system are set to zero. Figures 2(a) to (c) show the bifurcation comparison before and after installing the capacitive nonlinear energy trap at different joints in this invention, corresponding to the stability changes of the shoulder, elbow, and wrist joints, respectively. As can be seen from Figure 2, without the method proposed in this invention, the tremors of each joint in the arm are very severe, the system exhibits obvious instability, the tremor amplitude of each joint is large, and the tremor behavior displays complex dynamic characteristics. After using the method proposed in this invention, the tremor amplitude is significantly reduced, the system stability is significantly improved, the dynamic response of each joint in the arm becomes more stable, the tremor behavior tends to be orderly, and the bifurcation phenomenon of the system is effectively suppressed. Figure 3 is a further supplement to Figure 2, showing the phase diagram comparison before and after installing the capacitive nonlinear energy trap at different joints in this invention. Through comparison, the stability changes of each joint after control can be observed more intuitively, further verifying the effectiveness of the capacitive nonlinear energy trap in improving the dynamic stability of the arm system. Specifically, after installing the inertial capacitive nonlinear energy trap, the angular displacement and angular velocity of each joint of the arm were significantly suppressed, the oscillation behavior was significantly improved, and the arm system entered a more stable state.
[0105] The two figures above analyze changes in arm stability, while the study on changes in arm tremor suppression is shown through amplitude-frequency response curves, as detailed in Figure 4. This figure compares the amplitude-frequency responses of different joints before and after the installation of the capacitive nonlinear energy trap in this invention. As can be seen from Figure 4, after using this invention, the resonance peaks of each joint in the arm are significantly reduced, and the effective suppression frequency band becomes wider, indicating that the capacitive nonlinear energy trap has a superior vibration suppression effect. Furthermore, the capacitive nonlinear energy trap also plays a significant regulatory role in the anti-resonance peaks of the elbow and wrist joints. By increasing the amplitude at the anti-resonance frequency, it avoids problems such as muscle compensatory tension, limited joint mobility, and impaired motor coordination caused by excessively low amplitude. Figures 2, 3, and 4 fully demonstrate the effectiveness of the method of this invention, which can both enhance the dynamic stability of the arm during tremors and effectively reduce the amplitude of the tremor response.
[0106] The above examples are merely for verifying and illustrating the effectiveness of the present invention, and are not intended to limit the invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from its principles, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.
Claims
1. A method for suppressing arm tremor based on an inertial capacitive nonlinear energy trap, characterized in that, A model of arm tremor incorporating an inertial capacitive nonlinear energy trap is constructed. The energy transfer mechanism and dissipation characteristics of the nonlinear energy trap are utilized to suppress the amplitude of arm vibration. The steps include: Step 1: Based on the biomechanical characteristics of the human body and the mechanism of resting tremor, establish a three-degree-of-freedom motion equation for the human arm considering the nonlinear characteristics of muscles. With the shoulder joint as the origin, the angular displacements of the upper arm, forearm, and hand in the established coordinate system are θ1, θ2, and θ3, respectively. Then, the velocities of the center of mass of each part of the arm, v1, v2, and v3, can be expressed as follows: (1) The coefficients l1, l2, and l3 mentioned above represent the lengths of the three parts of the arm, and a1, a2, and a3 represent the distances from the joints of each part to the center of mass of the corresponding limb. The kinetic energy T of the arm system is, (2) The coefficients m1, m2, and m3 mentioned above represent the masses of the three parts of the arm, and I1, I2, and I3 represent the moments of inertia of the three parts of the arm. The potential energy V of the arm system is, (3) The coefficients k1, k2, and k3 mentioned above represent the muscle stiffness of the shoulder, elbow, and wrist joints, respectively. s Indicates the stiffness of the biceps brachii; The Rayleigh dissipation function R of the arm system is, (4) The coefficients c1, c2, and c3 mentioned above represent the muscle damping of the shoulder, elbow, and wrist joints, respectively. s Indicates the damping of the biceps brachii; The amplitude of vibration exhibited by the human arm during resting tremor is relatively small, therefore it has sinθ. i ≈ θ i cosθ i ≈ 1 (i=1,2,3), combining equations (1), (2), (3), and (4), we can obtain the three-degree-of-freedom dynamic equation of the arm as follows: (5) The above coefficient θ s1 θ s2 and θ s3 F1, F2, and F3 represent the angular displacement changes at the three parts of the arm, and F1, F2, and F3 represent the excitation amplitudes at the three parts of the arm. Step 2: Based on the mechanical properties of the inertial capacitive element, it is used as the mass component of a traditional nonlinear energy trap to construct an inertial capacitive nonlinear energy trap. Its dynamic equation is as follows: (6) The coefficient 'b' above represents the capacitance coefficient, which can be adjusted as needed. c b k represents the damping of the inertial capacitive nonlinear energy trap. b The stiffness of the inertial capacitive nonlinear energy trap is represented by the ball screw in this model. Step 3: Establish the four-DOF arm tremor motion equations including the inertial capacitive nonlinear energy trap. Since the object to be vibration damped is the human arm, the inertial capacitive nonlinear energy trap is installed near the wrist joint to avoid affecting the normal movement of the arm. The influence of mass on the arm's motion behavior is also considered. The final four-DOF arm tremor motion equations including the inertial capacitive nonlinear energy trap are as follows: (7) The above coefficient l b This represents the distance (m) from the elbow joint to the installation location of the inertial capacitive nonlinear energy trap. b x represents the mass of the capacitive nonlinear energy trap, and x2 represents the displacement of the capacitive nonlinear energy trap in the vertical direction of the forearm. Step 4: Based on the arm tremor motion equation established in Step 3, considering the influence of tremor frequency, calculate the dynamic response of each joint at different tremor frequencies; construct a bifurcation diagram of the three joints of the arm with the excitation frequency as the abscissa and the vibration amplitude of each joint as the ordinate, apply bifurcation theory to perform stability analysis on the arm tremor system, identify the stability region of each joint and the possible bifurcation phenomena, analyze the transformation between periodic solutions and chaotic solutions, and then determine the stability boundary of the system and the nonlinear behavior under tremor frequency changes. Step 5: Solve for an approximate solution to equation (7) using the harmonic balance method. Introduce the following parameter transformations to equation (7). (8) The system's equations of motion can then be transformed into, (9) Since resting arm tremor is a low-frequency, small-amplitude vibration, the first harmonic approximation is sufficient to characterize its main vibrational characteristics. Therefore, only the first harmonic component is retained, and the approximate solution of the equation is assumed to be... (10) The above coefficient a ij and b ij (i, j=1,2,3,4) represents the harmonic coefficients to be determined; Substituting the approximate solution into equation (9), and categorizing and rearranging the cosine and sine terms in the equation, we can obtain a set of nonlinear equations concerning the harmonic coefficients and the excitation frequency; among them, the set of equations concerning the cosine terms is as follows: (11) The system of equations concerning the sine term is as follows: (12) This allows us to obtain the response amplitudes of each joint and the inertial capacitive nonlinear energy trap in the human arm. (13) 2. The method for suppressing arm tremor based on an inertial capacitive nonlinear energy trap according to claim 1, characterized in that: Both steps 4 and 5 are studied using numerical simulation. By comparing the flutter stability and response amplitude before and after the arm is equipped with the capacitive nonlinear energy trap, the control effect of the capacitive nonlinear energy trap is evaluated, thereby verifying its practical application effect in flutter suppression.