Method for calculating counter-acting force borne by human body in sitting posture kicking training process
By combining human body dynamics modeling and Lagrangian dynamics equations with Newton-Euler dynamics analysis, the problem of high cost in calculating human body reaction force in traditional methods is solved, and efficient and low-cost reaction force calculation is achieved.
Patent Information
- Application Number
- CN202510784414.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-12
- Publication Date
- 2025-09-23
AI Technical Summary
When calculating the human body's reaction force during seated leg-pushing training, existing technologies have problems such as mechanical motion capture equipment hindering user movements, optical motion capture systems being expensive and complex in data processing, and three-dimensional force platforms increasing costs.
A reaction force calculation method based on human body dynamics modeling and the motion state of fixed equipment counterweights is adopted. By measuring the lower limb parameters of the trainees, the lower limb joint angles are calculated, and the joint torque is derived using the Lagrangian dynamics equation. The reaction force is calculated by combining Newton's law and Euler dynamics analysis.
It achieves efficient calculation of the interaction force between the human body and the outside world during training without using a three-dimensional force platform, reducing costs and improving calculation accuracy.
Smart Images
Figure CN120690377A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of biomedical engineering, and in particular to a method for calculating the reaction force exerted on a human body during training using a fixed device such as a seated leg press trainer. Background Art
[0002] During the training process, if the trainer can effectively analyze the muscle force output during the entire exercise process in a timely and quantitative manner, it can help athletes, fitness enthusiasts, and patients develop effective exercise plans in terms of rehabilitation treatment, fitness training, and sports skill assessment, so as to achieve scientific training and protection. Normally, if you want to use the open source software OpenSim to calculate muscle force, you usually need to input motion data and reaction force data into the established musculoskeletal model. However, traditional methods of acquiring motion data and mechanical data have many limitations: mechanical motion capture equipment will cause great obstacles and restrictions to the user's movements; although the optical motion capture system has high accuracy, it is expensive and the workload of post-data processing is huge; if the three-dimensional force platform used to collect reaction forces is installed on the pedals or seat of the trainer, it will also significantly increase the cost. Summary of the Invention
[0003] To address these shortcomings, the present invention proposes a reaction force calculation method based on human body dynamics modeling and the motion state of the weights used in fixed equipment. To avoid the use of traditional three-dimensional force platforms, the present invention proposes a new reaction force calculation method for fixed equipment seated leg press trainers. This method applies human body dynamics modeling to obtain the motion state of the weights during exercise, combined with a human lower limb dynamics model, to determine the interaction forces between the human body and the external environment during training.
[0004] To achieve the above object, the present invention adopts the following technical solution, which includes the following steps:
[0005] Step 1: Measure the lower limb parameters of the trainees;
[0006] Step 2: Calculate the trainee's lower limb joint angles during the seated leg press training according to the trainee's lower limb parameters;
[0007] Step 3: Calculate the reaction force on the trainee's lower limbs during the seated leg push training according to the trainee's lower limb joint angles.
[0008] As another preferred embodiment, in step 1 of the present invention, the lengths of the thigh, calf, and foot of the trainee are measured (the measurement can be performed according to the "Anthropometric Methods" GB 5703-1985 and the "Chinese Adult Human Body Dimensions" GB 10000-1988);
[0009] According to the binary regression coefficient table (from "Establishment of National Standards for Human Inertia Parameters of Adults in China" published by Liu Jingmin of Beijing Sport University in 2004), a binary regression equation was used to determine thigh mass, calf mass, foot mass, thigh center of mass position, calf center of mass position, foot center of mass position, thigh moment of inertia, calf moment of inertia, and foot moment of inertia. The binary regression equation is:
[0010] y=B0+B1X1+B2X2 (1)
[0011] In Formula 1, B0, B1, and B2 are binary regression coefficients. Specific values are shown in Table 1. In Table 1, M represents males and WM represents females; X1 represents the trainee's weight (kg); X2 represents the trainee's height (mm). y represents mass, center of mass position, and moment of inertia. The moment of inertia of the foot about the coronal axis uses the default value scaled by the OpenSim musculoskeletal model.
[0012] Table 1. Coefficients of binary regression equations for mass, center of mass, and moment of inertia around the coronal axis of lower limb segments in Chinese adult males and females
[0013]
[0014] As another preferred embodiment, in step 2 of the present invention, for a fixed apparatus seated leg press trainer (the seated leg press trainer can be the Shuhua SH-6809 seated leg press trainer), after the trainee sits down on the trainer (toes facing up, ensuring that the hip joint, knee joint, and ankle joint are in the same plane, and both feet are symmetrically placed on the trainer pedal), the horizontal distance and vertical distance from the hip joint of the lower limb to the ankle joint of the foot are measured. By measuring the vertical distance H1 from the ankle joint to the ground and the vertical distance H2 from the hip joint to the ground, the vertical distance H=H1-H2 (m) of the lower limb of the human body between the trainer chair and the pedal is calculated by subtracting the two. The horizontal distance L (m) from the hip joint of the human lower limb to the ankle joint of the foot on the trainer is obtained by measuring the horizontal distance from the hip joint to the trainer pedal minus the horizontal distance from the ankle joint to the pedal.
[0015] During training, the upper limbs remain stationary, and the feet remain attached to the pedals throughout the entire training process. The trainer pedals reciprocate linearly along their trajectory. Using the lengths of the lower limbs (thigh d1, calf d2), the linear distance C of the load, and the horizontal (L) and linear distance (H) from the hip to the knee joint on the seated trainer, kinematic formulas were established to determine the values of angles α1 and α2.
[0016] Furthermore, the equation for solving the angle is:
[0017]
[0018] Furthermore, the angles α1 and α2 are converted into the lower limb hip joint angle θ1, knee joint angle θ2, and ankle joint angle θ3 during training. The conversion process is:
[0019]
[0020] As another preferred embodiment, in step 3 of the present invention, the Lagrangian dynamic equations during the seated leg press training are established to obtain expressions for the joint torques of the lower limb hip, knee, and ankle joints. The derivation process is as follows:
[0021] The Lagrangian function L is defined as the difference between the kinetic energy K and the potential energy P of the system (K and P can be expressed in any convenient coordinate system), that is,
[0022] L=kP (4)
[0023] The system dynamics equation, namely the Lagrange equation, is as follows:
[0024]
[0025] Among them, q represents the generalized coordinates of the rigid body in the system, which are the hip joint angle θ1, knee joint angle θ2, ankle joint angle θ3 (q i =θ i , i=1, 2, 3), the angle is positive if it rotates counterclockwise and negative if it rotates clockwise. Represents the generalized velocity of the rigid body in the system, which is the derivative of the generalized coordinate with respect to time T i is the joint torque of the i-th joint.
[0026] The dynamics analysis of the three-link system of the lower limbs during seated leg-pushing training was conducted, and the kinetic energy and potential energy of the thigh, calf, foot, and load were calculated respectively.
[0027] Location of the thigh center of mass:
[0028]
[0029] Kinetic energy and potential energy of the thigh:
[0030]
[0031] P1=m1gy1 (8)
[0032] Location of the center of mass of the lower leg:
[0033]
[0034] Kinetic energy and potential energy of the lower leg:
[0035]
[0036] P2=m2gy2 (11)
[0037] Position of the foot's center of mass:
[0038]
[0039] Kinetic and potential energy of the foot:
[0040]
[0041] y4=C+x3-c (14)
[0042] During the seated leg press exercise, the trainer load moves only up and down along the Y-axis. The distance moved along the positive Y-axis during exercise is equal to the distance the foot moves along the positive X-axis. The movement speed is equal to the horizontal speed of the foot's center of mass. The initial position of the foot's center of mass on the X-axis is x3 = c, and the position after the exercise is x3. Assume that the initial position of the load on the Y-axis is C. The load movement expression is:
[0043] y4=C+x3-c (15)
[0044]
[0045] Kinetic and potential energy of the load:
[0046]
[0047] P4=m4gy4 (18)
[0048] Add the kinetic energy and potential energy of the thigh, calf, foot, and load counterweight together to obtain the total kinetic energy K and total potential energy P of the system. Subtract the total kinetic energy from the total potential energy to obtain the Lagrangian function L of the system:
[0049]
[0050] Derive the Lagrangian equations of dynamics T1, T2, T3. Use the Lagrangian function L to generalize the coordinates (θ1, θ2, θ3) and the generalized velocity Taking the partial derivative we get and Then use Derived with respect to time t. Substituted into the Lagrange equation (Formula 5), the dynamic equations for the hip joint torque (T1), knee joint torque (T2), and ankle joint torque (T3) are derived.
[0051] In the following formulas, some formulas are simplified for the convenience of description, and θ3-θ2+θ1 is simplified to θ 3-2+1 ,Will Simplified to Simplify cos(θ1+θ2+θ3) to
[0052] The dynamic equation of hip joint torque T1 is:
[0053]
[0054] The dynamic equation of knee joint torque T2 is:
[0055]
[0056] The dynamic equation of ankle joint torque T3 is:
[0057]
[0058] Among them, I1, I2, and I3 are the moments of inertia of the thigh, calf, and foot respectively; are the first differential of the angle, representing the angular velocity; are the second derivatives of the angles, representing angular velocity. The hip joint angle θ1 is the angle between the thigh L1 and the X-axis, the knee joint angle θ2 is the angle between the thigh L2 and the shank L3, and the ankle joint angle θ3 is the angle between the shank L2 and the foot L3 (unit: rad). d1 and d2 represent the lengths of the thigh and shank, respectively (unit: m), r1 represents the distance from the hip joint's center of rotation to the thigh's center of mass, r2 represents the distance from the knee joint's center of rotation to the shank's center of mass, and r3 represents the distance from the ankle joint's center of rotation to the foot's center of mass (unit: m). m1, m2, and m3 represent the weights of the shank, thigh, and foot, respectively. The mass of half the trainer's load counterweight is m4 (unit: kg). T1 represents the hip joint torque, T2 represents the knee joint torque, and T3 represents the ankle joint torque (unit: NM).
[0059] As another preferred embodiment, in step 3 of the present invention, the calculation process of the horizontal reaction force exerted on the foot during training is as follows:
[0060] The distance the pedal moves horizontally is the same as the distance the load moves vertically upwards, and the pedal's motion is consistent with the load. Figure 6 As shown. F1 is the horizontal component of the force applied by the foot to the pedal, and F2 is the gravity of the load applied to the pedal through the steel cable. The acceleration during pedal training is a, and the equation is:
[0061] F1-F2=ma (23)
[0062] According to Newton's third law, the action and reaction forces between two interacting objects are equal in magnitude and opposite in direction, acting on the same straight line. The force applied by the foot to the pedal is equal in magnitude and opposite in direction to the force applied by the pedal to the foot. Figure 8As shown, is the reaction force applied by the foot to the pedal. Same size, opposite direction.
[0063]
[0064] Furthermore, the horizontal reaction force on the foot during training is analyzed.
[0065] First, a Newton-Euler inverse dynamics analysis of the seated leg press training system was performed from a force perspective. This yielded an expression for the relationship between force and joint torque. Combining this with previously acquired known quantities (angle, angular acceleration, joint torque, and horizontal force component on the foot), the vertical force component on the foot was derived. The force applied by the seat to the lower limb during training was then calculated.
[0066] and It is the horizontal and vertical components of the reaction force received by the foot in the sagittal plane during training. and The horizontal and vertical components of the force applied to the foot by the lower leg at the ankle joint are given in the equations using Newton's equations of motion and Euler's equations:
[0067]
[0068] in, and The linear acceleration of the foot's center of mass in the horizontal and vertical directions is obtained by taking the second-order derivative based on the position of the foot's center of mass.
[0069] Combined with known quantities The ankle joint torque T3 derived from the Lagrangian dynamic equation. The vertical component of the reaction force applied by the push foot to the pedal The expression:
[0070]
[0071] Calculate the force applied to the lower limbs by the seat during training. The lower limbs are affected by the horizontal force applied to the seat by the lower limbs in the sagittal plane. and vertical component The downward gravity m1g, m2g, and m3g of each part of the lower limbs, as well as the horizontal component of the reaction force applied by the lower limbs to the pedals and vertical component Get the reaction force applied by the lower limbs to the seat and The expression:
[0072]
[0073] The present invention has beneficial effects.
[0074] In traditional mechanical data acquisition, a force platform must be installed externally to obtain the interaction forces between the human body and the external environment during exercise. This invention, based on human body dynamics modeling and the motion state of fixed weights, calculates the interaction forces acting on the lower limbs during training using a seated leg press trainer. The combined calculation of steps 2 and 3 allows for the calculation of interaction forces during training, reducing the cost of obtaining the interaction forces between the human body and the external environment. BRIEF DESCRIPTION OF THE DRAWINGS
[0075] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The scope of protection of the present invention is not limited to the following description.
[0076] Figure 1 Schematic diagram of the measurement positions of various parts of the human lower limbs.
[0077] Figure 2 and Figure 3 Schematic diagram of lower limb joint angle calculation during training.
[0078] Figure 4 This is a system diagram of the seated leg press training process.
[0079] Figure 5 This is a flow chart for calculating the reaction force on the sagittal plane of the lower limbs during training.
[0080] Figure 6 This is the force analysis diagram of the pedal.
[0081] Figure 7 This is a force analysis diagram of the foot during training.
[0082] Figure 8 This is the overall force analysis diagram of the seated leg press training system. DETAILED DESCRIPTION
[0083] As shown in the figure, the present invention solves the reaction force exerted on the human body during the sitting leg-pushing training based on the dynamic modeling and force conditions of the human body.
[0084] As shown in Table 1 , the binary regression equation of Formula 1 was used, combined with the coefficients of the binary regression equation in Table 1 , to determine the mass, center of mass position, and moment of inertia of each link of the human lower limb.
[0085] like Figure 1 、 Figure 2 and Figure 3 As shown in Figure 2, the parameters of each link of the human lower limbs and the horizontal distance L and vertical distance H from the lower limb hip joint to the foot ankle joint when on the human trainer are measured. The changes in the lower limb joint angles during training are solved using Equations 2 and 3.
[0086] like Figure 4 As shown in the figure, the Lagrangian dynamic equations are established for the system to obtain the lower limb joint torque expressions. The parameters (joint angle, angular velocity, angular acceleration, inertia parameters) are substituted into equations (20, 21, 22) to calculate the joint torque during training.
[0087] like Figure 5 As shown in FIG, the flowchart for solving the reaction force on the sagittal plane of the lower limbs of the human body during training mainly includes the following steps:
[0088] Step 1: Figure 6 As shown, the force applied to the pedal during movement is analyzed, and Newton's second law is applied using Equation 23 to obtain the horizontal component of the force applied to the pedal by the foot. Then, Newton's third law is applied using Equation 24 to obtain the horizontal component of the reaction force received by the foot.
[0089] Step 2: Figure 7 The figure shows the force analysis diagram of the foot. Newton-Euler dynamics analysis is performed on it to obtain the expressions (25, 26, 27) between the reaction force on the foot and the ankle joint torque. Combining the ankle joint torque calculated by the Lagrangian dynamic equation and the horizontal reaction force on the foot obtained in the previous step, the vertical component of the reaction force on the foot is calculated using equations (28, 29, 30).
[0090] Step 3: Figure 8 To show the overall force situation of the lower limbs during seated leg-pushing training, the horizontal and vertical forces are combined using formulas (31, 32) to finally obtain the horizontal and vertical reaction forces exerted by the lower limbs on the seat.
[0091] It can be understood that the above specific description of the present invention is only used to illustrate the present invention and is not limited to the technical solutions described in the embodiments of the present invention. Those skilled in the art should understand that the present invention can still be modified or replaced by equivalents to achieve the same technical effects; as long as the use requirements are met, they are within the scope of protection of the present invention.
Claims
1. The method for calculating the reaction force on the human body during the sitting leg press training is characterized by The following steps are involved: Step 1: Measure the lower limb parameters of the trainees; Step 2: Calculate the trainee's lower limb joint angles during the seated leg press training according to the trainee's lower limb parameters; Step 3: Calculate the reaction force on the trainee's lower limbs during the seated leg push training according to the trainee's lower limb joint angles.
2. The method for calculating the reaction force exerted on the human body during the sitting leg kicking training according to claim 1 is characterized in that In step 1, the lengths of the trainee's thigh, calf, and foot are measured; According to the binary regression coefficient table, a binary regression equation is used to determine the thigh mass, calf mass, foot mass, thigh center of mass position, calf center of mass position, foot center of mass position, thigh moment of inertia, calf moment of inertia, and foot moment of inertia; the binary regression equation is: y=B0+B1X1+B2X2 (1) Among them, B0, B1, and B2 in formula (1) are binary regression coefficients. The specific values are shown in Table 1. In Table 1, M represents men and WM represents women; X1 is the weight of the trainee, in kg; X2 is the height of the trainee, in mm; y represents mass, center of mass position, and moment of inertia; the moment of inertia value of the foot around the coronal axis uses the default value after scaling by the OpenSim musculoskeletal model; Table 1. Coefficients of binary regression equations for mass, center of mass, and moment of inertia around the coronal axis of lower limb segments in Chinese adult males and females 3. The method for calculating the reaction force exerted on the human body during the sitting leg kicking training according to claim 1 is characterized in that In step 2, for the fixed apparatus seated leg press trainer, after the trainee sits down on the trainer, the trainee measures the horizontal and vertical distances from the hip joint of the lower limb to the ankle joint of the foot; by measuring the vertical distance H1 from the ankle joint to the ground and the vertical distance H2 from the hip joint to the ground, the vertical distance H=H1-H2 between the lower limb of the trainer chair and the pedal is calculated; by measuring the horizontal distance from the hip joint to the trainer pedal minus the horizontal distance from the ankle joint to the pedal, the horizontal distance L from the hip joint of the lower limb of the trainer to the ankle joint of the foot is obtained; During the training process, the upper limbs remain stationary, and the feet do not separate from the pedals throughout the entire process. The pedals of the trainer perform linear reciprocating motion along their trajectory. Using the lengths of the human thigh d1 and calf d2, the linear motion distance C of the load, and the horizontal distance L and linear distance H from the hip joint to the knee joint on the seated trainer, a kinematic formula is established to calculate the values of the angles α1 and α2. Furthermore, the equation for solving the angle is: Furthermore, the angles α1 and α2 are converted into the lower limb hip joint angle θ1, knee joint angle θ2, and ankle joint angle θ3 during training; the conversion process is:
4. The method for calculating the reaction force exerted on the human body during the sitting leg kicking training according to claim 1 is characterized in that In step 3, the Lagrangian dynamic equations during the seated leg press training are established to obtain expressions for the joint torques of the lower limb hip joint, knee joint, and ankle joint; the derivation process is as follows: The Lagrangian function L is defined as the difference between the kinetic energy K and the potential energy P of the system, that is, L=KP (4) The system dynamics equation, namely the Lagrange equation, is as follows: Among them, q represents the generalized coordinates of the rigid body in the system, which are the hip joint angle θ1, knee joint angle θ2, ankle joint angle θ3, q i =θ i , the angle is positive if it rotates counterclockwise and negative if it rotates clockwise; Represents the generalized velocity of the rigid body in the system, which is the derivative of the generalized coordinate with respect to time T i is the joint torque of the i-th joint; The dynamics analysis of the lower limb three-link system during the seated leg press training was conducted, and the kinetic energy and potential energy of the thigh, calf, foot, and load were calculated respectively. Location of the thigh center of mass: Kinetic energy and potential energy of the thigh: P1=m1gy1 (8) Location of the center of mass of the lower leg: Kinetic energy and potential energy of the lower leg: P2=m2gy2 (11) Position of the foot's center of mass: Kinetic and potential energy of the foot: y4=C+x3-c (14) During the seated leg press training, the load of the trainer moves only up and down along the Y-axis. The distance moved along the positive direction of the Y-axis during the movement is equal to the distance moved along the positive direction of the X-axis by the foot. The movement speed is equal to the horizontal speed of the center of mass of the foot. The initial position of the center of mass of the foot on the X-axis is x3 = c, and the position after the movement is x3. Assume that the initial position of the load on the Y-axis is C. The load movement expression is obtained as follows: y4=C+x3-c (15) Kinetic and potential energy of the load: P4=m4gy4 (18) Add the kinetic energy and potential energy of the thigh, calf, foot, and load counterweight together to obtain the total kinetic energy K and total potential energy P of the system. Subtract the total kinetic energy from the total potential energy to obtain the Lagrangian function L of the system: Derive the Lagrangian equations of dynamics T1, T2, T3; use the Lagrangian function L to generalize coordinates (θ1, θ2, θ3) and generalized velocities Taking the partial derivative we get and Then use Derivative with respect to time t; Substitute into the Lagrange equation to derive the dynamic equation expressions of hip joint torque T1, knee joint torque T2, and ankle joint torque T3; Simplify θ3-θ2+θ1 to θ 3-2+1 ,Will Simplified to Simplify cos(θ1+θ2+θ3) to The dynamic equation of hip joint torque T1 is: The dynamic equation of knee joint torque T2 is: The dynamic equation of ankle joint torque T3 is: Among them, I1, I2, and I3 are the moments of inertia of the thigh, calf, and foot respectively; are the first differential of the angle, representing the angular velocity; are the second derivatives of the angles, representing angular velocity; the hip joint angle θ1 is the angle between the thigh L1 and the X-axis, the knee joint angle θ2 is the angle between the thigh L2 and the calf L3, and the ankle joint angle θ3 is the angle between the calf L2 and the foot L3; d1 and d2 represent the lengths of the thigh and calf, respectively, r1 represents the distance from the hip joint rotation center to the thigh center of mass, r2 represents the distance from the knee joint rotation center to the calf center of mass, and r3 represents the distance from the ankle joint rotation center to the foot center of mass; m1, m2, and m3 represent the weight of the calf, thigh, and foot, respectively, and the mass of half of the trainer's load counterweight is m4; T1 represents the torque of the hip joint, T2 represents the torque of the knee joint, and T3 represents the torque of the ankle joint.
5. The method for calculating the reaction force exerted on the human body during the sitting leg kicking training according to claim 1 is characterized in that In step 3, the calculation process of the horizontal reaction force on the foot during training is as follows: The distance the pedal moves horizontally is the same as the distance the load moves vertically upwards, and the pedal's motion state is consistent with the load. For the horizontal force analysis of the pedal, F1 is the horizontal component of the force applied by the foot to the pedal, and F2 is the weight of the load applied to the pedal through the cable. The acceleration during pedal training is a, and the equation is: F1-F2=ma (23) According to Newton's third law, the action and reaction forces between two interacting objects are equal in magnitude and opposite in direction, acting in the same straight line; the force exerted by the foot on the pedal is equal in magnitude and opposite in direction to the force exerted by the pedal on the foot; is the reaction force applied by the foot to the pedal; F1 and Same size, opposite direction; Furthermore, the horizontal reaction force on the foot during training is analyzed; First, a Newton-Euler inverse dynamics analysis of the seated leg press training system was performed from the perspective of force, and the expression between force and joint torque was obtained. Combining the angle, angular acceleration, joint torque, and horizontal force component of the foot, the vertical force component of the foot was derived. Then calculate the force applied to the lower limbs at the seat during the training; and are the horizontal and vertical components of the reaction force received by the foot in the sagittal plane during training; and The horizontal and vertical components of the force applied to the foot by the lower leg at the ankle joint are given by Newton's equations of motion and Euler's equations: in, and The linear acceleration of the foot's center of mass in the horizontal and vertical directions is obtained by taking the second-order derivative based on the position of the foot's center of mass; Combined with known quantities The ankle joint torque T3 derived from the Lagrangian dynamic equation; the vertical component of the reaction force applied by the foot to the pedal is derived The expression: Calculate the force applied to the lower limbs by the seat during training. The lower limbs are affected by the horizontal force applied to the seat by the lower limbs in the sagittal plane. and vertical component The downward gravity m1g, m2g, and m3g of each part of the lower limbs, as well as the horizontal component of the reaction force applied by the lower limbs to the pedals and vertical component Get the reaction force applied by the lower limbs to the seat and The expression: