A method and system for optimizing production parameters of ultra-fine and highly flexible cables for dexterous hands

Abstract

The present invention relates to the field of cable production technology, and in particular to a method and system for optimizing production parameters of ultra-fine and highly flexible cables for dexterous hands. The method obtains cable twisting parameters, and generates a primary twisting constraint space, a secondary twisting constraint space, and a dual-stage twisting constraint space based on the cable twisting parameters. A hierarchical twisting parameter optimization is performed based on the primary twisting constraint space and the secondary twisting constraint space to obtain multiple primary twisting candidate parameters and multiple secondary twisting candidate parameters. Based on the dual-stage twisting constraint space, a linkage twisting parameter optimization is performed on the multiple primary twisting candidate parameters and the multiple secondary twisting candidate parameters to generate primary twisting preferred parameters and secondary twisting preferred parameters. Ultra-fine and highly flexible cable production is performed based on the primary twisting preferred parameters and the secondary twisting preferred parameters. The method achieves the technical effect of improving the efficiency of cable production parameter optimization and improving cable quality.

Description

Technical Field

[0001] The present invention relates to the technical field of cable production, and in particular to a method and system for optimizing production parameters of an extremely fine and flexible cable for dexterous hands. Background Art

[0002] Existing ultra-fine and highly flexible cables for dexterous hands must meet stringent requirements such as extreme thinness, high flexibility, and fatigue resistance. However, traditional production parameter optimization methods based on physical testing are inefficient and have high experimental costs. They are difficult to meet the cables' higher requirements for fatigue resistance and electrical performance under high-frequency and multi-directional dynamic deformation. There are technical problems such as low efficiency in cable production parameter optimization, which affects cable quality and production efficiency. Summary of the Invention

[0003] The present invention aims to solve the technical problem in the prior art that the production parameter optimization efficiency of ultra-fine and flexible cables for dexterous hands is low, which affects the cable quality and production efficiency, and provides a method and system for optimizing the production parameters of ultra-fine and flexible cables for dexterous hands to solve the problem.

[0004] The technical solution of the present invention to solve the above technical problems is as follows:

[0005] In a first aspect, the present invention provides a method for optimizing production parameters of ultra-fine and highly flexible cables for dexterous hands, comprising: obtaining cable twisting parameters, and generating a primary twisting constraint space, a secondary twisting constraint space, and a double-stage twisting constraint space according to the cable twisting parameters; performing hierarchical twisting parameter optimization based on the primary twisting constraint space and the secondary twisting constraint space to obtain multiple primary twisting candidate parameters and multiple secondary twisting candidate parameters; performing linkage twisting parameter optimization on the multiple primary twisting candidate parameters and the multiple secondary twisting candidate parameters based on the double-stage twisting constraint space to generate primary twisting preferred parameters and secondary twisting preferred parameters; and executing ultra-fine and highly flexible cable production according to the primary twisting preferred parameters and the secondary twisting preferred parameters.

[0006] Optionally, the cable twisting parameters include twisting tension, twisting pitch, twisting angle and core compression ratio.

[0007] Optionally, a first-level twisting constraint space, a second-level twisting constraint space and a second-level twisting constraint space are generated according to the cable twisting parameters, including: obtaining the first-level twisting constraint interval and the second-level twisting constraint interval of the cable twisting parameters; constructing a first-level twisting constraint space based on the first-level twisting constraint interval, and constructing a second-level twisting constraint space based on the second-level twisting constraint interval; constructing the second-level twisting constraint space based on the first-level twisting constraint interval and the second-level twisting constraint interval.

[0008] Optionally, hierarchical twisting parameter optimization is performed based on the first-level twisting constraint space and the second-level twisting constraint space to obtain multiple first-level twisting candidate parameters and multiple second-level twisting candidate parameters, including: randomly generating multiple first-level twisting initial parameters based on the first-level twisting constraint space, iteratively optimizing the multiple first-level twisting initial parameters, and generating first-level twisting candidate parameters; based on the first-level twisting candidate parameters and based on the second-level twisting constraint space, randomly generating multiple second-level twisting initial parameters, iteratively optimizing the multiple second-level twisting initial parameters, and generating second-level twisting candidate parameters; iteratively performing hierarchical twisting parameter optimization to obtain the multiple first-level twisting candidate parameters and the multiple second-level twisting candidate parameters.

[0009] Among them, based on the first-level twisting constraint space, multiple first-level twisting initial parameters are randomly generated, and the multiple first-level twisting initial parameters are iteratively optimized to generate first-level twisting candidate parameters, including: according to the first-level twisting constraint space, a plurality of first-level twisting samples are randomly selected from the historical first-level twisting production data, and a plurality of first-level twisting initial parameters are extracted, wherein the first-level twisting samples have a first-level flexibility identifier; based on the first-level twisting constraint space, the multiple first-level twisting initial parameters are randomly optimized multiple times to generate multiple random parameter optimization directions; according to the first-level flexibility identifier in the historical first-level twisting production data, the multiple random parameter optimization directions are screened, and the flexibility degradation directions are eliminated to obtain multiple selected parameter optimization directions, and the multiple selected parameter optimization directions correspond to multiple first-level twisting selected parameters; based on the multiple selected parameter optimization directions, the multiple first-level twisting selected parameters are iteratively optimized until convergence to generate the first-level twisting candidate parameters.

[0010] Among them, the multiple first-level twisting selected parameters are iteratively optimized based on multiple selected parameter optimization directions until convergence to generate the first-level twisting candidate parameters, including: obtaining a preset number of optimization intervals; according to the preset number of optimization intervals, directional iterative optimization is performed on the multiple selected parameter optimization directions based on the multiple selected parameter optimization directions to generate multiple first-level twisting intermediate parameter sequences; flexibility simulation is performed on the first-level twisting intermediate parameters in the multiple first-level twisting intermediate parameter sequences through a flexibility simulation model to simulate and generate multiple first-level simulation flexibility sequences; flexibility degradation directions are eliminated based on the multiple first-level simulation flexibility sequences, and flexibility improvement directions are retained; the directional iterative optimization, flexibility simulation and degradation direction elimination processes are repeated until the remaining parameter optimization directions converge to the same spatial point, and the parameters of the same space are output as the first-level twisting candidate parameters.

[0011] Optionally, based on the two-stage twisting constraint space, performing linked twisting parameter optimization on the plurality of primary twisting candidate parameters and the plurality of secondary twisting candidate parameters to generate primary twisting preferred parameters and secondary twisting preferred parameters includes:

[0012] Combining the plurality of primary twist candidate parameters and the plurality of secondary twist candidate parameters accordingly to generate a plurality of dual-stage twist parameter combinations;

[0013] Performing overall flexibility simulation on the multiple two-stage twisting parameter combinations using a flexibility simulation model to obtain a simulated overall flexibility corresponding to each of the two-stage twisting parameter combinations;

[0014] performing guided combination determination among the plurality of two-stage twisting parameter combinations according to the simulated overall flexibility to obtain a guided two-stage twisting parameter combination;

[0015] Based on the guiding two-stage twisting parameter combination, adjusting the remaining two-stage twisting parameter combinations to gradually approach the guiding two-stage twisting parameter combination to generate an updated two-stage twisting parameter combination;

[0016] The overall flexibility simulation, guide combination determination and parameter combination adjustment process are repeatedly performed until convergence, an optimal two-stage twisting parameter combination is obtained, and the primary twisting preferred parameters and the secondary twisting preferred parameters are extracted.

[0017] In a second aspect, the present invention provides a system for optimizing production parameters of ultra-fine and highly flexible cables for use with dexterous hands, comprising:

[0018] A constraint space generation module is used to obtain cable twisting parameters and generate a first-level twisting constraint space, a second-level twisting constraint space and a double-level twisting constraint space according to the cable twisting parameters;

[0019] a hierarchical twist parameter optimization module, configured to perform hierarchical twist parameter optimization based on the primary twist constraint space and the secondary twist constraint space, and obtain a plurality of primary twist candidate parameters and a plurality of secondary twist candidate parameters;

[0020] a linked twisting parameter optimization module, configured to perform linked twisting parameter optimization on the plurality of primary twisting candidate parameters and the plurality of secondary twisting candidate parameters based on the two-stage twisting constraint space, and generate primary twisting optimal parameters and secondary twisting optimal parameters;

[0021] The twisting optimal parameter execution module is used to execute the production of ultra-fine and highly flexible cables based on the first-level twisting optimal parameters and the second-level twisting optimal parameters.

[0022] By implementing the present invention, it is possible to obtain cable twist parameters, generate a primary twist constraint space, a secondary twist constraint space, and a dual twist constraint space based on the cable twist parameters, define a reasonable range for subsequent parameter optimization, ensure that the twist parameters are explored within a feasible domain that meets performance requirements such as flexibility, and improve optimization efficiency and accuracy.

[0023] By implementing the present invention, it is possible to perform hierarchical twist parameter optimization based on the primary twist constraint space and the secondary twist constraint space, obtain multiple primary twist candidate parameters and multiple secondary twist candidate parameters, achieve hierarchical decoupling of parameter optimization, reduce the complexity of multi-parameter collaborative optimization, and improve the accuracy of local parameter optimization;

[0024] By implementing the present invention, it is possible to achieve, based on the two-stage twisting constraint space, the linkage twisting parameter optimization of the multiple first-stage twisting candidate parameters and the multiple second-stage twisting candidate parameters to generate the first-stage twisting preferred parameters and the second-stage twisting preferred parameters, thereby solving the problem of insufficient coordination between parameters in hierarchical optimization, ensuring the overall optimal matching of the two-stage twisting parameters, and improving the comprehensive performance of the cable;

[0025] By implementing the present invention, it is possible to execute the production of ultra-fine and highly flexible cables based on the primary twisting preferred parameters and the secondary twisting preferred parameters, thereby achieving an efficient transformation from parameter optimization to production execution and ensuring the mass production quality of ultra-fine and highly flexible cables.

[0026] In summary, by implementing the present invention, the technical effects of improving the efficiency of cable production parameter optimization and improving cable quality can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A schematic diagram of a process for optimizing production parameters of an ultra-fine and highly flexible cable for dexterous hands provided by the present invention;

[0028] Figure 2 This is a structural schematic diagram of a production parameter optimization system for ultra-fine and highly flexible cables for dexterous hands provided by the present invention.

[0029] Figure 3 Schematic diagram of the cross-section of the multi-stage twisted structure of an extremely thin and flexible cable for use with dexterous hands.

[0030] In the accompanying drawings, the components represented by the reference numerals are as follows:

[0031] Constraint space generation module 11, hierarchical twist parameter optimization module 12, linkage twist parameter optimization module 13, twist optimal parameter execution module 14, secondary twist core A1, primary twist core A2, primary twist conductors B1, B2, B3, B4, B5, B., B.. and so on. DETAILED DESCRIPTION

[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative efforts shall fall within the scope of protection of the present invention.

[0033] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the specified features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0034] In the description of the present invention, the term "for example" is used to mean "used as an example, illustration or illustration". Any embodiment of the present invention described as "for example" is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is given to enable any person skilled in the art to implement and use the present invention. In the following description, details are listed for the purpose of explanation. It should be understood that a person of ordinary skill in the art can recognize that the present invention can be implemented without using these specific details. In other examples, well-known structures and processes are not elaborated in detail to avoid obscuring the description of the present invention with unnecessary details. Therefore, the present invention is not intended to be limited to the embodiments shown, but is consistent with the widest scope consistent with the principles and features disclosed herein.

[0035] Example 1, as Figure 1 As shown, an embodiment of the present invention provides a method and system for optimizing production parameters of an ultra-fine and highly flexible cable for dexterous hands, including:

[0036] S100: Acquire cable twisting parameters, and generate a primary twisting constraint space, a secondary twisting constraint space, and a double-stage twisting constraint space according to the cable twisting parameters;

[0037] S200: performing hierarchical twist parameter optimization based on the primary twist constraint space and the secondary twist constraint space to obtain a plurality of primary twist candidate parameters and a plurality of secondary twist candidate parameters;

[0038] S300: Based on the two-stage twisting constraint space, perform linked twisting parameter optimization on the plurality of primary twisting candidate parameters and the plurality of secondary twisting candidate parameters to generate primary twisting optimal parameters and secondary twisting optimal parameters;

[0039] S400: Execute production of an ultra-fine and highly flexible cable according to the primary twisting preferred parameters and the secondary twisting preferred parameters.

[0040] In step S100 of the embodiment of the present application, the cable twisting parameters include twisting tension, twisting pitch, twisting angle and core compression ratio.

[0041] Stranding tension refers to the tensile force applied to the conductors during the twisting process. When multiple extremely fine conductors are twisted helically around an elastic core, controlling the tension is crucial to ensure proper tightness between the conductors. Excessive tension can lead to excessive deformation and internal stress concentration in the conductors, making them susceptible to breakage when the cable is bent. Excessive tension can loosen the strands, compromising conductivity and structural stability. Proper stranding tension ensures optimal flexibility while maintaining good conductor geometry.

[0042] The strand pitch is the distance the conductor travels axially when completing one full spiral twist. In an N+1 twist structure, the conductors spiral around the elastic core, and the pitch determines the density of this spiral. A pitch that is too small means the twist is too tight, causing stress concentration when the cable is bent; a pitch that is too large makes the twist too loose, making the conductors susceptible to relative slippage. A reasonable strand pitch ensures that stress is evenly distributed across the conductors during dynamic cable bending, thereby improving overall fatigue resistance.

[0043] The lay angle is the angle between the conductor's twist trace and the cable's central axis. This angle reflects the inclination of the conductor's helical twist and is geometrically related to the twist pitch and twist radius. If the angle is too small, the conductors are arranged nearly parallel, resulting in poor twisting. If the angle is too large, the twist is too tight, increasing axial stress. Generally, a lay angle of around 45 degrees maintains good twisting while achieving good flexibility. This is because the conductors are better able to distribute stress when subjected to bending loads.

[0044] The core compression ratio refers to the degree to which the elastic core unit is compressed during the twisting process. It is calculated as the ratio of the compression deformation to the original size. In the bionic multi-stage twisted structure of the dexterous hand cable, elastic core A1 (secondary twisted core) and elastic core A2 (primary twisted core) act as a supporting skeleton, providing elastic support for the conductors twisted around them. An appropriate compression ratio can increase the fit between the conductor and the core, improving the stability of the overall structure while maintaining the elastic properties of the core. When the cable is bent, the compressed elastic core provides a rebound force, helping the cable return to its original shape. This is particularly important for dexterous hand applications that require frequent bending.

[0045] In step S100 of the embodiment of the present application, generating a primary twisting constraint space, a secondary twisting constraint space, and a double-stage twisting constraint space according to the cable twisting parameters includes:

[0046] Obtaining a primary twist constraint interval and a secondary twist constraint interval of the cable twist parameter;

[0047] constructing a primary twisting constraint space based on the primary twisting constraint interval, and constructing a secondary twisting constraint space based on the secondary twisting constraint interval;

[0048] The double-stage twisting constraint space is constructed based on the primary twisting constraint interval and the secondary twisting constraint interval.

[0049] like Figure 3 As shown, the ultra-fine, highly flexible cable structure for dexterous hands in the embodiments of this application includes primary and secondary stranding. The primary stranding consists of several conductors (B1, B2, B3, B4, B5, etc.) spirally wound around a primary stranded core A2, forming a primary stranded unit. The secondary stranding consists of several primary stranded units spirally wound around a secondary stranded core A2, forming a complete cable. The conductors are conductive metal wires, such as copper or gold.

[0050] In the embodiment of the present application, the primary twisting constraint interval and the secondary twisting constraint interval of the cable twisting parameters are obtained in order to determine a reasonable value range of the twisting parameters, so as to provide a reasonable limit for production parameter optimization and avoid unnecessary trial and error.

[0051] Among them, in the primary twisting, the twisting tension value range needs to be greater than the "minimum tension value to maintain close contact between the conductors" and less than the "elastic limit value of the conductor material". For example, the value range can be 5-20 cN.

[0052] The twist pitch must be greater than the "minimum geometrically feasible pitch value of spiral twisting" and less than the "maximum pitch value at which the conductor does not slip." For example, the value range can be 0.8 to 2.0 mm.

[0053] The twist angle range is centered around 45 degrees, and a certain deviation range (such as ±5 degrees) is allowed. The specific deviation range can be determined based on the performance of previously produced cables. For example, the range can be 40° to 50°.

[0054] The core compression ratio must be greater than the "minimum compression ratio for the core to provide basic support" and less than the "maximum compression ratio for the core to maintain elasticity." For example, the range can be 10% to 30%.

[0055] The specific value ranges of the above cable twisting parameters, i.e., the twisting constraint intervals, can be directly obtained by those skilled in the art through experiments according to the above standards. The experimental methods are existing technologies and will not be described in detail here.

[0056] The constraint logic for the parameters in the secondary stranding is the same as that for the primary stranding, and can be obtained through the same standard experiments. However, to adapt to the structural characteristics of the inner layer skeleton, the upper limit of the stranding tension of the secondary stranding must be lower than the yield strength of the A2 material to avoid plastic deformation. The stranding pitch must be larger than the primary stranding pitch (due to the larger radius of the A2 layer), and the angle is still optimized around 45° to ensure coordinated bending of the two-stage structure. The core compression ratio (A1) must be adjusted according to the elastic modulus of the A1 material. Excessive compression ratios may make A1 too rigid, affecting overall flexibility.

[0057] For example, the stranding tension in the secondary stranding may be 8-30 cN; the stranding pitch may be 1.5-3.5 mm; the stranding angle may be 40°-50°; and the core A1 compression ratio may be 15%-25%.

[0058] By using the above method, the primary twist constraint interval and the secondary twist constraint interval of the cable twist parameters can be obtained.

[0059] Next, we need to construct a constraint space based on the aforementioned primary and secondary twist constraint intervals. Specifically, we combine the feasible intervals of the four primary twist parameters (twisting tension, twist pitch, twist angle, and core compression ratio) into a four-dimensional space, requiring all parameters to simultaneously satisfy their respective constraints, namely:

[0060] The stranding tension must be within the range of [minimum tension value for primary stranding, maximum tension value for primary stranding], that is, greater than or equal to the minimum tension value to ensure close contact between conductors, and less than or equal to the elastic limit value of the conductor material, to avoid excessive deformation or breakage of the conductor due to excessive tension, and loose stranding structure due to too little tension.

[0061] The twist pitch must be within the range of [minimum pitch value for primary twisting, maximum pitch value for primary twisting], that is, greater than or equal to the minimum geometrically feasible pitch value for spiral twisting (to avoid bending stress concentration caused by over-dense twisting) and less than or equal to the maximum pitch value without relative slip between conductors (to ensure uniform stress distribution during dynamic bending).

[0062] The twist angle must be within the range of [45°-Δθ, 45°+Δθ] (Δθ is the allowable deviation angle), and should be optimized with 45 degrees as the center to balance the twist tightness and stress dispersion ability, avoiding poor twisting effect due to a too small angle or increased axial stress due to an excessively large angle.

[0063] The core compression ratio must be within the range of [minimum compression ratio of the primary stranded core, maximum compression ratio of the primary stranded core], that is, greater than or equal to the minimum compression ratio of the primary stranded core A2 to provide basic support stiffness, and less than or equal to the maximum compression ratio of the core to maintain elastic properties, to ensure that the primary stranded core A2 provides appropriate elastic support and fit for the conductors stranded around it.

[0064] Based on the same logic, a secondary twisting constraint space can be constructed, which will not be described here.

[0065] Furthermore, it is necessary to construct a two-stage twist constraint space. This two-stage twist constraint space must simultaneously meet the parameter conditions of the primary and secondary twist constraint spaces, and consider the synergistic effects of cross-stage parameters. For example, the mechanical transmission of the core compression ratio. The compression ratio of the secondary twist core A1 will affect the support stiffness of the inner core A2, which in turn affects the feasible tension range of the primary twist core A2 during twisting. For example, if the compression ratio of A1 is too small, resulting in insufficient support stiffness, the tension of the primary twist core A2 must be reduced to prevent structural collapse. For another example, the primary twist pitch (the pitch of the outer conductor B around A2) and the secondary twist pitch (the pitch of the inner layer A2 around A1) must satisfy the mathematical relationship of the helix angle (pitch = π × twist radius / tan(twist angle)). This ensures that the helical direction and density of the two-stage twist structure are coordinated to avoid overall distortion.

[0066] Finally, the parameters that conform to the primary and secondary twisting constraint spaces are combined into an eight-dimensional space to obtain a dual-level twisting constraint space. Parameter combinations that violate the cross-level coordination rules must be eliminated. For example, when the compression ratio of the secondary twisting core A1 falls below a certain critical value, the twisting tension of the primary twisting core A2 must be below the corresponding safe value to maintain structural stability.

[0067] In step S200 of the embodiment of the present application, hierarchical twisting parameter optimization is performed based on the primary twisting constraint space and the secondary twisting constraint space to obtain multiple primary twisting candidate parameters and multiple secondary twisting candidate parameters, including:

[0068] Based on the primary twist constraint space, randomly generating a plurality of primary twist initial parameters, and iteratively optimizing the plurality of primary twist initial parameters to generate primary twist candidate parameters;

[0069] Based on the primary twist candidate parameters and the secondary twist constraint space, a plurality of secondary twist initial parameters are randomly generated, and the plurality of secondary twist initial parameters are iteratively optimized to generate secondary twist candidate parameters;

[0070] Iteratively performing hierarchical twist parameter optimization to obtain the plurality of primary twist candidate parameters and the plurality of secondary twist candidate parameters.

[0071] The method of randomly generating a plurality of primary twisting initial parameters based on the primary twisting constraint space and iteratively optimizing the plurality of primary twisting initial parameters to generate primary twisting candidate parameters includes:

[0072] According to the primary twist constraint space, a plurality of primary twist samples are randomly selected from historical primary twist production data, and a plurality of primary twist initial parameters are extracted, wherein each of the primary twist samples has a primary flexibility identifier;

[0073] Performing multiple random direction optimizations on multiple primary twisting initial parameters based on the primary twisting constraint space to generate multiple random parameter optimization directions;

[0074] screening a plurality of random parameter optimization directions according to the first-level flexibility identifier in the historical first-level stranding production data, eliminating flexibility deterioration directions, and obtaining a plurality of selected parameter optimization directions, wherein the plurality of selected parameter optimization directions correspond to a plurality of first-level stranding selected parameters;

[0075] The plurality of primary twist selected parameters are iteratively optimized based on the plurality of selected parameter optimization directions until convergence, thereby generating the primary twist candidate parameters.

[0076] The randomly generated primary stranding initial parameters are derived from samples randomly selected from historical primary stranding production data that meet the primary stranding constraint space. This historical primary stranding production data can be a combination of primary stranding parameters for cables produced within a past period of time (e.g., one year). Each primary stranding sample corresponds to a set of primary stranding initial parameters (strand tension, strand pitch, strand angle, and core compression ratio) and is accompanied by a primary stranding flexibility indicator (e.g., fatigue life value and stress concentration factor, etc., as determined through bending testing).

[0077] Then, it is necessary to perform multiple random direction optimizations on multiple first-level twisting initial parameters to generate multiple random parameter optimization directions. Specifically, for each first-level twisting initial parameter, multi-dimensional parameter perturbation can be performed within the first-level twisting constraint space. For example, for a certain initial parameter (T0, P0, θ0, ε0), where T is the twisting tension, P is the twisting pitch, θ is the twisting angle, and ε is the core compression ratio, a random perturbation vector (ΔT, ΔP, Δθ, Δε) is generated, where ΔT∈[-5%, +5%]T0 (tension fluctuation range), ΔP∈[-0.2mm, +0.2mm] (pitch fine-tuning), Δθ∈[-3°, +3°] (angle fine-tuning), and Δε∈[-5%, +5%]ε0 (compression ratio fine-tuning) is formed to form a new parameter combination (T0+ΔT, P0+ΔP, θ0+Δθ, ε0+Δε).

[0078] Then, based on the flexibility indicators of the samples in the historical data, we determine whether the perturbed parameter combination improves flexibility. For example, if the fatigue life of the historical samples corresponding to the perturbed parameters increases (indicating improved flexibility), then this optimization direction is retained; if the fatigue life decreases or the stress concentration factor increases (indicating deteriorated flexibility), then this direction is eliminated.

[0079] The iterative optimization of the plurality of first-level twisting selected parameters based on the plurality of selected parameter optimization directions until convergence to generate the first-level twisting candidate parameters includes:

[0080] Get the preset number of optimization intervals;

[0081] performing directional iterative optimization on the multiple selected parameter optimization directions based on the multiple selected parameter optimization directions according to the preset optimization interval number, to generate multiple first-level twisting intermediate parameter sequences;

[0082] Performing flexibility simulation on the first-level twisting intermediate parameters in the plurality of first-level twisting intermediate parameter sequences by using a flexibility simulation model to simulate and generate a plurality of first-level simulation flexibility sequences;

[0083] Eliminating flexibility degradation directions according to the plurality of first-level simulation flexibility sequences and retaining flexibility improvement directions;

[0084] The directional iterative optimization, flexibility simulation and degraded direction elimination processes are repeatedly performed until the remaining parameter optimization directions converge to the same spatial point, and the parameters of the same space are output as the first-level twisting candidate parameters.

[0085] In this embodiment, the preset optimization interval (denoted as N) refers to the maximum number of parameter perturbations allowed in each iteration cycle, which is used to control the optimization rhythm and computational complexity. For example, if N = 10, 10 sets of parameter perturbations are generated in each iteration, and a direction screening is performed after completing 10 flexibility simulations.

[0086] Then it is necessary to perform directional iterative optimization to generate an intermediate parameter sequence. Assuming that M selected parameter optimization directions have been screened out (such as M=4 directions: stranding tension + stranding pitch-, stranding tension-stranding pitch+, stranding angle + core compression ratio-, stranding angle-core compression ratio+), it is necessary to perform unidirectional perturbation on each direction, that is, to make slight adjustments to the parameters along the selected direction. The adjustment amplitude is related to the position of the current parameters in the constraint space. For example: If the current first-level stranding selected parameters are (T, P, θ, ε) = (12cN, 1.5mm, 45∘, 20%), and the selected direction is "tension + pitch-", then the perturbation parameters are: T′ = T + α*(T max −T), P′=P−α*(P−P min), θ′=θ, ε′=ε, where α is the perturbation coefficient, such as 0.05, which determines the magnitude of each perturbation; and T max 、P min Represents the maximum and minimum values ​​of the respective parameters within the constraint range. Parameters in non-selected directions are not adjusted for the time being.

[0087] In each optimization interval, N×M groups of intermediate parameters are generated (e.g., 40 groups of parameters are generated when N=10 and M=4), forming a first-level twisted intermediate parameter sequence.

[0088] Next, a flexibility simulation model is needed to perform flexibility simulation on the primary stranding intermediate parameters in the multiple primary stranding intermediate parameter sequences, generating multiple primary simulation flexibility sequences. For each set of intermediate parameters, an existing simulation model (such as a finite element analysis tool or an empirical formula model) is directly called to quickly obtain key performance indicators (indicators that can reflect the flexibility of the cable), such as the maximum equivalent stress of the conductor, which must be less than the fatigue limit of the conductor material (such as 100 MPa for copper conductors); the predicted value of the overall fatigue life of the cable (target ≥10 million cycles); the core rebound force (reflecting the elastic recovery ability of the structure, for example, the compressed primary stranded core A2 must provide a rebound force ≥15 cN after bending), and other indicators. The above-mentioned flexibility simulation method is prior art and is well known to those skilled in the art and will not be repeated here.

[0089] For example, in this embodiment, the fatigue life prediction value can be selected as the first-level simulated flexibility. In other possible implementations, other indicators that can reflect cable flexibility can also be selected as flexibility parameters, or a fused flexibility parameter can be calculated by combining multiple indicators. This will not be further described here.

[0090] Using the above example as an example, we sort the fatigue life prediction values ​​from high to low to obtain a simulation flexibility sequence, retaining the top 50% of the directions in the flexibility sequence (e.g., the top 8 of the 16 directions). For example, direction 1 (twist tension +, twist pitch -). For example, if the fatigue life prediction value for the direction ranked 50% has a corresponding fatigue life prediction value of 700, then if the fatigue life prediction value for a particular direction is 8 million cycles, retain that direction; if the fatigue life prediction value is 5 million cycles, discard that direction.

[0091] For the retained optimization directions, common trends in parameter perturbations are analyzed. For example, for the majority (over 50%) of retained directions, the twist tension is between 12-13 cN, the twist pitch is between 1.4 and 1.6 mm, the twist angle is close to 45°, and the primary twist core compression ratio is between 19% and 21%. The directional iterative optimization, flexibility simulation, and degraded direction elimination process are then repeated. The mean and variance of the parameters for the retained directions are calculated. When the standard deviation of all parameters is less than a set threshold (e.g., twist tension ≤ 0.2 cN, twist pitch ≤ 0.05 mm, twist angle ≤ 1°, and core compression ratio ≤ 0.5%), the parameters are considered converged, and the parameter optimization directions are determined to have converged to the same spatial point. The parameter mean of the converged region is taken as the candidate primary twist parameters, for example: T = 12.2 cN, P = 1.52 mm, θ = 45.1∘, ε = 20.1%.

[0092] Furthermore, it is necessary to randomly generate multiple secondary twisting initial parameters based on the primary twisting candidate parameters and the secondary twisting constraint space, and iteratively optimize the multiple secondary twisting initial parameters to generate secondary twisting candidate parameters.

[0093] Using the candidate primary stranding parameters (including strand tension, strand pitch, strand angle, and primary strand core A2 compression ratio) obtained through primary stranding constraint space optimization as known conditions, the stranding parameters of the primary strand core A2 of outer conductor B are fixed. For example, the candidate primary stranding parameters might be: strand tension 12 cN, strand pitch 1.5 mm, strand angle 45°, and primary strand core A2 compression ratio 20%.

[0094] Next, it is necessary to randomly generate multiple sets of secondary twisting initial parameters based on the secondary twisting constraint space (involving the parameters of the primary twisting core A2 twisted around the secondary twisting core A1). The twisting tension, twisting pitch, twisting angle, and core compression ratio of the secondary twisting initial parameters all take values ​​within the range of the secondary twisting constraint space, and multiple secondary twisting initial parameters are randomly generated.

[0095] Furthermore, the multiple secondary twisting initial parameters are iteratively optimized to generate secondary twisting candidate parameters. The specific iterative optimization method is the same as the iterative optimization logic of the aforementioned iterative optimization method for obtaining the primary twisting intermediate parameter sequence, which will not be repeated here.

[0096] In step S300 of the embodiment of the present application, based on the two-stage twisting constraint space, the plurality of primary twisting candidate parameters and the plurality of secondary twisting candidate parameters are subjected to linked twisting parameter optimization to generate primary twisting optimal parameters and secondary twisting optimal parameters, including:

[0097] Combining the plurality of primary twist candidate parameters and the plurality of secondary twist candidate parameters accordingly to generate a plurality of dual-stage twist parameter combinations;

[0098] Performing overall flexibility simulation on the multiple two-stage twisting parameter combinations using a flexibility simulation model to obtain a simulated overall flexibility corresponding to each of the two-stage twisting parameter combinations;

[0099] performing guided combination determination among the plurality of two-stage twisting parameter combinations according to the simulated overall flexibility to obtain a guided two-stage twisting parameter combination;

[0100] Based on the guiding two-stage twisting parameter combination, adjusting the remaining two-stage twisting parameter combinations to gradually approach the guiding two-stage twisting parameter combination to generate an updated two-stage twisting parameter combination;

[0101] The overall flexibility simulation, guide combination determination and parameter combination adjustment process are repeatedly performed until convergence, an optimal two-stage twisting parameter combination is obtained, and the primary twisting preferred parameters and the secondary twisting preferred parameters are extracted.

[0102] In the embodiment of the present application, to generate multiple two-stage twist parameter combinations, the first-stage twist candidate parameters (e.g., 3 groups) and the second-stage twist candidate parameters (e.g., 4 groups) can be combined by Cartesian product to generate M×N two-stage twist parameter combinations (e.g., 3×4=12 groups). Each combination contains the complete first-stage twist parameters (twist tension, twist pitch, twist angle, first-stage twist core compression ratio A2) and the second-stage twist parameters (twist tension, twist pitch, twist angle, second-stage twist core compression ratio A1).

[0103] Then, the performance of each two-stage combination is simulated using the aforementioned flexibility simulation model to obtain flexibility indicators (such as fatigue life prediction values). The 12 combinations are then sorted from high to low according to fatigue life, and the last 50% of the combinations are eliminated (such as retaining the top 6 groups).

[0104] Next, the combination with the highest fatigue life (representing flexibility) is selected as the guiding two-stage twisting parameter combination (such as combination 5, life of 11.2 million times). The specific parameter combination can be:

[0105] Primary stranding parameters: stranding tension 13cN, stranding pitch 1.6mm, stranding angle 44°, core compression ratio A221%;

[0106] Secondary stranding parameters: stranding tension 22cN, stranding pitch 2.8mm, stranding angle 46°, core compression ratio A123%.

[0107] Furthermore, for the remaining non-guided combinations, parameter adjustments are made in a linear direction toward the parameter values ​​of the guided combination, with each adjustment increment being 30% of the current deviation. For example, for combination 2, the primary twisting tension is 13 cN (the same as the guided combination) and the secondary twisting tension is 20 cN (the guided combination is 22 cN). After adjustment, the primary twisting tension remains unchanged, while the secondary twisting tension is 20 + (22 − 20) × 30% = 20.6 cN. The adjusted parameters must be within the two-stage twisting constraint space. Using the above method, the remaining two-stage twisting parameter combinations are adjusted to gradually approach the guided two-stage twisting parameter combination, generating an updated two-stage twisting parameter combination.

[0108] Finally, the fatigue life of the updated, adjusted two-stage twisting parameter combination is recalculated. If a combination with a higher lifespan emerges (e.g., combination 2, which has an adjusted lifespan of 11 million cycles), the original guiding combination is replaced, and all combinations are then approximated to the new guiding combination. If the fatigue life fluctuation of the guiding combination remains ≤3% over three consecutive iterations, the guiding combination is output as the optimal two-stage twisting parameter combination. The preferred primary and secondary twisting parameters are then extracted from the optimal two-stage twisting parameter combination.

[0109] In step S400 of the embodiment of the present application, the production of ultra-fine and highly flexible cables is performed according to the primary twisting preferred parameters and the secondary twisting preferred parameters, which means that the primary twisting preferred parameters (such as twisting tension, twisting pitch, twisting angle, core compression ratio A2) and the secondary twisting preferred parameters (such as twisting tension, twisting pitch, twisting angle, core compression ratio A1) determined in the above steps are driven by twisting equipment (such as a precision stranding machine) to perform production, so as to achieve efficient conversion from parameter optimization to mass production, and ensure that the cables meet the stringent requirements of dexterous hands for ultra-fineness, high flexibility and fatigue resistance. In the second embodiment, as Figure 2 As shown, based on the same inventive concept as the method for optimizing production parameters of an ultra-fine and highly flexible cable for a dexterous hand provided in Example 1, an embodiment of the present invention further provides a system for optimizing production parameters of an ultra-fine and highly flexible cable for a dexterous hand, comprising:

[0110] The constraint space generation module 11 is used to obtain the cable twisting parameters and generate the first-level twisting constraint space, the second-level twisting constraint space and the double-level twisting constraint space according to the cable twisting parameters;

[0111] a hierarchical twist parameter optimization module 12, configured to perform hierarchical twist parameter optimization based on the primary twist constraint space and the secondary twist constraint space, and obtain a plurality of primary twist candidate parameters and a plurality of secondary twist candidate parameters;

[0112] A linked twist parameter optimization module 13 is configured to perform linked twist parameter optimization on the plurality of primary twist candidate parameters and the plurality of secondary twist candidate parameters based on the two-stage twist constraint space to generate primary twist optimal parameters and secondary twist optimal parameters;

[0113] The twisting optimal parameter execution module 14 is used to execute the production of ultra-fine and highly flexible cables according to the primary twisting optimal parameters and the secondary twisting optimal parameters.

[0114] Furthermore, the constraint space generation module 11 includes the following execution steps:

[0115] Obtaining a primary twist constraint interval and a secondary twist constraint interval of the cable twist parameter;

[0116] constructing a primary twisting constraint space based on the primary twisting constraint interval, and constructing a secondary twisting constraint space based on the secondary twisting constraint interval;

[0117] The double-stage twisting constraint space is constructed based on the primary twisting constraint interval and the secondary twisting constraint interval.

[0118] Furthermore, the hierarchical twisting parameter optimization module 12 includes the following execution steps:

[0119] Based on the primary twist constraint space, randomly generating a plurality of primary twist initial parameters, and iteratively optimizing the plurality of primary twist initial parameters to generate primary twist candidate parameters;

[0120] Based on the primary twist candidate parameters and the secondary twist constraint space, a plurality of secondary twist initial parameters are randomly generated, and the plurality of secondary twist initial parameters are iteratively optimized to generate secondary twist candidate parameters;

[0121] Iteratively performing hierarchical twist parameter optimization to obtain the plurality of primary twist candidate parameters and the plurality of secondary twist candidate parameters.

[0122] The method of randomly generating a plurality of primary twisting initial parameters based on the primary twisting constraint space and iteratively optimizing the plurality of primary twisting initial parameters to generate primary twisting candidate parameters includes:

[0123] According to the primary twist constraint space, a plurality of primary twist samples are randomly selected from historical primary twist production data, and a plurality of primary twist initial parameters are extracted, wherein each of the primary twist samples has a primary flexibility identifier;

[0124] Performing multiple random direction optimizations on multiple primary twisting initial parameters based on the primary twisting constraint space to generate multiple random parameter optimization directions;

[0125] screening a plurality of random parameter optimization directions according to the first-level flexibility identifier in the historical first-level stranding production data, eliminating flexibility deterioration directions, and obtaining a plurality of selected parameter optimization directions, wherein the plurality of selected parameter optimization directions correspond to a plurality of first-level stranding selected parameters;

[0126] The plurality of primary twist selected parameters are iteratively optimized based on the plurality of selected parameter optimization directions until convergence, thereby generating the primary twist candidate parameters.

[0127] The iterative optimization of the plurality of first-level twisting selected parameters based on the plurality of selected parameter optimization directions until convergence to generate the first-level twisting candidate parameters includes:

[0128] Get the preset number of optimization intervals;

[0129] performing directional iterative optimization on the multiple selected parameter optimization directions based on the multiple selected parameter optimization directions according to the preset optimization interval number, to generate multiple first-level twisting intermediate parameter sequences;

[0130] Performing flexibility simulation on the first-level twisting intermediate parameters in the plurality of first-level twisting intermediate parameter sequences by using a flexibility simulation model to simulate and generate a plurality of first-level simulation flexibility sequences;

[0131] Eliminating flexibility degradation directions according to the plurality of first-level simulation flexibility sequences and retaining flexibility improvement directions;

[0132] The directional iterative optimization, flexibility simulation and degraded direction elimination processes are repeatedly performed until the remaining parameter optimization directions converge to the same spatial point, and the parameters of the same space are output as the first-level twisting candidate parameters.

[0133] Furthermore, the linked twisting parameter optimization module 13 includes the following execution steps:

[0134] Combining the plurality of primary twist candidate parameters and the plurality of secondary twist candidate parameters accordingly to generate a plurality of dual-stage twist parameter combinations;

[0135] Performing overall flexibility simulation on the multiple two-stage twisting parameter combinations using a flexibility simulation model to obtain a simulated overall flexibility corresponding to each of the two-stage twisting parameter combinations;

[0136] performing guided combination determination among the plurality of two-stage twisting parameter combinations according to the simulated overall flexibility to obtain a guided two-stage twisting parameter combination;

[0137] Based on the guiding two-stage twisting parameter combination, adjusting the remaining two-stage twisting parameter combinations to gradually approach the guiding two-stage twisting parameter combination to generate an updated two-stage twisting parameter combination;

[0138] The overall flexibility simulation, guide combination determination and parameter combination adjustment process are repeatedly performed until convergence, an optimal two-stage twisting parameter combination is obtained, and the primary twisting preferred parameters and the secondary twisting preferred parameters are extracted.

[0139] It should be noted that, in the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0140] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0141] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0142] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0143] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0144] Although preferred embodiments of the present invention have been described, additional changes and modifications to these embodiments may occur to those skilled in the art once the basic inventive concepts become known.

[0145] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the present invention and its equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for optimizing production parameters of ultra-fine and highly flexible cables for dexterous hands, characterized in that: The method comprises: Acquire cable twisting parameters, including twisting tension, twisting pitch, twisting angle, and core compression ratio, and generate a primary twisting constraint space, a secondary twisting constraint space, and a double-stage twisting constraint space according to the cable twisting parameters, including: Obtaining a primary twist constraint interval and a secondary twist constraint interval of the cable twist parameter; constructing a primary twisting constraint space based on the primary twisting constraint interval, and constructing a secondary twisting constraint space based on the secondary twisting constraint interval; Constructing the double-stage twisting constraint space based on the primary twisting constraint interval and the secondary twisting constraint interval; Performing hierarchical twist parameter optimization based on the primary twist constraint space and the secondary twist constraint space to obtain a plurality of primary twist candidate parameters and a plurality of secondary twist initial parameters; Based on the two-stage twisting constraint space, performing linkage twisting parameter optimization on the plurality of primary twisting candidate parameters and the plurality of secondary twisting candidate parameters to generate primary twisting optimal parameters and secondary twisting optimal parameters; According to the primary twisting preferred parameters and the secondary twisting preferred parameters, ultra-fine and highly flexible cables are produced.

2. The method according to claim 1, characterized in that Performing hierarchical twisting parameter optimization based on the primary twisting constraint space and the secondary twisting constraint space to obtain a plurality of primary twisting candidate parameters and a plurality of secondary twisting initial parameters includes: Based on the primary twist constraint space, randomly generating a plurality of primary twist initial parameters, and iteratively optimizing the plurality of primary twist initial parameters to generate primary twist candidate parameters; Based on the primary twist candidate parameters and the secondary twist constraint space, a plurality of secondary twist initial parameters are randomly generated, and the plurality of secondary twist initial parameters are iteratively optimized to generate secondary twist candidate parameters; The hierarchical twist parameter optimization is iteratively performed to obtain the plurality of primary twist candidate parameters and the plurality of secondary twist initial parameters.

3. The method according to claim 2, characterized in that Based on the primary twist constraint space, a plurality of primary twist initial parameters are randomly generated, and the plurality of primary twist initial parameters are iteratively optimized to generate primary twist candidate parameters, including: According to the primary twist constraint space, a plurality of primary twist samples are randomly selected from historical primary twist production data, and a plurality of primary twist initial parameters are extracted, wherein each of the primary twist samples has a primary flexibility identifier; Performing multiple random direction optimizations on multiple primary twisting initial parameters based on the primary twisting constraint space to generate multiple random parameter optimization directions; screening a plurality of random parameter optimization directions according to the first-level flexibility identifier in the historical first-level stranding production data, eliminating flexibility deterioration directions, and obtaining a plurality of selected parameter optimization directions, wherein the plurality of selected parameter optimization directions correspond to a plurality of first-level stranding selected parameters; The plurality of primary twist selected parameters are iteratively optimized based on the plurality of selected parameter optimization directions until convergence, thereby generating the primary twist candidate parameters.

4. The method according to claim 3, characterized in that Iteratively optimizing the plurality of first-level twisting selected parameters based on the plurality of selected parameter optimization directions until convergence to generate the first-level twisting candidate parameters includes: Get the preset optimization interval times; performing directional iterative optimization on the multiple selected parameter optimization directions based on the multiple selected parameter optimization directions according to the preset optimization interval number, to generate multiple first-level twisting intermediate parameter sequences; Performing flexibility simulation on the first-level twisting intermediate parameters in the plurality of first-level twisting intermediate parameter sequences by using a flexibility simulation model to simulate and generate a plurality of first-level simulation flexibility sequences; Eliminating flexibility degradation directions according to the plurality of first-level simulation flexibility sequences and retaining flexibility improvement directions; The directional iterative optimization, flexibility simulation and degraded direction elimination processes are repeatedly performed until the remaining parameter optimization directions converge to the same spatial point, and the parameters of the same spatial point are output as the first-level twisting candidate parameters.

5. The method according to claim 1, characterized in that Based on the two-stage twisting constraint space, performing linked twisting parameter optimization on the plurality of primary twisting candidate parameters and the plurality of secondary twisting candidate parameters to generate primary twisting optimal parameters and secondary twisting optimal parameters, including: Combining the plurality of primary twist candidate parameters and the plurality of secondary twist candidate parameters accordingly to generate a plurality of dual-stage twist parameter combinations; Performing overall flexibility simulation on the multiple two-stage twisting parameter combinations using a flexibility simulation model to obtain a simulated overall flexibility corresponding to each of the two-stage twisting parameter combinations; performing guided combination determination among the plurality of two-stage twisting parameter combinations according to the simulated overall flexibility to obtain a guided two-stage twisting parameter combination; Based on the guiding two-stage twisting parameter combination, adjusting the remaining two-stage twisting parameter combinations to gradually approach the guiding two-stage twisting parameter combination to generate an updated two-stage twisting parameter combination; The overall flexibility simulation, guide combination determination and parameter combination adjustment process are repeatedly performed until convergence, an optimal two-stage twisting parameter combination is obtained, and the primary twisting preferred parameters and the secondary twisting preferred parameters are extracted.

6. A production parameter optimization system for ultra-fine and highly flexible cables for dexterous hands, characterized in that: The system comprises: The constraint space generation module is used to obtain cable twisting parameters, including twisting tension, twisting pitch, twisting angle, and core compression ratio, and generate a primary twisting constraint space, a secondary twisting constraint space, and a double-stage twisting constraint space based on the cable twisting parameters, including: Obtaining a primary twist constraint interval and a secondary twist constraint interval of the cable twist parameter; constructing a primary twisting constraint space based on the primary twisting constraint interval, and constructing a secondary twisting constraint space based on the secondary twisting constraint interval; Constructing the double-stage twisting constraint space based on the primary twisting constraint interval and the secondary twisting constraint interval; a hierarchical twist parameter optimization module, configured to perform hierarchical twist parameter optimization based on the primary twist constraint space and the secondary twist constraint space, and obtain a plurality of primary twist candidate parameters and a plurality of secondary twist initial parameters; a linked twisting parameter optimization module, configured to perform linked twisting parameter optimization on the plurality of primary twisting candidate parameters and the plurality of secondary twisting candidate parameters based on the two-stage twisting constraint space, and generate primary twisting optimal parameters and secondary twisting optimal parameters; The twisting optimal parameter execution module is used to execute the production of ultra-fine and highly flexible cables based on the first-level twisting optimal parameters and the second-level twisting optimal parameters.

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