Jul 01, 2026
Comprehensive characterization protocol for a 2-DOF pneumatic flexible wrist with controllable braking torque
- Hongbo Liu1
- 1Beihua University
- BEIHUA
Protocol Citation: Hongbo Liu 2026. Comprehensive characterization protocol for a 2-DOF pneumatic flexible wrist with controllable braking torque. protocols.io https://dx.doi.org/10.17504/protocols.io.kxygxrp24g8j/v1
License: This is an open access protocol distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Protocol status: Working
We use this protocol and it's working
Created: June 29, 2026
Last Modified: July 01, 2026
Protocol Integer ID: 320032
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Abstract
To standardize the overall performance evaluation of pneumatic flexible wrists, this paper proposes a complete unified experimental workflow covering multi-dimensional tests: actuator elongation and output force, wrist deflection angles, brake airbag force, braking torque, combined drive-brake load resistance, dynamic response, static pose retention and practical handling performance.
The test platform was assembled and calibrated per design requirements, with dedicated sensors for data acquisition. Uniform wiring, hardware arrangement and test protocols were adopted to guarantee identical test conditions, reliable measurements, favorable operability and repeatability.
This workflow provides a universal benchmark for flexible wrist testing, improves result repeatability and credibility, and supports comparative performance analysis of prototypes with varied structural parameters and control algorithms.
Attachments
Materials
| A | B | C | |
| Parameter name | Value | Unit | |
| Total length | 120 | mm | |
| Operating pressure | [0, 0.30] | MPa | |
| Mass | 88 | g | |
| Effective deformation length | 110 | mm | |
| Initial inner and outer diameters of the silicone tube | 12×15 | mm | |
| Silicone tube elastic modulus | 1.042 | MPa | |
| Constraint ring thickness | 2 | mm | |
| Initial inner and outer diameters of the elastic washer | 15×17 | mm | |
| Elastic washer thickness | 2 | mm | |
| Distances from each of the two artificial muscles to the actuator center | 15 | mm | |
| Upper and lower connecting end cover thickness | 7 | mm | |
| Silicone tube total length | 32 | mm | |
| Silicone tube effective deformation length | 25 | mm | |
| Initial inner and outer diameters of silicone tube | 20×24 | mm | |
| Initial inner and outer diameters of sleeve | 25×30 | mm | |
| Sleeve height | 35 | mm | |
| Clearance between friction plate and brake ball | 0.5 | mm | |
| Brake ball radius | 20 | mm | |
| Brake ball center distance to upper & lower end covers | 60 | mm | |
| Four lug plates distance to brake ball center | 54 | mm | |
| Upper and lower end cover thickness | 3.5 | mm | |
| Pneumatic cross-hinge brake mass | 460 | g | |
| Operating pressure | [0, 0.40] | MPa | |
| Pulse duration | 0.5、1.0、1.5 | s | |
| Operating mode | Actuators 2 and 3 are pressurized; Actuator 1 is not pressurized | Actuators 2 and 3 are pressurized; Actuator 1 is not pressurized. | |
| Driving air pressure | 0.10、0.20、0.30 | MPa | |
| Braking air pressure | 0、0.05、0.10、 0.15 | MPa | |
| Sampling frequency | 500 | Sps (points·s⁻¹) |
Comprehensive characterization protocol for a 2-DOF pneumatic flexible wrist with controllable braking torque
Core structural parameters and simplified manufacturing process of the prototype
Parameters of core components
(1) The pneumatic actuator
The pneumatic actuator primarily consists of upper and lower connecting end covers, silicone tubes, constraint rings, elastic washers, and plugs. Actuator parameters are presented in Table 1.
c
| A | B | C | |
| Parameter name | Value | Unit | |
| Total length | 120 | mm | |
| Operating pressure | [0, 0.30] | MPa | |
| Mass | 88 | g | |
| Effective deformation length | 110 | mm | |
| Initial inner and outer diameters of the silicone tube | 12×15 | mm | |
| Silicone tube elastic modulus | 1.042 | MPa | |
| Constraint ring thickness | 2 | mm | |
| Initial inner and outer diameters of the elastic washer | 15×17 | mm | |
| Elastic washer thickness | 2 | mm | |
| Distances from each of the two artificial muscles to the actuator center | 15 | mm | |
| Upper and lower connecting end cover thickness | 7 | mm |
(2)Function of the pneumatic cross-hinge brake
The brake primarily consists of upper and lower end covers, braking airbags, friction plates, braking balls, sleeves, and lug plates. The upper and lower end covers are identical in structure and size, with mounting holes for the lugs, the sleeve, and pneumatic connectors machined on their end faces. The lugs on the upper end cover are structurally identical to those on the lower end cover,with an installation phase difference of 90°. A threaded hole is provided on the bottom end face of each lug plate for bolt connection with the end cover, while a countersunk through hole is arranged at the other end, in which a deep groove ball bearing is installed. A braking airbag is mounted inside the sleeve, and both ends of the airbag are sealed with upper and lower plugs to form a sealed cavity. The end of the upper plug plate is equipped with a threaded hole, which is fixedly connected to the friction plate via bolts, and the lower plug plate is also provided with a threaded hole for connection with the pneumatic connector. A thin-walled braking ball with the same curvature as the two friction plates is installed between them, with the center of the ball 60 mm away from the upper and lower end covers. Four stepped shafts are uniformly distributed along the equator of the braking ball, each forming an interference fit with the bearing installed at the end of the corresponding lug. The four lug plates are uniformly distributed along a 54-mm circumference.
The total weight of the pneumatic brake is 460 g. It can produce continuously adjustable braking torque ranging from 0 to 0.84 N·m via air pressure regulation, and achieves braking when pressurized and free rotation when depressurized. Brake parameters are presented in Table 2.
Table 2. Structural parameters of pneumatic cross-hinge actuator
| A | B | C | |
| Parameter name | Value | Unit | |
| Silicone tube total length | 32 | mm | |
| Silicone tube effective deformation length | 25 | mm | |
| Initial inner and outer diameters of silicone tube | 20×24 | mm | |
| Initial inner and outer diameters of sleeve | 25×30 | mm | |
| Sleeve height | 35 | mm | |
| Clearance between friction plate and brake ball | 0.5 | mm | |
| Brake ball radius | 20 | mm | |
| Brake ball center distance to upper & lower end covers | 60 | mm | |
| Four lug plates distance to brake ball center | 54 | mm | |
| Upper and lower end cover thickness | 3.5 | mm | |
| Pneumatic cross-hinge brake mass | 460 | g | |
| Operating pressure | [0, 0.40] | MPa |
(3)Two-degree-of-freedom (2-DOF) flexible wrist
The wrist features a cylindrical flexible structure, which is configured in a parallel manner with three circumferentially distributed pneumatic actuator groups and a central pneumatic cross-hinge brake. The three actuator groups are evenly arranged at 120° intervals. The wrist possesses an initial height of 128 mm and a radial dimension of 132 mm, with each actuator group installed at a radial distance of 55 mm from the central axis. Each actuator group consists of two extensile pneumatic artificial muscles arranged in parallel to improve the overall driving capability and output stability.
Seven linkage rings are axially mounted at a uniform spacing of 15 mm, which guarantees equidistant distribution of actuators and high consistency of structural deformation during motion. Except for the flexible components including elastic airbags, restraint rings, elastic washers, and linkage rings, most structural parts of the wrist are fabricated from aluminum alloy. The total mass of the developed flexible wrist is 738 g. Benefiting from the parallel configuration of actuators and the central brake, the wrist can realize coordinated performance of bidirectional flexible deflection and controllable braking torque.
Prototype manufacturing process
1.2.1 Material preparation
(1) Constraint rings: Rapidly fabricated via nylon 3D printing, followed by polishing of the inner and outer surfaces to remove burrs and protrusions, thereby preventing damage to the silicone tubes and ensuring assembly accuracy.
(2) Elastic washers: VMQ silicone O-rings are adopted as standard parts, which can be purchased from physical stores or online suppliers.
(3) Components of the brake mechanism: The sleeve, upper and lower end covers, lug plates, plugs, friction plates, and braking ball are all made of aluminum alloy and fabricated by conventional machining according to the design drawings.
(4) Other connecting parts: Bolts, pneumatic quick-connect fittings and air tubes are standard components and can be procured directly.
1.2.2 Actuator fabrication
The actuator assembly adopts a stepwise sealing process, which mainly consists of five steps.
(1) First, the silicone tube is press-fitted with the upper and lower end plugs, and a steel wire binding Experimental method is used to complete the sealing of the silicone tube and the end plugs.
(2) To ensure overall airtightness, a preliminary pneumatic leak test is conducted after assembling the constraint ring and elastic washers; the formal assembly process proceeds only after confirming the absence of leakage.
(3) The lower end cover is designed with a matching installation groove. The lower plug is equipped with lateral threaded holes and is connected to the lower end cover via screws. A central through-threaded hole is reserved in the lower plug for the installation of a pneumatic quick-connect fitting.
(4) After passing the airtightness test, the constraint ring and elastic washer are sequentially mounted on the outer surface of the silicone tube.
(5) The upper plug, which is press-fitted with the silicone tube, contains a central threaded hole; finally, the upper plug is connected to the upper end cover using screws, completing the assembly of a single pneumatic actuator.
Following the above standardized process, three sets of pneumatic actuators with identical structures and parameters are manufactured in batches.
1.2.3 Brake fabrication
The brake adopts a modular, layered assembly process from the inner components to the outer structure. The main fabrication procedure consists of six steps:
(1) The brake airbag is first press-fitted and sealed with the upper and lower end plugs to form an independent sealed pneumatic chamber. A pneumatic quick-connect fitting is installed at the lower plug to ensure smooth and airtight airflow.
(2) The integrated airbag assembly is then embedded and fixed inside the sleeve.
(3) Two friction plates are mounted on the upper end face of the sleeve and bolted to the upper plug of the braking airbag through countersunk holes at the bottom of the friction plates.
(4) A thin-walled braking ball is assembled between the two friction plates, ensuring that the center of the ball is positioned 60 mm from the reference height of the upper and lower end covers.
(5) Four groups of stepped shafts uniformly distributed at the equatorial region of the braking ball are interference-fitted with the end bearings of lug plates arranged at a circumferential diameter of 54 mm, forming a cross-hinge rotational mechanism.
(6) Finally, identically dimensioned upper and lower symmetric end covers are assembled to complete the system integration.
The phase of the lug plates at both ends is adjusted to a 90° stagger before bolting and locking.
After assembly, low-pressure gas is introduced to perform airtightness and rotational flexibility tests, ensuring that the structure is free of leakage and operates without sticking.
1.2.4 Wrist prototype assembly
The three manufactured pneumatic actuators are symmetrically mounted on the upper and lower end covers of the pneumatic cross-hinge brake. All actuators are evenly arranged at circumferential intervals of 120° and fixed by screws to maintain a uniform radial distance from the brake center. This symmetric assembly ensures consistent and coordinated structural deformation during wrist motion.
After assembly, a sealing re-inspection was conducted for all pneumatic interfaces and chamber junctions. Compressed air at 0.30 MPa was introduced and maintained for 30 s to perform a preliminary system-level airtightness test. The prototype was deemed qualified for subsequent performance experiments only after confirming the absence of leakage and pressure loss.
Detailed parameters of experimental equipment and sensors
The experimental system mainly consists of three parts: a pneumatic control system, a sensing and measurement system, and a control system. The main equipment, sensor models, measurement ranges, and accuracies are listed as follows.
Pneumatic control system
(1) Air compressor (or Air pump): Model 1100W-30L. It is equipped with a 30 L air tank, with a rated discharge pressure of 0.7 MPa and a maximum safe output pressure of 0.8 MPa. Its theoretical air displacement is 120 L/min, which serves as the air source for the entire pneumatic system.
(2) Pneumatic triple unit: Model AC2000-02. The rated flow rate is 500 L/min, and the pressure regulation range is 0.05~0.85 MPa.
(3) Precision pressure reducing valve: Model IR2000-02BG. The pressure regulation range is 0.01~0.8 MPa, with a sensitivity of 0.2% FS and a repeat accuracy of ±0.5% FS.
(4) Electro-pneumatic proportional valve: Model SMC ITV1030-312L. Its pressure regulation range is 0.0005~0.5 MPa, regulation accuracy is ±0.001 MPa, response time is no more than 10 ms, repeat accuracy is ±0.5% FS, and the sensitivity is less than 0.2% FS.
(5) Electromagnetic directional valve: Model SYJ314-5LZD-M5. The rated voltage is DC 24 V, the maximum operating frequency is 10 Hz, and the working pressure range is 0.15~0.7 MPa.
(6) Pressure sensor: Model SMC-PSE560. The measuring range is 0~1.0 MPa with a power supply of DC 12~24 V. The overall accuracy is ±1% FS and the repeat accuracy is ±0.2% FS.
(7) PU tubes: Specifications of 4×2.5 mm and 6×4 mm in outer and inner diameters.
(8) Various two-way and three-way pneumatic fittings.
Sensing and measurement system
(1) Laser displacement sensor: Model HG-C1200CDK. It has a central distance of 200 mm and a measuring range of 0–160 mm, with an accuracy of 200 μm and linearity of ±0.2% FS.
(2) Digital push–pull force gauge: Model HF-100. Its measuring range is 0–100 N, with an accuracy of ±0.5% FS and a resolution of 0.01 N. It is adopted to acquire the steady-state output force of actuators and braking airbags.
(3) Attitude/angle sensor: Model HWT905-TTL. Measurement ranges are ±180° (X, Z) and ±90° (Y), with accuracies of 0.05° (X, Y) and 1° (Z). Output frequency is 0.1–200 Hz. It supports TTL communication with baud rates from 2400 to 921600 bps and operates at 3.3–5 V. The sensor is used to measure wrist pivot angles under different pneumatic pressures.
(4) Pivoting direction angle measuring instrument. It consists of a dual-ball inclinometer and a digital angle gauge (Model: 82311-200P). It features a measuring range of 0–360° with an accuracy of ±0.1°, and is used to real-timely collect pivoting direction angle data of the wrist under various pneumatic pressure combinations.
(5) 3D Motion Capture System：Model NDI Optotrak Certus. It features a resolution of 0.01 mm and a 3D measurement accuracy of 0.15 mm, supporting up to 512 marker points with a marker sampling frequency as high as 4600 Hz. The system enables multi-channel synchronous signal acquisition with a data transmission error no greater than 0.1%.
(6) DC power supply: Model PS3003. It accepts an input voltage of 220 V, provides adjustable output voltage ranging from 0-30 V and adjustable output current ranging from 0–3 A, with a maximum output power of approximately 90 W.
Main Electronic Components of the Controller
(1) Programmable Logic Controller (PLC): Model S7-200CN. It is powered by 24 V DC and supports expansion of digital and analog I/O modules, with compatibility with STEP7-Micro/WIN software. Control programs are developed in software and downloaded to the PLC. Based on the programmed logic, the PLC regulates the electric proportional valve and solenoid valve bank to drive the flexible wrist through predefined motions.
(2) Analog Input Module EM231: Model 6ES7 231-0HC22-0XA8. It converts analog signals (voltage or current) into digital values readable by the PLC.
(3) Analog Output Module EM232: Model 6ES7 232-0HD22-0XA0. It enables the PLC to output continuous analog signals (voltage or current) to control proportional valves, solenoid valve banks, and other actuators.
(4) Communication Module: Siemens USB/PPI programming cable (6ES7901-3DB30-0XA0) is used to connect the host computer and the S7-200CN. With STEP 7 Micro/WIN software, control programs can be downloaded to the PLC, enabling real-time monitoring and debugging of program execution and I/O status.
Pre-experiment preparation
The lower end covers of the wrist, actuator, and brake prototypes are fixedly installed on the experimental platform, which thoroughly eliminates test errors caused by base vibration and displacement during the experiment.
The pneumatic system is built by sequentially connecting an air pump, a pneumatic triple unit, a precision pressure reducing valve, an air pressure sensor, and pneumatic pipelines. The driving air circuit and the braking air circuit are independently arranged without mutual interference, so as to avoid experimental accuracy errors induced by pressure crosstalk.
According to the target experimental measurement parameters, a force sensor, an angle sensor, and a direction angle measuring instrument are installed at the center of the upper end cover of the wrist, actuator, and brake as required. The laser displacement sensor and the 3D motion capture system adopt a non-contact measurement Experimental method, which only needs to meet the respective specified measurement distances.
All devices are powered on and started, and the corresponding sensor acquisition software is opened for zero calibration of sensors (including the angle sensor and 3D motion capture system) to eliminate initial offset errors. Digital display sensors (laser displacement sensor and digital push-pull force gauge) are equipped with built-in zero-set buttons. After zeroing, the elongation and output force under different air pressures can be directly recorded.
System air tightness test is carried out. The rated working air pressure is applied to all actuators and brakes, and the pressure is maintained for 30 seconds. No air leakage or pressure drop occurs in the air circuits and cavity interfaces. Formal experiments can be conducted only after the system air tightness is confirmed to be qualified.
Division of Experimental Modules
The driving, braking, kinematic, load-bearing, dynamic response, and static posture-holding performances of the flexible wrist are experimentally evaluated through six sub-experiments: actuator performance experiment, wrist pivot experiment without braking, braking performance experiment, coupled driving–braking load experiment, dynamic characteristic experiment, and practical application experiment.
Figure 1 Experimental setup.
(a) Actuator elongation; (b) Axial output force; (c) Wrist pivot angle and direction; (d) Wrist braking torque; (e) Wrist dynamic characteristics.
Each experiment is repeated five times under identical operating conditions, and the average of measured values is adopted as the final valid data to suppress random errors and guarantee reliable experimental results. Six dedicated experimental rigs are developed accordingly, as shown in Figure 1.
Actuator Performance Experiment
4.1.1 Axial elongation experiment of actuator
Experimental objective: To characterize the axial elongation of the actuator under varying pneumatic pressures, plot the characteristic curve of elongation versus air pressure, and compare the elongation behaviors between the pressurization and depressurization cycles.
Experimental method: A static characterization test was conducted using the axial elongation measurement setup shown in Figure 1(a). The input air pressure was varied in a stepwise manner, while the axial elongation was measured using a laser displacement sensor. Based on the experimental data obtained during pressurization and depressurization, the deformation characteristics of the actuator were analyzed and compared.
Experimental procedure:
(1) The lower end cover of the actuator was fixed on the experimental platform. The laser displacement sensor and the actuator were installed in the same vertical plane, with the sensor optical axis aligned with the central axis of the actuator. Subsequently, the air supply line and measurement system were connected and calibrated.
(2) The initial input air pressure was set to 0 MPa, and the system was zeroed under the initial condition.
(3) The air pressure was regulated using a precision pressure-reducing valve with a step size of 0.02 MPa over a range of 0 to 0.16 MPa.
(4) The accuracy of the injected air pressure was monitored using a pressure sensor. At each pressure level, the system was held for 30 s to ensure stabilization, after which the axial elongation of the actuator was recorded.
(5) After reaching the maximum pressure of 0.16 MPa, the pressure was subsequently released stepwise with the same pressure interval down to 0 MPa, while the elongation was recorded during the depressurization process.
(6) After the actuator fully returned to its initial state, the complete pressurization–depressurization cycle was repeated five times under identical conditions to reduce random experimental errors and ensure data reliability.
(7) The experimental data were processed and analyzed to plot the pressure–elongation curve and characterize the axial deformation behavior of the actuator.
4.1.2 Axial output force experiment of the actuator
Experimental objective: To investigate the axial force output characteristics of the actuator, the variation of normal force under different elongation-constrained contact conditions was measured, and the mapping relationship between input air pressure and axial output force was established. The results provide experimental support for mechanical modeling and performance optimization of the actuator.
Experimental method: A static mechanical performance test was conducted using the axial force measurement setup shown in Figure 1(b). During the experiments, the input air pressure was regulated in a stepwise manner. An HF-100 digital push–pull force gauge was employed to accurately measure the axial output force of the actuator under different displacement constraints and varying pneumatic pressures.
Experimental procedure:
(1) The lower end cover of the actuator was mounted in a sleeve-type fixture on a parallel experimental platform. A clearance fit was adopted to allow the upper end cover of the actuator to freely extend in the axial direction within the fixture.
(2) Five axial displacement constraint planes were set along the actuator axis to limit different elongation positions, that is ∆l=0 mm, 52 mm, 28 mm, 82 mm, 160 mm. Based on the results of the preliminary elongation characterization experiment, these five constraint planes corresponded to the actuator elongation states under air pressures of 0 MPa, 0.05 MPa, 0.10 MPa, 0.15 MPa, and 0.20 MPa, respectively.
(3) For each limiting plane, the experiment proceeded as follows: (i) The air pressure of the actuator was adjusted using a precision pressure-reducing valve until the actuator elongated to the position corresponding to the limiting plane; (ii) The sliding stage was adjusted so that the force sensor probe made full surface contact with the actuator’s upper end cover; (iii) The air pressure was then increased stepwise with an increment of 0.05 MPa, and each pressure level was maintained for 30 s; (iv) After stabilization, the axial output force at different pressure levels was recorded using the force sensor.
(4) The above experiments were repeated five times under identical conditions to reduce random errors and ensure data reliability.
(5) The measured data were processed and analyzed to plot the relationship between air pressure and output force, thereby investigating the axial force characteristics of the actuator.
Wrist pivot experiment without braking
Experimental objective: To characterize the spatial pivot performance of the wrist, combinations of air pressures for different actuators were adjusted to measure and record the wrist’s pivot angles and pivoting direction angles. The experiments verified the validity, accuracy and feasibility of the theoretical models for the wrist’s pivot angle and deflection angle. The measured data provided reliable support for subsequent analyses of wrist motion characteristics, model optimization and attitude control research.
Experimental method: The experimental setup is illustrated in Figure 1(c). The wrist is vertically mounted to effectively eliminate gravitational interference. When different air pressures are supplied to the three actuators, the wrist pivots arbitrarily within the X–Y plane. Owing to gravity, the steel ball inside the dual-ball inclinometer slides to the lowest point, which indicates the wrist’s pivoting direction. After recording this directional angle, the rotating dial of the digital angle gauge is adjusted to match the wrist’s pivoting direction. The reading from the angle sensor is then recorded as the wrist’s pivot angle.
Experimental procedure:
(1) The wrist is vertically fixed to the experimental platform to eliminate gravitational effects on the measured pivot angle and and direction angles, and the braking pneumatic circuit is closed simultaneously.
(2) A dual-ball inclinometer and a digital angle gauge are mounted on the upper end cover of the wrist, followed by equipment calibration: the center of the inclinometer is aligned with the geometric center of the wrist’s upper end cover, and the zero graduation line points to the positive X-axis.
(3) The angle sensor is fixed to the rotating dial of the digital angle gauge, so that the sensor can synchronously move with the wrist during pivoting to guarantee real-time and accurate data acquisition.
(4) The wrist is actuated by three parallel actuators. The air pressure of each single actuator ranges from 0 to 0.30 MPa with an increment of 0.05 MPa, generating a total of 343 combined working conditions. The precision pressure reducing valves are adjusted stepwise at a pressure gradient of 0.05 MPa to alter the internal cavity pressure of each actuator, thereby driving the wrist to perform spatial pivoting motions with various angles and orientations.
(5) After each pressure adjustment, the air pressure is maintained for 30 s until the wrist posture stabilizes. The corresponding pivoting direction and pivot angle data are then collected and recorded.
(6) Five parallel tests are conducted under identical experimental conditions to reduce random experimental errors.
(7) The acquired data are processed to analyze the spatial pivoting characteristics of the wrist.
Brake performance experiment
4.3.1 Output force characterization of the brake airbag
Experimental objective: To measure the axial output force of the brake airbag under different air pressures, verify the accuracy of the theoretical force model in combination with the structural parameters of the brake device, and investigate the influence of air pressure on the axial force output characteristics of the brake airbag.
Experimental method: The axial output force test of the brake airbag was conducted using the experimental setup shown in Figure 1(b). A 3D-printed fixture with dimensions identical to the actual brake sleeve was employed to assemble the brake airbag, ensuring consistency between the experimental configuration and the real working condition. The input air pressure of the brake airbag was precisely regulated using a precision pressure-reducing valve, and the corresponding axial output force was measured using a digital push–pull force gauge.
Experimental procedure:
(1) The brake airbag equipped with upper and lower end plugs was installed into a dimension-matched 3D-printed fixture to ensure consistency with the actual operating condition.
(2) The sliding stage was adjusted so that the probe of the digital force gauge was in firm contact with the upper end plug of the brake airbag, ensuring that the airbag deformation was constrained to purely axial loading during pressurization, thereby improving measurement accuracy.
(3) The input air pressure was increased stepwise from 0 to 0.40 MPa with a pressure increment of 0.02 MPa. At each pressure level, At each pressure level, the system was allowed to stabilize before recording the corresponding axial output force of the brake airbag.
(4) All measured data were sorted and processed. Comparative calculations were performed using the brake structural parameters and the theoretical output force formula to calibrate the deformation compatibility coefficient of the model. The variation characteristics and laws governing the axial output force of the brake airbag against air pressure were summarized.
4.3.2 Braking torque experiment of the brake
Experimental objective: To investigate the braking performance and load-bearing capacity of the brake device under different air pressures, the maximum resistance to external loading corresponding to each braking pressure was measured. The study aims to analyze the influence of input air pressure on the braking torque and ultimate braking load capacity of the brake.
Experimental method: The braking torque experiment was conducted using the setup shown in Figure 1(d). The brake was installed vertically to eliminate gravitational interference, and a pulley guide was adopted to ensure stable tension loading. The damping performance of the friction pair was adjusted by varying the internal air pressure of the brake. The sudden change in the brake rotation angle was defined as the criterion for braking failure. The ultimate bearing load of the brake under different air pressures was tested to reveal the influence law of air pressure parameters on the braking performance.
Experimental procedure:
(1) The brake was vertically mounted on the experimental platform to eliminate the influence of gravity on the braking performance measurements.
(2) A rope was connected between the upper end cover of the brake and the center of a digital push–pull force gauge. A pulley-guided configuration was adopted to correct the loading direction, ensuring that the applied tensile force remained parallel to the axial direction of the upper end cover, thereby improving loading accuracy.
(3) The internal air pressure of the brake was regulated from 0 to 0.4 MPa using a precision pressure-reducing valve, with an increment of 0.05 MPa. This process altered the frictional damping between the friction plates and the braking ball.
(4) A continuous load was slowly applied to the brake through the push–pull force gauge, and the angular variation state of the brake was collected and monitored in real time.
(5) When an abrupt angular change and braking failure of the brake was observed, the reading of the push–pull force gauge was immediately recorded as the ultimate bearing load of the brake under the corresponding air pressure condition.
(6) After completing all pressure conditions, the experimental data were organized and analyzed to reveal the relationship between braking air pressure and the ultimate load-bearing capacity of the brake.
Coupled driving-braking load experiment
Experimental objective: The established theoretical model for wrist pivot angles can characterize the wrist deformation behavior, yet it takes an implicit form and involves heavy computational costs. To further simplify the model for real-time control implementation, experimental investigations are conducted under two separate test conditions: constant pivot angle and constant friction torque. The correlations among the maximum external resisting load Mzk of the wrist, pivot angle θ, friction torque Mf, and driving air pressure increment ∆p are explored, namely the impedance torque model Mzk=f1(Δp,θ,ϕ) and the swing angle model θ=f2(Δp,Mf,ϕ). A compact, explicit simplified model with low computational overhead is developed to describe the wrist impedance torque and pivot angle, which replaces the original complicated theoretical model and provides experimental data and model foundations for the design and parameter tuning of real-time wrist control algorithms.
Experimental method: The experiment are to refine the theoretical model of the wrist and derive an explicit correlation between the impedance torque model and pivot angle characteristics. The controlled-variable approach is utilized to conduct two comparative test series under constant pivot angle and constant friction torque conditions, respectively. Measurement instruments including angle sensors and digital push-pull force gauges are employed to record experimental data for each test group. The coupling relationships among various variables are summarized, and a simplified model is established accordingly.
A single-variable control strategy is maintained throughout the entire testing process to clearly distinguish the two separate operating conditions (constant pivot angle and constant friction torque). Standardized experimental operations, uniform data acquisition protocols, and consistent parallel testing criteria are implemented to ensure test repeatability and data credibility. Multiple parameter gradient levels are configured for all working conditions, with five replicate parallel tests performed for each group. Outliers induced by equipment vibration, unstable operating states and data glitches are removed during testing. Uniform data fitting and model refinement are carried out upon completion of all measurements. The detailed stepwise experimental procedure is described as follows.
Experimental procedure: The flexible wrist test platform shown in Figure 1(d). All equipment is calibrated before testing to ensure accurate measurement of air pressure, swing angle, force and voltage. The wrist is vertically mounted to eliminate gravitational measurement interference, and the data acquisition system is debugged for synchronous real-time recording of drive pressure, brake pressure and pivot angle.
4.4.1 Influence of brake air pressure on wrist impedance torque at a constant pivot angle
The pivot angle and pivot orientation of the wrist are adjusted by controlling the air supply combinations of different actuators, and multiple gradient levels of fixed pivot angles are set as the baseline experimental working conditions. Subsequently, the wrist pivot angle is kept constant, and the braking pressure increment is taken as the sole variable to investigate the mapping correlation between this increment and the maximum load-bearing capacity of the wrist. An explicit impedance torque model is established accordingly. The detailed experimental procedures are presented as follows.
(1) The pivot angle of the wrist is preset within a range of 0–40° with a uniform interval of 10°, yielding five groups of fixed pivot angle conditions. The air pressure of the three actuators is regulated via precision pressure reducing valves, and real-time wrist angle data are continuously acquired by the angle sensor to maintain the wrist at the preset pivot angle. The operating condition is considered stable once the angle reading remains fluctuation-free for 30 consecutive seconds.
(2) Under the condition of a constant pivot angle, the braking pressure increment is adjusted stepwise at a uniform gradient of 0.05 MPa. After the air pressure is fully stabilized, an external load is applied slowly and uniformly to the wrist through the load regulation device in a smooth and non-impact manner. The loading process is terminated immediately once a slight variation in the wrist pivot angle is observed. The core experimental data under the current condition, including the fixed pivot angle, braking air pressure, and external bearing load of the wrist, are recorded synchronously.
(3)Each fixed pivot angle and brake pressure combination undergoes five repeated loading and data acquisition cycles to suppress mechanical and pneumatic random errors. After finishing one test group, the swing angle is adjusted to the next gradient, and the full test process repeats until all working conditions are covered.
(4) Valid fixed-pivot-angle data are compiled to analyze wrist maximum load capacity versus swing angle and brake pressure. Data fitting derives explicit variable correlations and a simplified constant-angle impedance torque model. This model requires minimal computation and fast response, fulfilling real-time engineering control needs.
4.4.2 Influence of air pressure on wrist pivot angle under constant friction torque
Adjusting actuator brake pressure fixes the wrist friction torque. With driving air pressure increment as the single variable, its correlations with friction torque and swing angle are explored to build an explicit swing angle model. Detailed test procedures are given below:
(1) According to the operating range of 0–0.40 MPa for the braking air pressure, multiple groups of braking air pressure values are set at a uniform gradient of 0.05 MPa. The experimental condition is confirmed to be stable when the braking air pressure is fully maintained and no obvious wrist jitter occurs.
(2) With the braking air pressure kept constant, the driving air pressure increment is adjusted stepwise at a preset gradient of 0.05 MPa. After the air pressure stabilizes completely, the pivot angle of the wrist under the current fixed braking air pressure and driving air pressure increment is measured and recorded by the angle sensor.
(3) The braking air pressure with different gradient values is switched to fully cover the entire operating range of the actuator for completing all gradient experiments. Five parallel tests are repeated for each parameter configuration to reduce accidental errors and ensure the authenticity and validity of experimental data.
(4) Valid experimental data are processed to analyze how driving air pressure affects wrist deflection at fixed friction torque. Parameter correlations are derived via fitting to build a simplified wrist deflection model for constant friction torque.
Wrist dynamic characteristic experiment
Experimental objective: The wrist contains three actuators and one brake, featuring time-varying parameters, and nonlinearity. Numerous coupled parameters complicate theoretical derivation of its dynamic characteristics, so experimental single-variable comparison tests are performed to investigate the brake’s influence on wrist dynamics. Measured dynamic responses under diverse excitations are analyzed to reveal its inherent nonlinear dynamic behaviors.
Experimental method: The experimental setup is depicted in Figure 1(e). The wrist is vertically fixed on the platform with markers mounted on its upper and lower end caps. Using the wrist’s geometric dimensions, marker coordinates are transformed to the brake ball center and upper end cap geometric center for accurate motion characterization.
Tests comply strictly with the working conditions in Table 3. A single-variable control method is applied, with braking pressure, driving pressure and pulse width set as variables for dynamic comparison under step and pulse excitation. Wrist motion data are captured by a 3D motion capture system for comparative analysis.
Table 3 Dynamic experiment conditions Parameter name
| A | B | C | |
| Parameter name | Value | Unit | |
| Pulse duration | 0.5、1.0、1.5 | s | |
| Operating mode | Actuators 2 and 3 are pressurized; Actuator 1 is not pressurized. | ||
| Driving air pressure | 0.10、0.20、0.30 | MPa | |
| Braking air pressure | 0、0.05、0.10、 0.15 | MPa | |
| Sampling frequency | 500 | Sps (points·s⁻¹) |
4.5.1 Time-domain response experiment
This group of experiments take the types of excitation (step, pulse), braking air pressure, driving air pressure, and excitation pulse width as variables to investigate the effects of each parameter on the time-domain dynamic response, steady-state pivot angle, and reset characteristics of the wrist. The detailed experimental procedures are described as follows.
(1) Step excitation time-domain tests are conducted at a constant driving air pressure of 0.30 MPa, with braking pressure varying from 0 to 0.15 MPa at 0.05 MPa intervals. Standard step excitation signals are delivered by the PLC to drive wrist motion. Full-cycle time-domain responses are acquired via a 3D motion capture system to compare the variation trends of the wrist’s response speed and steady-state pivot angle under different braking pressures.
(2) Pulse excitation test without braking. The brake unit is deactivated, and two groups of single-variable comparative working conditions are established:
① With the driving air pressure fixed at 0.30 MPa, time-domain response data of the wrist are collected under various excitation pulse widths to analyze the pulse width effect on the steady-state deformation characteristics.
② With the standard excitation pulse width fixed at 1.5 s, the driving air pressure is adjusted in gradient steps to measure the steady-state pivot angle and vibration characteristics during pressure release under various air pressures.
(3) Comparative pulse excitation test with active braking. The brake is enabled while the excitation pulse width remains constant at 1.5 s, and two comparative test groups are arranged:
① With a constant driving air pressure of 0.30 MPa and graded braking pressures, the attenuation trends of the wrist’s steady pivot angle and angular deviation during pressure release and reset are tested;
② The braking air pressure is fixed at 0.15 MPa, and the driving air pressure is adjusted in gradient levels to explore the influence mechanism of driving air pressure on the reduction range of wrist pivot angle and reset deviation.
(4) Data collation and comparison: all time-domain test data are processed to plot response curves for each condition, revealing how brake pressure, drive air pressure and excitation pulse width affect wrist response speed, steady deformation, pressure-release vibration and reset precision.
4.5.2 Limiting frequency experiments at different pivot angles without braking
This test defines limit frequency as the maximum excitation frequency enabling the wrist to reach the target swing angle. With the brake released, the experiment explores the wrist’s dynamic frequency response limit under various pivot angles.
(1) The driving air pressure is precisely regulated via the pneumatic pressure control system to stabilize the wrist at three typical preset pivot angles of 15°, 30° and 45°, which serve as the target deformation working conditions for the tests.
(2) Three target pivot angles are tested with gradient alternating excitation frequencies. The PLC outputs frequency-varying signals to drive reciprocating wrist swing, while a 3D motion capture system records real-time motion data and judges whether each frequency meets the target swing angle.
(3) The deformation response performance of the wrist at each frequency is compared and analyzed to determine the limit frequency ranges corresponding to the three pivot angles. It is clarified that excessive excitation frequency and insufficient response time are the root causes preventing the wrist deformation from reaching the preset pivot angle.
(4) A bisection-based refined test scheme is applied to preliminary limit frequency intervals with finer gradients to narrow the frequency range and boost test accuracy.
4.5.3 Frequency-domain response experiments
Fourier transforms are performed on the time-domain experimental data acquired in this series of tests. Under both non-braking and braking operating conditions, the influence laws of driving air pressure, excitation pulse width and braking air pressure on the natural frequency, amplitude-frequency characteristics and vibration amplitude of the wrist are investigated. The detailed experimental procedures are listed as follows.
(1) Frequency-domain response analysis without braking
Time-domain motion data of the wrist under step excitation and pulse excitations with various pulse widths are collected separately, followed by Fourier transform processing to extract frequency-domain response characteristics. The influence of driving air pressure on the low-frequency natural frequency of the wrist is analyzed under step excitation. The coupling effects of driving air pressure and pulse width on the wrist’s natural frequency and vibration amplitude are also explored to reveal the mechanism of the pulse width threshold affecting the wrist’s inherent dynamic characteristics.
(2) Frequency-domain response analysis with braking
At a fixed drive air pressure of 0.30 MPa, step and 1.5 s pulse excitations are tested under graded brake pressures. Time-domain data for each condition are transformed to frequency domain to compare amplitude-frequency responses and analyze how braking alters system damping, natural frequency and vibration amplitude.
(3) Summary of frequency-domain characteristic laws
All frequency-domain experimental results are summarized to clarify the action mechanisms of driving air pressure, excitation pulse width and braking air pressure, and verify the effectiveness of the drive-brake coordinated scheme in suppressing wrist vibration and improving dynamic stability.
Experiments on application performance of the wrist
Experimental objective：This parallel drive-brake wrist exhibits drastically varied stiffness and damping under braking. To verify its pose adjustment, retention and load-handling performance, we serially integrate it with a self-developed five-finger manipulator for no-load pose adjustment and loaded grasping-transport tests. Comparisons between depressurized and locked brake states reveal braking improvements in overall stiffness, anti-eccentric load capacity and pose retention accuracy.
Experimental method: An integrated prototype comparison method is used. The flexible wrist and five-finger manipulator are serially fixed on a linear sliding table, with actuator and brake air pressure as well as motion sequences uniformly controlled by a pneumatic system. With brake status set as the single variable, two test conditions are arranged: no-load depressurized state and loaded pressurized braking. Multi-directional pose adjustment and object grasping-transport tests are carried out to compare the wrist’s mobility, deformation behavior and pose retention performance.
4.6.1 Pose tests under no-load conditions
(1) Assemble the wrist and five-finger manipulator, mount the unit on a linear sliding table and link it to the pneumatic control system, debug air circuits and control programs for stable operation.
(2) Depressurize the wrist brake to release braking constraints, placing the wrist in a flexible free-driving state.
(3) Adjust the air pressure of the three sets of actuators through the pneumatic control system to drive the wrist to realize two-degree-of-freedom motions, including upward pitching, downward pitching, inward yaw and outward yaw.
(4) Record the wrist’s multi-directional swing motions and neutral posture, analyze manipulator self-weight-induced sagging deflection without braking, and quantify the wrist’s flexible-state stiffness performance.
4.6.2 Yaw motion of the wrist under load
(1) Taking a mineral water bottle as the operation object, control the linear sliding table to drive the five-finger manipulator close to the target and adjust the wrist posture to a state suitable for grasping.
(2) Apply pressure to the pitch brake to improve the stiffness and posture retention capability of the wrist in the pitching direction. Subsequently, control the five fingers of the manipulator to stably grasp the target object.
(3) Maintain the pressurized locking state of the pitch brake and depressurize the yaw brake to release the degree of freedom for wrist yaw motion.
(4) Adjust the air pressure of the yaw actuator to drive the wrist to complete small-amplitude swinging and pose adjustment under load, so as to realize small-range object handling operations.
(5) Observe and record wrist posture under loaded braking, and verify its outstanding stiffness and deformation resistance by comparison with no-load unbraced test results.