Force Error Research Articles

Fabrication of three-dimensional orthodontic force detecting brackets and preliminary clinical test for tooth movement simulation

This study aimed to develop an ultraminiature pressure sensor array to measure the force exerted on teeth. Orthodontic force plays an important role in effective, rapid, and safe tooth movement. However, owing to the lack of an adequate tool to measure the orthodontic force in vivo, it remains challenging to determine the best orthodontic loading in clinical and basic research. In this study, a three-dimensional (3D) orthodontic force detection system based on piezoresistive absolute pressure sensors was designed. The 3D force sensing array was constructed using five pressure sensors on a single chip. The size of the sensor array was only 4.1 × 2.6 mm, which can be placed within the bracket base area. Based on the barometric calibration, conversion formulas for the output voltage and pressure of the five channels were constructed. Subsequently, a 3D linear mechanical simulation model of the voltage and stress distribution was established using 312 tests of the applied force in 13 operating modes. Finally, the output voltage was first converted to pressure and then to the resultant force. The 3D force-detection chip was then tested to verify the accuracy of force measurement on the teeth. Based on the test results, the average output force error was only 0.0025 N (0.7169%) (p = 0.958), and the average spatial positioning error was only 0.058 mm (p = 0.872) on the X-axis and 0.050 mm (p = 0.837) on the Y-axis. The simulation results were highly consistent with the actual force applied (intraclass correlation efficient (ICC): 0.997–1.000; p < 0.001). Furthermore, through in vivo measurements and a finite element analysis, the movement trends generated when the measured orthodontic forces that acted on the teeth were simulated. The results revealed that the device can accurately measure the orthodontic force, representing the first clinical test of an orthodontic-force monitoring system. Our study provides a hardware basis for clinical research on efficient, safe, and optimal orthodontic forces, and has considerable potential for application in monitoring the biomechanics of tooth movement.

A Highly Sensitive Iontronic Bimodal Sensor with Pressure‐Temperature Discriminability for Robot Skin

Iontronic sensors, with the electrical double layer effect at the iontronic film /electrode interface as well as the temperature‐sensitive characteristic of the iontronic film, demonstrate the potential to be robot skin with pressure‐temperature perception. Herein, a highly sensitive iontronic bimodal sensor (IBS) with pressure‐temperature discriminability for robot skin is reported. With the elaborate design of the structure, especially the reasonable arrangement of electrodes, the resistance‐capacitance dual‐measurement modes on the iontronic film are realized. Based on the temperature‐sensitive resistance of the iontronic film, together with a pressure‐sensitive normalized variable of the capacitance of the IBS, a pressure‐temperature decoupling strategy is proposed, terminating in the maximum temperature error of 1.6% in 20–80 °C and the maximum force error of 5.9% in 3–10 N. Moreover, the hierarchically compressible microstructure of the iontronic film, with slender protrusions and stubby protrusions, is readily prepared, empowering the IBS with a pressure sensitivity of 25.9 kPa−1 and a broad pressure range up to 796 kPa. The IBS and the 5 × 5 IBS array, function as the skin for a robot in the scenarios of temperature sensing, writing calligraphy, and object manipulation, manifesting gigantic potential in human‐robot interaction.

Load-independent multi-objective sensor placement method for localization and reconstruction of external excitations under interval uncertainties

The direct measurement of external excitations under operation conditions remains challenging in many engineering applications. This study proposes a method of optimal sensor placement for the best localization and reconstruction of external excitations when considering multi-source uncertainties. The excitation inversion is achieved in the framework of minimizing the discrepancy between the forward and inversed modal loads. To accurately obtain the modal force in the time-domain excitation reconstruction algorithm, three combined indicators of the interested modal matrix are defined, which integrate measures of effectiveness, stability, orthogonality, and robustness of inverse modal transformation. The optimal sensor placement is determined by multi-objective particle swarm optimization and Pareto optimal solution. In addition, to alleviate the computational burden of loading localization, a surrogate model based on an interval kriging interpolation model and sequential sampling strategies is established for the forward modal forces. And a time-dependent interval error of modal forces inspired by the theory of second-order narrow bounds in system reliability is developed to guide the inversion process. Notably, the developed sensor selection and excitation inversion methods are independent of the type, location, and time evolution of external excitations. Eventually, two numerical examples and an experimental case are discussed to demonstrate the validity and feasibility of the developed approach.

The Influence of Transcranial Alternating Current Stimulation on Fatigue Resistance.

Previous research has shown that some forms of non-invasive brain stimulation can increase fatigue resistance. The purpose of this study is to determine the influence of transcranial alternating current stimulation (tACS) on the time to task failure (TTF) of a precision grip task. The study utilized a randomized, double-blind, SHAM-controlled, within-subjects design. Twenty-six young adults completed two experimental sessions (tACS and SHAM) with a 7-day washout period between sessions. Each session involved a fatiguing isometric contraction of the right hand with a precision grip with either a tACS or SHAM stimulation applied to the primary motor cortex (M1) simultaneously. For the fatiguing contraction, the participants matched an isometric target force of 20% of the maximum voluntary contraction (MVC) force until task failure. Pre- and post-MVCs were performed to quantify the force decline due to fatigue. Accordingly, the dependent variables were the TTF and MVC force decline as well as the average EMG activity, force error, and standard deviation (SD) of force during the fatiguing contractions. The results indicate that there were no significant differences in any of the dependent variables between the tACS and SHAM conditions (p value range: 0.256-0.820). These findings suggest that tACS does not increase the TTF during fatiguing contractions in young adults.

Cutting Force Fluctuation Suppression and Error Homogenization of Noncircular Gear Hobbing Based on the Tool Shifting Method

The current research on noncircular hobbing mainly focuses on the linkage model and motion realization. However, the intermittent cutting characteristics of hobbing would increase uncertainties in the manufacturing process. In this paper, a hobbing machining model with tool-shifting characteristics was proposed to solve the problems of cutting force fluctuation and inconsistency of tooth profile envelope accuracy at different positions of the pitch curve in noncircular gear hobbing. Based on the unit cutting force coefficient method, the undeformed chip volume generated by interrupted cutting was used to characterize the fluctuation trend of the hobbing force. The fluctuation characteristics of the cutting force generated by different hobbing models were compared and analyzed. Using the equivalent gear tooth and hob slotting numbers, an analysis model of the tooth profile envelope error of the noncircular gear was constructed. Subsequently, the tooth profile envelope errors at different positions of the pitch curve were compared and analyzed based on the constructed model. The transmission structure of the electronic gearbox was constructed based on the proposed hobbing model, and the hobbing experiment was conducted based on the self-developed noncircular gear CNC hobbing system. This paper proposes a hobbing method that can effectively suppress the fluctuation of the peak and whole circumference cutting force and reduce the maximum envelope error of the whole circumference gear teeth.

Crashworthiness analysis and structural optimization of shrink tube under interference condition

This paper aims to study the crashworthiness of shrink tubes for rail vehicles under axial impact loading. A theoretical model of shrink tube for platform force prediction under interference fit conditions was proposed. The trolley crash test was used to experimentally study the structural energy absorption and characteristics during collision, and a corresponding finite element model was constructed and validated. The finite element model validated the accuracy of the theoretical model. The influence of structural parameters on the crashworthiness of shrink tube under interference conditions was then studied. Structural design variables, including the magnitude of interference (int_pre), thickness (T), long right-angle edge (tri_x) and short right-angle edge (tri_z) were sampled using a full factorial and a Latin hypercube design method. Based on the above samples, the moving least squares method (MLSM) was used to construct an approximate model of peak force (Fmax), specific energy absorption (SEA), and platform force (Fplt). The main effects analysis illustrated that the tri_z had the most significant effects on the peak force, specific energy absorption and platform force. To minimize Fmax and maximize SEA, the global response surface method (GRSM) was employed for parameter optimization. Finally, the optimized configurations were obtained with int_pre=0.067mm, T=10.003mm, tri_x=21.485mm, and tri_z=6.101mm. Compared to the initial design, the SEA value was increased by 16.41 %, while the Fmax value was decreased by 2.21%. The error of platform force derived from the optimal solution and theoretical prediction was 3.62%, which verified that the theoretical prediction model was credible within an acceptable range.

A Single Application of Cerebellar Transcranial Direct Current Stimulation Fails to Enhance Motor Skill Acquisition in Parkinson's Disease: A Pilot Study.

Parkinson's disease (PD) is a progressive neurodegenerative disorder that leads to numerous impairments in motor function that compromise the ability to perform activities of daily living. Practical and effective adjunct therapies are needed to complement current treatment approaches in PD. Transcranial direct current stimulation applied to the cerebellum (c-tDCS) can increase motor skill in young and older adults. Because the cerebellum is involved in PD pathology, c-tDCS application during motor practice could potentially enhance motor skill in PD. The primary purpose was to examine the influence of c-tDCS on motor skill acquisition in a complex, visuomotor isometric precision grip task (PGT) in PD in the OFF-medication state. The secondary purpose was to determine the influence of c-tDCS on transfer of motor skill in PD. The study utilized a double-blind, SHAM-controlled, within-subjects design. A total of 16 participants completed a c-tDCS condition and a SHAM condition in two experimental sessions separated by a 7-day washout period. Each session involved practice of the PGT concurrent with either c-tDCS or SHAM. Additionally, motor transfer tasks were quantified before and after the practice and stimulation period. The force error in the PGT was not significantly different between the c-tDCS and SHAM conditions. Similarly, transfer task performance was not significantly different between the c-tDCS and SHAM conditions. These findings indicate that a single session of c-tDCS does not elicit acute improvements in motor skill acquisition or transfer in hand and arm tasks in PD while participants are off medications.

Hybrid and adaptive control of functional electrical stimulation to correct hemiplegic gait for patients after stroke.

Introduction: Gait, as a fundamental human movement, necessitates the coordination of muscles across swing and stance phases. Functional electrical stimulation (FES) of the tibialis anterior (TA) has been widely applied to foot drop correction for patients with post-stroke during the swing phase. Although the gastrocnemius (GAS) during the stance phase is also affected, the Functional electrical stimulation of the gastrocnemius received less attention. Methods: To address this limitation, a timing- and intensity-adaptive Functional electrical stimulation control strategy was developed for both the TA and GAS. Each channel incorporates a speed-adaptive (SA) module to control stimulation timing and an iterative learning control (ILC) module to regulate the stimulation intensity. These modules rely on real-time kinematic or kinetic data during the swing or stance phase, respectively. The orthotic effects of the system were evaluated on eight patients with post-stroke foot drop. Gait kinematics and kinetics were assessed under three conditions: no stimulation (NS), Functional electrical stimulation to the ankle dorsiflexor tibialis anterior (SA-ILC DS) and FES to the tibialis anterior and the ankle plantarflexor gastrocnemius (SA-ILC DPS). Results: The ankle plantarflexion angle, the knee flexion angle, and the anterior ground reaction force (AGRF) in the SA-ILC DPS condition were significantly larger than those in the NS and SA-ILC DS conditions (p < 0.05). The maximum dorsiflexion angle during the swing phase in the SA-ILC DPS condition was similar to that in the SA-ILC DS condition, with both being significantly larger than the angle observed in the NS condition (p < 0.05). Furthermore, the angle error and force error relative to the set targets were minimized in the SA-ILC DPS condition. Discussion: The observed improvements can be ascribed to the appropriate stimulation timing and intensity provided by the SA-ILC DPS strategy. This study demonstrates that the hybrid and adaptive control strategy of functional electrical stimulation system offers a significant orthotic effect, and has considerable potential for future clinical application.

Police lethal force errors and stress physiology during video and live evaluation simulations

ABSTRACT Police officers are regularly evaluated for their competency in a variety of skills related to use of force (UOF), including lethal force decision-making, which is usually tested using stressful reality-based scenarios in virtual or live formats. The current observational study fills a literature gap by examining performance (i.e., shoot/no-shoot errors) and stress physiology among 187 police officers during virtual (i.e., video-based) and live UOF scenarios as part of their agency’s annual requalification assessment. While moderately low rates of lethal force errors we\\re observed overall, there were significantly fewer errors in live (0.81%) versus video scenarios (5.92%). Both conditions elicited significant stress physiology, as measured by heart rate (HR) relative to rest, with higher maximum heart rate in live scenarios. Based on emerging empirical literature and the current findings, we contribute to the discussion on the practical benefits and limitations of video and live simulation approaches in policing. We also provide evidence-based recommendations on how each approach may be most effectively employed for the purpose of evaluating police officers’ UOF skills.

Bridging semiempirical and abinitio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation.

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at abinitio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl-, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N-C and C-Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from -12.4 to -41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Δ-Learning applied to coarse-grained homogeneous liquids.

Coarse-grained molecular dynamics (CGMD) simulations address lengthscales and timescales that are critical to many chemical and material applications. Nevertheless, contemporary CGMD modeling is relatively bespoke and there are no black-box CGMD methodologies available that could play a comparable role in discovery applications that density functional theory plays for electronic structure. This gap might be filled by machine learning (ML)-based CGMD potentials that simplify model development, but these methods are still in their early stages and have yet to demonstrate a significant advantage over existing physics-based CGMD methods. Here, we explore the potential of Δ-learning models to leverage the advantages of these two approaches. This is implemented by using ML-based potentials to learn the difference between the target CGMD variable and the predictions of physics-based potentials. The Δ-models are benchmarked against the baseline models in reproducing on-target and off-target atomistic properties as a function of CG resolution, mapping operator, and system topology. The Δ-models outperform the reference ML-only CGMD models in nearly all scenarios. In several cases, the ML-only models manage to minimize training errors while still producing qualitatively incorrect dynamics, which is corrected by the Δ-models. Given their negligible added cost, Δ-models provide essentially free gains over their ML-only counterparts. Nevertheless, an unexpected finding is that neither the Δ-learning models nor the ML-only models significantly outperform the elementary pairwise models in reproducing atomistic properties. This fundamental failure is attributed to the relatively large irreducible force errors associated with coarse-graining that produces little benefit from using more complex potentials.

Robotic Drilling of Aluminum Alloy

This paper presents an experimental approach to evaluate the ability of a six-axis industrial robot to drill aluminum alloy parts. A strategy based on statistical tests has been studied to quantify and predict the relative contribution of cutting parameters on cutting force and shape errors during drilling. This technique is based on the identification of relevant sources of error during high-speed robotic fitting. The machining quality was quantified in terms of dimensional and geometric tolerance, chip formation and evacuation, burr formation, edge build-up, tool wear and surface damage. Statistical analysis of the experimental results reveals a strong dependence between part accuracy and drilling force. An experimental model was developed to represent and predict the cutting force during drilling and an accurate error prediction capability was distinguished. It was found that at high cutting speed and feed rate, the cutting force was the main source of error affecting the accuracy of the machined parts. Verification experiments are performed, and the results reveal that dimensional defects are significantly reduced by a heat treatment effect (90 HRE) and the thrust force decreases with an increase in cutting speed. The recommended cutting speed for robotic drilling is 6000 rpm with a feed rate of 0.15 mm/min. This study provides important technical guidance for improving the robotic drilling of aluminum alloy in practice.

An RDL Modeling and Thermo-Mechanical Simulation Method of 2.5D/3D Advanced Package Considering the Layout Impact Based on Machine Learning.

The decreasing-width, increasing-aspect-ratio RDL presents significant challenges to the design for reliability (DFR) of an advanced package. Therefore, this paper proposes an ML-based RDL modeling and simulation method. In the method, RDL was divided into blocks and subdivided into pixels of metal percentage, and the RDL was digitalized as tensors. Then, an ANN-based surrogate model was built and trained using a subset of tensors to predict the equivalent material properties of each block. Lastly, all blocks were transformed into elements for simulations. For validation, line bending simulations were conducted on an RDL, with the reaction force as an accuracy indicator. The results show that neglecting layout impact caused critical errors as the substrate thinned. According to the method, the reaction force error was 2.81% and the layout impact could be accurately considered with 200 × 200 elements. For application, the TCT maximum temperature state simulation was conducted on a CPU chip. The simulation indicated that for an advanced package, the maximum stress was more likely to occur in RDL rather than in bumps; both RDL and bumps were critically impacted by layouts, and RDL stress was also impacted by vias/bumps. The proposed method precisely concerned layout impacts with few resources, presenting an opportunity for efficient improvement.

Age-Related Changes in Plantar Sensation and Ankle Proprioception in Adolescents to Older Adults.

Plantar sensation and ankle proprioception occur in a stage-like variance across the life span. However, changes in adolescents, young adults, middle-aged adults, and older adults remain unclear. The aim of this study was to investigate the differences of plantar sensation and ankle proprioception in adolescents to older adults. A total of 212 participants were recruited in the study and were divided into four groups, including adolescents (n = 46), young adults (n = 55), middle-aged adults (n = 47), and older adults (n = 54). Plantar tactile sensitivity/tactile acuity/vibration threshold and ankle movement threshold/joint position sense/force sense were assessed in all groups. The Kruskal-Wallis H test was used to analyze the differences in Semmes-Weinstein monofilaments between different age groups in different plantar positions. One-way analysis of variance was used to determine differences in foot vibration threshold, two-point discrimination, and ankle proprioception between different age groups. Significant differences were found in the Semmes-Weinstein monofilament test (p < .001), the two-point discrimination test (p < .05), and the vibration threshold test (p < .05) in the six tested plantar positions among adolescents, young adults, middle-aged adults, and older adults. For ankle proprioception, significant differences were found in movement thresholds in ankle plantar flexion (p = .01), ankle dorsiflexion (p < .001), ankle inversion (p < .001), and ankle eversion (p < .001), as well as relative absolute errors in the ankle force senses of ankle plantar flexion (p = .02) and ankle dorsiflexion (p = .02) across the four age groups. Plantar sensation and ankle proprioception were sensitive in adolescents and young adults than in middle-aged adults and older adults.

Internal force analysis of beams on elastic foundation using differential evolutionary optimization algorithm based on hybrid mutation technique

The paper presents the Finite element method (FEM) that calculates the internal force and the displacement of beams on elastic foundation in the case of the uncertainty input parameters described in terms of the number intervals. Using the interval function optimization algorithm combined with the FEM to determine the internal force values of the span reinforced concrete beam structure. This study applies the hybrid differential evolutionary optimization algorithm combined with FEM interval functions to determine the required internal force results of reinforced concrete beams placed on an elastic foundation. The calculation process is programmed using Maple.17 software to determine the displacement output and the resulting internal force in the beam. To check the correctness of the program calculated on Maple.17, the input declared dataset corresponds to the central values of the interval numbers and is recalculated by SAP2000v21 software, then evaluates the results error of internal force on the beam under consideration.

A new model for thermal-mechanical coupled of gradient temperature rolling force based on geometrical unified yield criterion

In order to precisely describe the yield deformation behavior of various materials, a generalized yield criterion known as geometrical unified (GU) yield criterion is firstly established in this paper. Based on this yield criterion, an analytical rolling force model of gradient temperature rolling process was established, and the impact of the temperature field was taken into consideration. The GU yield criterion is a function of shear tension ratio, and the classical yield criteria can be obtained as its special cases. The gradient temperature rolling process of an ultra-heavy plate was analyzed depending on the GU yield criterion, and the corresponding energy functional was established. In the meanwhile, the temperature field expression was developed by taking temperature permeability into account. Finally, the analytical model of the force and energy parameters of the gradient temperature rolling process was constructed by fusing the temperature field with the energy functional. The model can very precisely estimate the rolling force and rolling torque when compared to the measured data. The errors of the rolling force and rolling torque are less than 3.27 %.

Theoretical model for predicting stabbing resistance of soft body armor comprising fibrous composites

Soft body armor can effectively safeguard lives from stabbing attacks and they are mainly composed of fibrous composites. Currently, the evaluation of protective performance for soft body armor is mainly conducted by experiments or numerical simulations, with theoretical methods have been rarely mentioned. In this study, a spring-mass based theoretical model has been established to predict the stabbing resistant performance of a soft body armor comprising aramid with resin or unidirectional UHMWPE composites. The theoretical results agree well with the experimental results where the error in maximum impact force of the knife is within 3.2% and the displacement within 1.7%. The layers of penetration are also identical. By only inputting hardness and stiffness of the specimen, the theoretical model can efficiently provide the performance of a soft body armor composed of fiber composite material under different impact energy levels. With the aid of this theoretical model, one can optimize the composition of a soft body armor to achieve minimum weight and thickness in practical applications.

Hydrodynamic Analysis of Shallow Water Sloshing in Ship Chamber Under Longitudinal Earthquake

Shallow water sloshing-structure interaction under the coupled longitudinal and pitch motions resulted by the longitudinal earthquake directly affects the structural safety of the shiplift. However, no matter in shiplift or other related fields, there is little research on this aspect at present. As a basis of structural dynamics analysis and earthquake resistant design, an analytical method including a developed modal system and new engineering formulas is presented to predict the hydrodynamic moment and force in the ship chamber. Based on the linear modal theory, a modal system describing shallow water sloshing under longitudinal earthquake is developed with infinite set of modal functions. Then, new engineering formulas for calculating the hydrodynamic moment and force are proposed with only retaining the lowest sloshing mode (n=1). Case simulations suggest that the maximum error of hydrodynamic moment and force between n=1 and n=100 are lower than 1.3% and 10.5%, respectively. In addition, the hydrodynamic moment resulting from pressure on the walls can be reasonably ignored, which accounts for less than 0.5% percent of total hydrodynamic moment. With respect to the currently used Housner model, the presented formulas are greatly improved in computational accuracy and rationally supplement the missing part in the seismic design part of the Design code for shiplift.

Mathematical Modeling and Experimental Study of Cutting Force for Cutting Hard and Brittle Materials in Fixed Abrasive Trepanning Drill.

Hard and brittle materials have excellent physical and mechanical performance, which are widely applied in the fields of microelectronics and optoelectronics. However, deep-hole machining of hard and brittle materials is very difficult and inefficient due to the high hardness and brittleness of these materials. To improve the quality and efficiency of deep-hole machining of hard and brittle materials, according to the brittle crack fracture removal mechanism of hard and brittle materials and the cutting model of the trepanning cutter, an analytical cutting force prediction model of hard and brittle materials processed using a trepanning cutter is established. This experimental study of K9 optical glass machining shows that as the feeding rate increase, the cutting force increase, and as the spindle speed increase, the cutting force decrease. By comparing and verifying the theoretical and experimental values, the average errors of axial force and torque are 5.0% and 6.7%, respectively, and the maximum error is 14.9%. This paper analyzes the reasons for the errors. The results indicate that the cutting force theoretical model can be used to predict the axial force and torque of machining hard and brittle materials under the same conditions, which provides a theory for optimizing machining process parameters.

Design of an adjustable constant-force mechanism using a geared Sarrus linkage and spring

This paper presents the design of a novel adjustable constant-force mechanism (CFM) using a geared Sarrus linkage and a linear spring. The uniqueness of this design is that it provides a constant force over a wide range of displacement and the constant-force level can be adjusted energy-freely by varying the spring position without a preload. In this work, the construction, geometric constraints, and constant-force design of the CFM are expressed. The desired parameters of the mechanism, with consideration of gear friction, are also determined. A numerical example is then given to illustrate the constant-force performance and the effect of gear friction. This paper also shows a prototype of a CFM and experimental studies on it. It was found that the CFM delivered a constant force of up to 20 N within a stroke of 140 mm, and the force error was less than 6%. Moreover, the CFM compensated for masses of 1 and 2 kg with a torque reduction of more than 90%.