Actuator-level kinematic analysis of a PAM-driven dual four-bar knee exoskeleton for rehabilitation gait assistance

Fariesha Jani; Tuan Muhammad Ariff Ihsan Tuan Asmadi; Mohd Hanif Mohd Ramli; Wan Sulaiman Wan Mohamad

Authors

Fariesha Jani Institute of Postgraduate Studies, Faculty of Mechanical Engineering, Universiti Teknologi MARA, Shah Alam, 40450 Selangor, Malaysia
Tuan Muhammad Ariff Ihsan Tuan Asmadi Faculty of Mechanical Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
Mohd Hanif Mohd Ramli Department of Control and Engineering, Faculty of Mechanical Engineering, Universiti Teknologi MARA, Shah Alam 40450 Selangor, Malaysia
Wan Sulaiman Wan Mohamad Department of Control and Engineering, Faculty of Mechanical Engineering, Universiti Teknologi MARA, Shah Alam 40450 Selangor, Malaysia

Keywords:

knee exoskeleton, dual four-bar linkage, pneumatic artificial muscle, gait rehabilitation, closed-loop kinematics

Abstract

Stroke-related gait impairment commonly produces reduced knee coordination and insufficient toe clearance, motivating the development of compliant rehabilitation exoskeletons. Pneumatic artificial muscles (PAMs) offer compliant, biomimetic actuation well suited to rehabilitation gait training; however, existing four-bar linkage exoskeleton studies have focused on mechanism synthesis and joint-level trajectory reproduction without analytically characterising the continuous actuator-level kinematic demands that PAM actuation imposes across the gait cycle. This study develops a closed-loop kinematic framework for a PAM-driven dual four-bar knee exoskeleton, actuated by Festo DMSP-20 fluidic muscles, that maps prescribed rehabilitation knee trajectories to actuator displacement and contraction-rate demands at the preliminary design stage. The mechanism was reconstructed from the KNEXO structural concept using MotionGen simulation and modelled analytically through vector loop-closure analysis and Freudenstein’s equation. A continuous quartic stroke-map formulation was introduced to replace repeated inverse-kinematic computation with a single analytical expression, enabling efficient actuator evaluation throughout the gait cycle. The reconstructed mechanism reproduced the normative knee trajectory with a root-mean-square error of 2.69° over the eight gait-event boundaries, with all gait-event angles remaining within the Perry normative variability band and Freudenstein loop-closure residuals below 5% for both the primary and secondary mechanisms. All PAM contractions remained below 20% of the nominal actuator length, within the 25% practical operating limit of the selected actuator, while the quartic stroke-map reproduced the actuator-contraction relationship with root-mean-square errors of 0.23 cm and 0.37 cm. The proposed framework provides designers with an analytical tool for evaluating actuator contraction displacement, contraction-rate demands, and transmission kinematics in dual four-bar rehabilitation exoskeletons before committing to hardware fabrication.

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References

V. L. Feigin, M. Brainin, B. Norrving, S. O. Martins, J. Pandian, P. Lindsay, M. F. Grupper, and I. Rautalin, "World Stroke Organization: Global Stroke Fact Sheet 2025," Int. J. Stroke, vol. 20, no. 2, pp. 132–144, Feb. 2025, doi: 10.1177/17474930241308142.

S. J. Olney and C. Richards, "Hemiparetic gait following stroke. Part I: Characteristics," Gait Posture, vol. 4, no. 2, pp. 136–148, 1996, doi: 10.1016/0966-6362(96)01063-6.

J. Mehrholz, S. Thomas, J. Kugler, M. Pohl, and B. Elsner, "Electromechanical-assisted training for walking after stroke," Cochrane Database Syst. Rev., vol. 2020, no. 10, Art. no. CD006185, Oct. 2020, doi: 10.1002/14651858.CD006185.pub5.

N. Aliman, R. Ramli, and M. S. Amiri, "Actuators and transmission mechanisms in rehabilitation lower limb exoskeletons: A review," Biomed. Tech. (Berl.), vol. 69, no. 4, pp. 327–345, Aug. 2024, doi: 10.1515/bmt-2022-0262.

P. Beyl, M. Van Damme, R. Van Ham, B. Vanderborght, and D. Lefeber, "Design and control of a lower limb exoskeleton for robot-assisted gait training," Appl. Bionics Biomech., vol. 6, no. 2, pp. 229–243, Jul. 2009, doi: 10.1080/11762320902784393.

B. Kalita, A. Leonessa, and S. K. Dwivedy, "A Review on the Development of Pneumatic Artificial Muscle Actuators: Force Model and Application," Actuators, vol. 11, no. 10, Art. no. 288, Oct. 2022, doi: 10.3390/act11100288.

P. Beyl, M. Van Damme, R. Van Ham, B. Vanderborght, and D. Lefeber, "Pleated pneumatic artificial muscle-based actuator system as a torque source for compliant lower limb exoskeletons," IEEE/ASME Trans. Mechatron., vol. 19, no. 3, pp. 1046–1056, Jun. 2014, doi: 10.1109/TMECH.2013.2268942.

L. Wu, C. Wang, J. Liu, B. Zou, S. Chakrabarty, T. Bao, and S. Q. Xie, "Novel Design on Knee Exoskeleton with Compliant Actuator for Post-Stroke Rehabilitation," Sensors, vol. 25, no. 1, Art. no. 153, Jan. 2025, doi: 10.3390/s25010153.

A. Niyetkaliyev, A. Turganbayev, M. Karasheva, R. Zhylkaidarov, and Y. Turlybek, "Exploring the Potential of Four-Bar Linkages in Robotic Exoskeletons: A Comprehensive Review," J. Mech. Des., vol. 147, no. 10, Art. no. 100801, Oct. 2025, doi: 10.1115/1.4068107.

S. Kittisares, T. Ide, H. Nabae, and K. Suzumori, "Ergonomic dual four-bar linkage knee exoskeleton for stair ascent assistance," Front. Robot. AI, vol. 10, Art. no. 1285520, Dec. 2023, doi: 10.3389/frobt.2023.1285520.

M. Gao, Z. Wang, S. Li, J. Li, Z. Pang, S. Liu, and Z. Duan, "Design and optimization of exoskeleton structure of lower limb knee joint based on cross four-bar linkage," AIP Advances, vol. 11, no. 6, Art. no. 065124, Jun. 2021, doi: 10.1063/5.0053899.

A. Purwar, S. Deshpande, and Q. J. Ge, "MotionGen: Interactive design and editing of planar four-bar motions for generating pose and geometric constraints," J. Mech. Robot., vol. 9, no. 2, Art. no. 024504, Apr. 2017, doi: 10.1115/1.4035899.

J. Perry and J. M. Burnfield, Gait Analysis: Normal and Pathological Function, 2nd ed. Thorofare, NJ, USA: SLACK, 2010.

A. Rodríguez-Fernández, J. Lobo-Prat, and J. M. Font-Llagunes, "Systematic review on wearable lower-limb exoskeletons for gait training in neuromuscular impairments," J. NeuroEng. Rehabil., vol. 18, no. 1, Art. no. 22, Feb. 2021, doi: 10.1186/s12984-021-00815-5.

D. A. Winter, Biomechanics and Motor Control of Human Movement, 4th ed. Hoboken, NJ, USA: John Wiley & Sons, 2009.

Festo AG & Co. KG, "Fluidic Muscle DMSP," Product datasheet, Esslingen, Germany. [Online]. Available: https://www.festo.com/us/en/p/fluidic-muscle-id_DMSP/ (accessed May 21, 2026).

R. L. Norton, Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines, 5th ed. New York, NY, USA: McGraw-Hill, 2012.

L. Biagiotti and C. Melchiorri, Trajectory Planning for Automatic Machines and Robots, 1st ed. Berlin, Germany: Springer, 2008.

B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, Robotics: Modelling, Planning and Control, 1st ed. London, U.K.: Springer, 2009.

R. L. Burden and J. D. Faires, Numerical Analysis, 9th ed. Boston, MA, USA: Brooks/Cole, Cengage Learning, 2010.

S. Krishna, T. Nagarajan, and A. M. A. Rani, "Review of Current Development of Pneumatic Artificial Muscle," J. Appl. Sci., vol. 11, no. 10, pp. 1749–1755, 2011, doi: 10.3923/jas.2011.1749.1755.