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Damping Coefficients and Torque Calculations for the Joint's Stability of Lower Extremity Exoskeleton Robots

Yıl 2014, Cilt: 18 Sayı: 3, 35 - 51, 04.01.2015

Öz

Exoskeleton robots are wearable electromechanical structures which can work interacting with human limbs. Theserobotsareused as assistivelimbs, rehabilitationandpoweraugmentationpurposesforelderly or paralyzedpersons andhealthypersons respectively.Human body neuro-muscular system varies the stiffness and damping of the human joints regularly and thus provides flexible and stable movement capability with minimum energy consumption. Damping coefficients and torques in the joints needs to be adjusted with the change of stiffness to provide stable behavior during walking cycles. Magneto-rheological brake are the passive actuators that can adjust the damping torques in a very short response time. However, the maximum values of damping coefficients and torques are needed for the design of MR dampers to be used in the joints of exoskeleton robots. Shamaei et. al. (2013) derived a set of statistical equations to predict thejoint stiffnessin a gait cycle for the persons with different height and weights. In this paper, the maximum values of damping coefficients and torques are calculated for the design of MR dampers to provide stability in the joints of exoskeleton robots. The results can be used as initial design criteria of MR dampers which will be added to the biomimetic joints of exoskeleton robots, prostheses, ortheses and humanoid robots

Kaynakça

  • Andriacchi, T.P., Ogle, J.A., Galante, J.O., 1977. Walking speed as a basis for normal and abnormal gait measurements. Journal of Biomechanics, 10, 261– 268.
  • Bovi, G., Rabuffetti, M., Mazzoleni, P., Ferrarin, M., 2010. A multiple-task gait analysis approach: kinematic, kinetic and EMG reference data for healthy young and adult subjects. Gait and Posture, 33, 6-13.
  • Chesney, C.W., 2002. Implementation of planar hybrid actıve/passıve forcefeedback user input device. (PhD Thesis), Unıversıty of Florida.
  • Collins, S., Kuo, A., 2010. Recycling energy to restore impaired ankle function during human walking. Plos One 5: e9307.
  • Contini, R., 1972. Body Segment Parameters Part II, Artificial Limbs,16, 1–19.
  • Crenna, P., Frigo, C., 2011. Dynamics of the ankle joint analyzed through moment-angle loops during human walking: gender and age effects. Human Movement Science, 30, 1185–1198.
  • Dempster, W. T., 1955. Space Requirements of the Seated Operator, WADC-TR-55-159.
  • Dempster, W. T., Gabel, W. C., Felts, W. J. L., 1959. The Anthropometry of Manual Work Space for the Seated Subjects, Am. J. Phys. Anthrop.,17, 289–317.
  • Drillis, R., Contini, R., 1966. Body Segment Parameters, Rep. 1163-03, Office of Vocational Rehabilitation, Department of Health, Education, and Welfare, New York,.
  • Dollar, A.M., Herr, H., 2008. Lower extremity exoskeletons and active orthoses: challenges and state-of-the-art. IEEE Transactions on Robotics, 24, 144–158.
  • Elftman, H., 1966. Biomechanics of Muscle, with Particular Application to Studies of Gait. J. Bone Joint Surg., 48-A, 363–377.
  • Enoch, A., Sutas, A., Nakaokay, S., Vijayakumar, S., 2012. BLUE: A Bipedal Robot with Variable Stiffness and Damping. Proc. 12th IEEE-RAS Intl. Conference on Humanoid Robots, Osaka-Japan.
  • Ferris, D., Lewis, C., 2009. Robotic lower limb exoskeletons using proportional myoelectric control. EMBC Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2119– 2124.
  • Frigo, C., Crenna, P., Jensen, L., 1996. Moment-angle relationship at lower limb joints during human walking
  • Electromyography and Kinesiology, 6, 177–190. velocities. Journal
  • of Gordon, K., Ferris, D., 2007. Learning to walk with a robotic ankle exoskeleton. Journal of Biomechanics, 40, 2636–2644.
  • Grieve, D. W., Cavanagh, P. R., Pheasant, S., 1978. Prediction of Gastrocnemius Length from Knee and Ankle Joint Posture. Biomechanics, cilt. VI-A, E. Asmussen and K. Jorgensen, Eds. University Park Press, Baltimore, MD, 405–412.
  • Haxton, H. A., 1944. Absolute Muscle Force in the Ankle Flexors of Man. J. Physiol., 103, 267–273.
  • Hatze, H., 1975. A New Method for the Simultaneous Measurement of the Moment of Inertia, the Damping Coefficient and the Location of the Center of Mass of a Body Segment in situation. Eur. J. Appl. Physiol., 34, 217–266.
  • Herr, H., Wilkenfeld, A., 2003. User-adaptive control of a magnetorheological prosthetic knee, Industrial Robot. An International Journal, 30(1), 42–55.
  • Hitt, J., Sugar, T., Holgate, M., Bellman, R., Hollander, K., 2009. Robotic transtibial prosthesis with biomechanical energy regeneration. Industrial Robot- an International Journal, 36, 441–447.
  • Hollander, K. W., Ilg, R., Sugar, T. G., Herring, D., 2006. An efficient robotic tendon for gait assistance. J. Biomech. Eng., 128(5), 788–791.
  • Horak, F. B., Nashner., L. M., 1986. Central Programming of Postural Movements: Adaptation to Altered Surface
  • Neurophysiol., 55, 1369–1381, Configurations.
  • J. Horak, F. B., Nutt, J. G., Nashner., L. M., 1992. Postural Inflexibility in Parkinsonian Subjects. J. Neurol. Sci., 111, 46–58.
  • Jian, Y., Winter, D. A., Ishac, M. G., Gilchrist, L., 1992. Trajectory of the Body COG and COP During Initiation and Termination of Gait. Gait and Posture, 1, 9–22.
  • MacKinnon, C. D., Winter, D. A., 1993. Control of Whole Body Balance and Posture in the Frontal Plane During Walking. J. Biomech.,26, 633–644.
  • Maughan, R. J., Watson, J. S., Weir, J., 1983. Strength and Cross-Sectional Area of Human Skeletal Muscle. J. Physiol.,338, 37–49.
  • Migliore, S. A., Brown, E. A., DeWeerth, S. P., 2005. Biologically inspired joint stiffness control, in Proc. IEEE Int. Conf. Robotics and Automation (ICRA’05), Nisan, 4519–4524.
  • Morita, T., Sugano S., 1997. Development of an anthropomorphic forcecontrolled manipulator WAM- 10. Int. Conf. on Advanced Robotics, 701–706 .
  • Ogata, K., 2010. Modern Control Engineering . ISBN: 0136156738, Prentice Hall.
  • Perry J., 1992. Gait analysis : normal and pathological function. Slack, Thorofare, NJ.
  • Poynor, J.C., 2001. Innovative designs for magneto- rheological dampers. MS Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
  • Radulescu, A.,Howard, M., BraunD.J., Vijayakumar, S.,2012. Exploiting variable physical damping in rapid movement tasks. IEEE/ASME Int. Conference on Advanced Intellegent Machatronics, Taiwan.
  • Sawicki, G.S., Domingo, A., Ferris, D., 2006. The effects of powered ankle-foot orthoses on joint kinematics and muscle activation during walking in individuals with incomplete spinal cord injury. Journal of Neuroengineering and Rehabilitation, 3, 3.
  • Sawicki, G.S., Lewis, C., Ferris, D., 2009. It pays to have a spring in your step. Exercise and Sport Sciences Reviews, 37, 130–138.
  • Shamaei, K., Dollar, A., 2011. On the Mechanics of the Knee During the Stance Phase of the Gait. IEEE- International Conference on Rehabilitation Robotics (ICORR), Seattle.
  • Shamaei, K., Napolitano, P., Dollar, A., 2013. A Quasi- Passive Compliant Stance Control Knee-Ankle-Foot Orthosis.
  • Rehabilitation Robotics (ICORR), Seattle. Conference
  • on Shamaei, K, Sawicki, G.S., Dollar, A.M., 2013. Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle. The Stance Phase of Walking, 8(3), 1-12.
  • Shamaei, K., Sawicki, G.S., Dollar, A.M., 2013. Estimation of Quasi-Stiffness of the Human Knee. The Stance Phase of Walking, 8(3), 1-10.
  • Shamaei, K., Sawicki, G.S., Dollar, A.M., 2013. Estimation of Quasi-Stiffness of the Human Hip. The Stance Phase of Walking, 8(12), 1-11.
  • Skinner, S., Antonelli, D., Perry, J., Lester, D., 1985. Functional demands on the stance limb in walking. Orthopedics, 8, 355–361.
  • Smidt, G. L., 1973. Biomechanical Analysis of Knee Flexion and Extension. J. Biomech., 6, 79–92.
  • http://dx.doi.org/10.1016/j.robot.2013.06.009 .
  • Van Ham, R., Sugar, T. G., Vanderborght, B., Hollander K. W., ve Lefeber, D., 2009. Compliant Actuator Design; Review of actuators with passive adjustable compliance/controllable
  • applications. IEEE robotics & automation magazine, Eylül. stiffness for
  • robotic Veneman, J.F., Ekkelenkamp, R., Kruidhof, R., van der Helm,F.C.T., van der Kooij, H., 2006. A Series Elastic and Bowden-Cable-Based Actuation System For Use as Torque Actuator İn Exoskeleton-Type Robots. The Internatioanl Journal of Robotics Research, 25 (3), 261-281 .
  • Walsh, C., Paluska, D., Pasch, K., Grand, W., Valiente, A., vd., 2006. Development of a lightweight, underactuated
  • augmentation. Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 15– 19 Mayıs, 3485–3491. for
  • load-carrying Wickiewcz, T. L., Roy, R. R., Powell, P. L., Edgerton, V. R., 1983. Muscle Architecture of the Human Lower Limb. Clin. Orthop. Rel. Res., 179, 275–283.
  • Wilkie, D. R., 1950. The Relation between Force and Velocity in Human Muscle. J. Physiol.,110, 249–280.
  • Winter, D. A., Patla, A. E., Prince, F., Ishac, M. G., Gielo- Perczak, K., 1998. Stiffness Control of Balance in Quiet Standing. J. Neurophysiol., 80, 1211–1221.
  • Winter, D.A., Robertson, D.G.E., 1978. Joint torque and energy patterns in normal gait. Biological Cybernetics, 29, 137–142.
  • Winter, D., 2005. Biomechanics and motor control of human movement. John Wiley & Sons, Hoboken, New Jersey.
  • Winter, D. A., 1984. Kinematic and Kinetic Patterns in Human Gait: Variability and Compensating Effects. Hum. Movement Sci., 3, 51–76.
  • Zhu, X.,Jing, X., Cheng, L., 2012.Magnetorheological Fluid Dampers: A Review on Structure Design and Analysis,Journal of Intelligent Material Systems and Structures. 28(3), 839-873.

Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları ve Momentlerinin Hesaplanması

Yıl 2014, Cilt: 18 Sayı: 3, 35 - 51, 04.01.2015

Öz

Dış iskelet robotlar, insan uzuvları ile etkileşim halinde çalışan, giyilebilir
elektromekanik yapılardır. Bu robotlar, yürüme engeli olan ya da yaşlı kişilerde
yardımcı uzuv, felçli kişilerde rehabilitasyon ve sağlıklı insanlarda güç artırımı
amacı ile kullanılmaktadır. İnsan vücudunun sinir-kas sistemi, bağlı
bulundukları eklemlerde sertlik ve sönümlemeyi devamlı değiştirerek
minimum enerji sarfiyatı ile esnek ve kararlı bir hareket kabiliyeti
sağlamaktadır. Yürüme sırasında eklemlerin sertliğinin değişmesi ile birlikte
kararlı bir yürümenin gerçeklenebilmesi için eklemlerdeki sönümleme
katsayılarının ve sönümleme momentlerinin eş zamanlı olarak değiştirilmesi
gerekmektedir. Manyeto-reolojik (MR) frenler, bu farklı sönümleme
momentlerini en hızlı şekilde ayarlayabilen pasif eyleyicilerdir. Ancak, dış
iskelet robotların eklemlerinde kullanılacak MR fren tasarımları için istenen
maksimum sönümleme katsayısı ve sönümleme momenti değerlerinin
bilinmesi gerekmektedir. Shamaei ve arkadaşları (2013) biyomekanik bir
çalışma gerçekleştirerek farklı boy ve kilolardaki kişiler için yürüme sırasında
eklem sertlik katsayısı değişimini genel istatiksel formüller ile ifade
etmişlerdir. Bu makalede; alt uzuv dış iskelet robotların eklemlerinde kararlı
bir yürüme davranışını sağlayabilecek MR fren tasarımları için gerekli olan
sönümleme katsayısı ve momentlerinin maksimum değerleri hesaplanmıştır.
Elde edilen sonuçlar, dış iskelet robotların, ortezlerin, protezlerin ve insansı
robotların biyomimetik eklemelerine yerleştirilecek MR frenlerin başlangıç
tasarım kriteri olarak kulllanılabilecektir.

Kaynakça

  • Andriacchi, T.P., Ogle, J.A., Galante, J.O., 1977. Walking speed as a basis for normal and abnormal gait measurements. Journal of Biomechanics, 10, 261– 268.
  • Bovi, G., Rabuffetti, M., Mazzoleni, P., Ferrarin, M., 2010. A multiple-task gait analysis approach: kinematic, kinetic and EMG reference data for healthy young and adult subjects. Gait and Posture, 33, 6-13.
  • Chesney, C.W., 2002. Implementation of planar hybrid actıve/passıve forcefeedback user input device. (PhD Thesis), Unıversıty of Florida.
  • Collins, S., Kuo, A., 2010. Recycling energy to restore impaired ankle function during human walking. Plos One 5: e9307.
  • Contini, R., 1972. Body Segment Parameters Part II, Artificial Limbs,16, 1–19.
  • Crenna, P., Frigo, C., 2011. Dynamics of the ankle joint analyzed through moment-angle loops during human walking: gender and age effects. Human Movement Science, 30, 1185–1198.
  • Dempster, W. T., 1955. Space Requirements of the Seated Operator, WADC-TR-55-159.
  • Dempster, W. T., Gabel, W. C., Felts, W. J. L., 1959. The Anthropometry of Manual Work Space for the Seated Subjects, Am. J. Phys. Anthrop.,17, 289–317.
  • Drillis, R., Contini, R., 1966. Body Segment Parameters, Rep. 1163-03, Office of Vocational Rehabilitation, Department of Health, Education, and Welfare, New York,.
  • Dollar, A.M., Herr, H., 2008. Lower extremity exoskeletons and active orthoses: challenges and state-of-the-art. IEEE Transactions on Robotics, 24, 144–158.
  • Elftman, H., 1966. Biomechanics of Muscle, with Particular Application to Studies of Gait. J. Bone Joint Surg., 48-A, 363–377.
  • Enoch, A., Sutas, A., Nakaokay, S., Vijayakumar, S., 2012. BLUE: A Bipedal Robot with Variable Stiffness and Damping. Proc. 12th IEEE-RAS Intl. Conference on Humanoid Robots, Osaka-Japan.
  • Ferris, D., Lewis, C., 2009. Robotic lower limb exoskeletons using proportional myoelectric control. EMBC Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2119– 2124.
  • Frigo, C., Crenna, P., Jensen, L., 1996. Moment-angle relationship at lower limb joints during human walking
  • Electromyography and Kinesiology, 6, 177–190. velocities. Journal
  • of Gordon, K., Ferris, D., 2007. Learning to walk with a robotic ankle exoskeleton. Journal of Biomechanics, 40, 2636–2644.
  • Grieve, D. W., Cavanagh, P. R., Pheasant, S., 1978. Prediction of Gastrocnemius Length from Knee and Ankle Joint Posture. Biomechanics, cilt. VI-A, E. Asmussen and K. Jorgensen, Eds. University Park Press, Baltimore, MD, 405–412.
  • Haxton, H. A., 1944. Absolute Muscle Force in the Ankle Flexors of Man. J. Physiol., 103, 267–273.
  • Hatze, H., 1975. A New Method for the Simultaneous Measurement of the Moment of Inertia, the Damping Coefficient and the Location of the Center of Mass of a Body Segment in situation. Eur. J. Appl. Physiol., 34, 217–266.
  • Herr, H., Wilkenfeld, A., 2003. User-adaptive control of a magnetorheological prosthetic knee, Industrial Robot. An International Journal, 30(1), 42–55.
  • Hitt, J., Sugar, T., Holgate, M., Bellman, R., Hollander, K., 2009. Robotic transtibial prosthesis with biomechanical energy regeneration. Industrial Robot- an International Journal, 36, 441–447.
  • Hollander, K. W., Ilg, R., Sugar, T. G., Herring, D., 2006. An efficient robotic tendon for gait assistance. J. Biomech. Eng., 128(5), 788–791.
  • Horak, F. B., Nashner., L. M., 1986. Central Programming of Postural Movements: Adaptation to Altered Surface
  • Neurophysiol., 55, 1369–1381, Configurations.
  • J. Horak, F. B., Nutt, J. G., Nashner., L. M., 1992. Postural Inflexibility in Parkinsonian Subjects. J. Neurol. Sci., 111, 46–58.
  • Jian, Y., Winter, D. A., Ishac, M. G., Gilchrist, L., 1992. Trajectory of the Body COG and COP During Initiation and Termination of Gait. Gait and Posture, 1, 9–22.
  • MacKinnon, C. D., Winter, D. A., 1993. Control of Whole Body Balance and Posture in the Frontal Plane During Walking. J. Biomech.,26, 633–644.
  • Maughan, R. J., Watson, J. S., Weir, J., 1983. Strength and Cross-Sectional Area of Human Skeletal Muscle. J. Physiol.,338, 37–49.
  • Migliore, S. A., Brown, E. A., DeWeerth, S. P., 2005. Biologically inspired joint stiffness control, in Proc. IEEE Int. Conf. Robotics and Automation (ICRA’05), Nisan, 4519–4524.
  • Morita, T., Sugano S., 1997. Development of an anthropomorphic forcecontrolled manipulator WAM- 10. Int. Conf. on Advanced Robotics, 701–706 .
  • Ogata, K., 2010. Modern Control Engineering . ISBN: 0136156738, Prentice Hall.
  • Perry J., 1992. Gait analysis : normal and pathological function. Slack, Thorofare, NJ.
  • Poynor, J.C., 2001. Innovative designs for magneto- rheological dampers. MS Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
  • Radulescu, A.,Howard, M., BraunD.J., Vijayakumar, S.,2012. Exploiting variable physical damping in rapid movement tasks. IEEE/ASME Int. Conference on Advanced Intellegent Machatronics, Taiwan.
  • Sawicki, G.S., Domingo, A., Ferris, D., 2006. The effects of powered ankle-foot orthoses on joint kinematics and muscle activation during walking in individuals with incomplete spinal cord injury. Journal of Neuroengineering and Rehabilitation, 3, 3.
  • Sawicki, G.S., Lewis, C., Ferris, D., 2009. It pays to have a spring in your step. Exercise and Sport Sciences Reviews, 37, 130–138.
  • Shamaei, K., Dollar, A., 2011. On the Mechanics of the Knee During the Stance Phase of the Gait. IEEE- International Conference on Rehabilitation Robotics (ICORR), Seattle.
  • Shamaei, K., Napolitano, P., Dollar, A., 2013. A Quasi- Passive Compliant Stance Control Knee-Ankle-Foot Orthosis.
  • Rehabilitation Robotics (ICORR), Seattle. Conference
  • on Shamaei, K, Sawicki, G.S., Dollar, A.M., 2013. Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle. The Stance Phase of Walking, 8(3), 1-12.
  • Shamaei, K., Sawicki, G.S., Dollar, A.M., 2013. Estimation of Quasi-Stiffness of the Human Knee. The Stance Phase of Walking, 8(3), 1-10.
  • Shamaei, K., Sawicki, G.S., Dollar, A.M., 2013. Estimation of Quasi-Stiffness of the Human Hip. The Stance Phase of Walking, 8(12), 1-11.
  • Skinner, S., Antonelli, D., Perry, J., Lester, D., 1985. Functional demands on the stance limb in walking. Orthopedics, 8, 355–361.
  • Smidt, G. L., 1973. Biomechanical Analysis of Knee Flexion and Extension. J. Biomech., 6, 79–92.
  • http://dx.doi.org/10.1016/j.robot.2013.06.009 .
  • Van Ham, R., Sugar, T. G., Vanderborght, B., Hollander K. W., ve Lefeber, D., 2009. Compliant Actuator Design; Review of actuators with passive adjustable compliance/controllable
  • applications. IEEE robotics & automation magazine, Eylül. stiffness for
  • robotic Veneman, J.F., Ekkelenkamp, R., Kruidhof, R., van der Helm,F.C.T., van der Kooij, H., 2006. A Series Elastic and Bowden-Cable-Based Actuation System For Use as Torque Actuator İn Exoskeleton-Type Robots. The Internatioanl Journal of Robotics Research, 25 (3), 261-281 .
  • Walsh, C., Paluska, D., Pasch, K., Grand, W., Valiente, A., vd., 2006. Development of a lightweight, underactuated
  • augmentation. Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 15– 19 Mayıs, 3485–3491. for
  • load-carrying Wickiewcz, T. L., Roy, R. R., Powell, P. L., Edgerton, V. R., 1983. Muscle Architecture of the Human Lower Limb. Clin. Orthop. Rel. Res., 179, 275–283.
  • Wilkie, D. R., 1950. The Relation between Force and Velocity in Human Muscle. J. Physiol.,110, 249–280.
  • Winter, D. A., Patla, A. E., Prince, F., Ishac, M. G., Gielo- Perczak, K., 1998. Stiffness Control of Balance in Quiet Standing. J. Neurophysiol., 80, 1211–1221.
  • Winter, D.A., Robertson, D.G.E., 1978. Joint torque and energy patterns in normal gait. Biological Cybernetics, 29, 137–142.
  • Winter, D., 2005. Biomechanics and motor control of human movement. John Wiley & Sons, Hoboken, New Jersey.
  • Winter, D. A., 1984. Kinematic and Kinetic Patterns in Human Gait: Variability and Compensating Effects. Hum. Movement Sci., 3, 51–76.
  • Zhu, X.,Jing, X., Cheng, L., 2012.Magnetorheological Fluid Dampers: A Review on Structure Design and Analysis,Journal of Intelligent Material Systems and Structures. 28(3), 839-873.
Toplam 57 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Özel Sayı
Yazarlar

Mehmet Demiray Bu kişi benim

Özgür Başer Bu kişi benim

Ergin Kılıç Bu kişi benim

Yayımlanma Tarihi 4 Ocak 2015
Yayımlandığı Sayı Yıl 2014 Cilt: 18 Sayı: 3

Kaynak Göster

APA Demiray, M., Başer, Ö., & Kılıç, E. (2015). Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları ve Momentlerinin Hesaplanması. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 18(3), 35-51.
AMA Demiray M, Başer Ö, Kılıç E. Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları ve Momentlerinin Hesaplanması. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. Ocak 2015;18(3):35-51.
Chicago Demiray, Mehmet, Özgür Başer, ve Ergin Kılıç. “Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları Ve Momentlerinin Hesaplanması”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 18, sy. 3 (Ocak 2015): 35-51.
EndNote Demiray M, Başer Ö, Kılıç E (01 Ocak 2015) Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları ve Momentlerinin Hesaplanması. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 18 3 35–51.
IEEE M. Demiray, Ö. Başer, ve E. Kılıç, “Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları ve Momentlerinin Hesaplanması”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 18, sy. 3, ss. 35–51, 2015.
ISNAD Demiray, Mehmet vd. “Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları Ve Momentlerinin Hesaplanması”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 18/3 (Ocak 2015), 35-51.
JAMA Demiray M, Başer Ö, Kılıç E. Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları ve Momentlerinin Hesaplanması. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2015;18:35–51.
MLA Demiray, Mehmet vd. “Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları Ve Momentlerinin Hesaplanması”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 18, sy. 3, 2015, ss. 35-51.
Vancouver Demiray M, Başer Ö, Kılıç E. Alt Uzuv Dış İskelet Robot Eklemlerinde Kararlılık İçin Sönümleme Katsayıları ve Momentlerinin Hesaplanması. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2015;18(3):35-51.

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