Inverse Dynamics of Bipedal Gait: The Assumption of the Center of Pressure as an Instantaneous Center of Rotation

Öz

In the study, an alternative 7-dof dynamical model that can be used in gait analysis of human, bipedal robots and exoskeleton systems is proposed. The dimensions and kinematic data of the model are specified on the basis of anthropometry and kinematic data of real human gait. The 7-link model consists of the trunk, two thighs, two shanks and two feet links. The movement is examined in the sagittal plane and during the single support phase (SSP). Unlike the rotation about a fixed point, it is assumed that the right foot rotates about the center of pressure (COP). The part between the COP and the tip of the toe is considered to be a passive limb which is horizontally on the ground. The effect of this part on dynamic analysis is neglected. The equations of motions are derived by applying Lagrange equations. Using the kinematic data obtained in clinical gait analysis (CGA) conducted by Winter [1], the net joint torques are calculated and then compared with CGA torque data. As a result of the comparisons, it is seen that the curves are overlapped significantly.

Anahtar Kelimeler

• Bipedal gait
• single support phase
• joint torques
• center of pressure (COP
• center of pressure (COP)
• instantaneous center of rotation(IC)

İki Bacaklı Yürüyüşün Ters Dinamiği : Basınç Merkezinin Bir Ani Dönme Merkezi Olduğu Varsayımı

Öz

Bu çalışmada, gerçek insan, iki ayaklı yürüyen robotlar ve dış iskelet sistemlerinin yürüyüş analizlerinde kullanılabilecek, 2 boyutlu alternatif bir dinamik model önerilmiştir. Modelin boyutları ve kinematik verileri, antropometrik veriler ve gerçek insan yürüyüşünün kinematik verileri esas alınarak belirlenmiştir. 7 uzuvlu model; gövde, iki adet üst bacak (uyluk), iki adet alt bacak (baldır) ve iki adet ayak uzuvlarından oluşmaktadır. Hareket, sagital düzlemde ve tek ayak destek fazında incelenmiştir. Sağ ayağın, sabit bir nokta etrafında dönmesinden farklı olarak, ayak basınç merkezi (COP) etrafında dairesel hareket yaptığı kabul edilmiştir. Basınç merkezi (COP) ile ayak başparmağı ucu arasındaki kısım, yatay olarak yerde hareketsiz bulunan pasif bir uzuv gibi değerlendirilmiştir. Bu kısmın dinamik analize etkisi ihmal edilmiştir. Lagrange denklemleri ile hareket denklemleri elde edilmiştir. Winter [1] tarafından yapılmış klinik yürüyüş deneylerinde elde edilen kinematik veriler kullanılarak, her bir uzvun hareketi için gerekli net mafsal torkları belirlenmiş ve grafikler üzerinde deneysel sonuçlarla karşılaştırılmıştır. Karşılaştırmalar neticesinde, analitik ve deneysel sonuçlardan elde edilen eğrilerin önemli oranda örtüştüğü görülmüştür.

Anahtar Kelimeler

• İki Ayaklı Yürüme
• tek ayak destek fazı
• mafsal torkları
• basınç merkezi
• ani dönme merkezi

Kaynakça

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