Abstract
Legged robots have a potential of being a walking machine on irregular ground. Eleven-bar linkages, Theo Jansen mechanism reproduces a smooth locomotion pattern as gait. Parallel motions have widely used in the heavy machinery and recently highlighted in a model of biological motions. The close-loop linkage simply provides a designed end-effector trajectory, whereas the trajectory is considered to be less modifiable due to the singularity problem. In the present study, the singularity on the modified Theo Jansen mechanism was addressed by introducing the parametric orbit as a new freedom point in the joint center, and analyzed its kinematics and dynamics by using multibody dynamics (MBD). The extendability of the mechanism in the viewpoint of flexibility in the gait trajectory was clearly demonstrated in the numerical simulation, providing new functional gait trajectories controlled by two control parameters that change the shape of the parametric oval in the joint center. In systematic determinant analyses of how broken trajectories were generated depending on four parameters, i.e., horizontal and vertical amplitudes and rotation angle of the joint center movement and its phase difference with the driving link, morpho-logical changes of generated trajectories in the phase-rotation-amplitude parameter space were revealed. Thus the extension capability of Theo Jansen mechanism was validated not only in smooth walking but also in jumping, climbing and running-like motions. In considering the ways of control, the present results indicated that there exists a inverse relationship between the rotation angle and the phase difference to significantly reduce the occurrence of the singularity and breakage failures of the mechanism, which is consistent with biological evidences of coupling oscillators that enables the nervous system to control the complex musculoskeletal system by using a few of simple parameters frequently represented by the phase and rotation in a torus state space.
Highlights
Flexible and adaptive movements generated from biological systems are of interest to academics in the area of biomechanics and to engineers to improve traditional mechanical schemes
Theo Jansen proposed a kinematics for providing of legged robots in the form of the closed-loop linkage with eleven linkbars, called Theo Jansen mechanism and demonstrated that it worked for heavy payload conditions in a various type of similar mechanisms
“Hypothesis,” extended functional motions are able to be generated by adding a synchronous movement of O2 joint center, which represents a kind of knee position as an analogy so that the driving cycle of O1 and the end effector motion of G are assumed to be inguinal and toe, respectively [12]
Summary
Flexible and adaptive movements generated from biological systems are of interest to academics in the area of biomechanics and to engineers to improve traditional mechanical schemes. Bio-inspired mechatronics to mimic biological mechanisms in motions and behaviors have been investigated [1], and the legged motions are frequently modeled by the serial mechanism connected by joints with dampers and springs such as the passive walker [2], known as openloop linkages. It implies that the maxi-mum payload relies on the torque performance of individual actuators embedded in joints of the open-loop linkage. Theo Jansen proposed a kinematics for providing of legged robots in the form of the closed-loop linkage with eleven linkbars, called Theo Jansen mechanism and demonstrated that it worked for heavy payload conditions in a various type of similar mechanisms [7]. Kim [9] demonstrated a real remote-controllable robot based on the mechanism to test the walking performance on shore and marsh place
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