1990 年 10 巻 p. 85-95
Bipedal dinosaurs are huge and curious animals that have short forelimbs, powerful hindlimbs, and a long and heavy tail. The restoration of their posture and locomotion is difficult because of the lack of resemblant living animals. In this study, we paid attention to the harmony between animal motion and body shape, and conversely estimated the posture and locomotion of the bipedal dinosaurs from the characteristics of the body proportions using a computer simulation method. The mathematical model was constructed by the three-dimensional rigid link system with the following fourteen segments: head, neck, thorax, pelvis, upper arms, forearms, thighs, shanks, bottom tail, and top tail. An axis of the central body segments rotates about the vertical axis with a constant pitch angle defined by the initial posture. Each limb moves in the sagittal plane of the thorax or pelvis segment. Body weight is supported by the lumbar joint. Both torque spring and damper element are attached in each joint to prevent large relative rotation. Nonlinear elasticity is given in the knee and elbow joints to avoid hyper-extension of the joint. Using these assumptions, we can deduce seventeen simultaneous second-order differential equations. The numerical calculation of the oscillation mode was performed by using the fourth-order Runge-Kutta method. By means of this method, we analyzed Allosaurus, which was a typical bipedal dinosaur in the Jurassic period. The length of each segment was estimated from measured data of fossil skeletons. Other physical parameters, such as weight, moment of inertia and center of mass of each segment, were calculated geometrically from the restored shape. The torque spring and damper elements of each joint were referred from living animals. The numerical calculations were performed by assuming several body proportions and postures. The following results were obtained: Stability and walking speed with erect posture are inferior to the horizontal posture. The long and heavy tail is useful to obtain harmonic motion and greater speed. But the weight of the short forelimbs has almost no effects on the locomotion. The narrow distance between the hip joints increases the walking speed and decreases the swing of the body. The walking speed calculated by the stride of fossil pit and the oscillation frequency of the hindlimbs is 5.6km/h, which is within the speed range of mammals. Consequently, we can reconstruct the walking of Allosaurus, which held its trunk and tail horizontal and moved stably at almost mammalian speed.