Angular displacement

About: Angular displacement is a research topic. Over the lifetime, 5102 publications have been published within this topic receiving 46081 citations. The topic is also known as: rotational displacement.

Experimental control for initiating and maintaining rotation of parametric pendulum

Abstract: In this paper, the authors have studied experimentally the control methods of a parametric pendulum excited harmonically to initiate and maintain a period one rotation – the most superior response for energy harvesting. For initiating the period one rotation inherent in the system, first the bang-bang method is applied. Then a new method where velocity is monitored is proposed and applied and finally the time-delayed feedback method with multi-switching is considered. Ultimately the problem of maintaining the rotation of the pendulum is addressed. For first time, robustness and sensitivity of the latter method to change of frequency and amplitude of excitation and added noise are studied. Finally, it has been demonstrated how the delayed feedback method can be applied in a system of two pendula to ensure synchronized rotation.

Stabilisation aid for a vehicle- or vessel-borne search unit

Abstract: A stabilisation aid for a vehicle- or vessel-borne search unit comprises two servomechanisms for stabilising the observation part (3) of the search unit about two mutally perpendicular axes (8 1 and S 2 ) mounted on the part of the search unit which rotates about the search axis (1). The stabilisation aid comprises a computer (7) for determining, from the instantaneous angle of inclination (a) of the platform (2) supporting the search unit with respect to an earth-fixed reference axis and the instantaneous angular position (B) of the search unit about the search axis (1), measured in the plane of said platform (2), input signals for the servomechanisms. A portion of these input signals are compensating signals for the control errors in the servomechanisms, the principal causes of which control errors being the disturbing torques arising through the non-uniformity in the search motion and the rotational velocity of each of the stators with respect to the rotors of the servomechanism motors on their axes.

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

Abstract: New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.

A Simple One Dimensional Robot Joint Based on the ER Linear Reversing Mechanism

Abstract: The feasibility of using a well-known twin ER clutch linear reversing mechanism as a robotic actuator is demonstrated. High speed of response, displacement and positional accuracy can be obtained bi-directionally. A validated mathematical model of the apparatus provides a basis for the control strategy. Positional accuracy is enhanced by an ER brake which works in sequence with the clutch excitation switches. The robot arm, in rotational displacement is tested over a large number of cycles, speeds, displacements and inertial loads and the quality of control compared to that of competitive conventional servo motors.

Nonlinear elasticity and damping govern ultrafast dynamics in click beetles.

Abstract: Many small animals use springs and latches to overcome the mechanical power output limitations of their muscles. Click beetles use springs and latches to bend their bodies at the thoracic hinge and then unbend extremely quickly, resulting in a clicking motion. When unconstrained, this quick clicking motion results in a jump. While the jumping motion has been studied in depth, the physical mechanisms enabling fast unbending have not. Here, we first identify and quantify the phases of the clicking motion: latching, loading, and energy release. We detail the motion kinematics and investigate the governing dynamics (forces) of the energy release. We use high-speed synchrotron X-ray imaging to observe and analyze the motion of the hinge’s internal structures of four Elater abruptus specimens. We show evidence that soft cuticle in the hinge contributes to the spring mechanism through rapid recoil. Using spectral analysis and nonlinear system identification, we determine the equation of motion and model the beetle as a nonlinear single-degree-of-freedom oscillator. Quadratic damping and snap-through buckling are identified to be the dominant damping and elastic forces, respectively, driving the angular position during the energy release phase. The methods used in this study provide experimental and analytical guidelines for the analysis of extreme motion, starting from motion observation to identifying the forces causing the movement. The tools demonstrated here can be applied to other organisms to enhance our understanding of the energy storage and release strategies small animals use to achieve extreme accelerations repeatedly.