Double Pendulum

It is well-known that a suitably designed unpowered mechanical biped robot can “walk” down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, time period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. A passive motion has the distinction of being “natural” and is likely to enjoy energy optimality. Investigation of such motions may potentially lead us to strategies useful for controlling active walking machines. In this paper we demonstrate that the nonlinear dynamics of a simple passive “compass gait” biped robot can exhibit periodic and stable limit cycle. Kinematically the robot is identical to a double pendulum (or its variations such as the Acrobot and the Pendubot). Simulation results also reveal the existence of a stable gait with unequal step lengths. We also present an active control scheme which enlarges the basin of attraction of the passive limit cycle

Harvesting electrical energy from various human motions using piezoelectric energy harvesters (PEH) is gaining research attention in recent years. The energy harvested could potentially power hand held electronic devices and medical devices without the need of external power source for recharging batteries. In this study, an attempt is made to improve the efficiency of PEH to harvest energy from human motions by adopting a double pendulum system coupled with magnetic force interactions. For the purpose of comparison, three configurations of PEH which includes the conventional PEH with cantilever beam (PEHCB), the PEH with single pendulum system (PEHSP) and the PEH with double pendulum system (PEHDP) are experimentally studied. Excitations by both mechanical shaker and major human body parts during walking and jogging motions are investigated. The performance of each configuration, in terms of voltage and power produced as well as the idle time between each cycle, are analysed, compared and discussed. ANSYS© software is used to analyse the proposed model and MAT-LAB© software is used to calculate the output power. The results demonstrate that, with the use of the proposed double pendulum system, multiple impacts in each motion cycle is generated, thus producing higher voltage and power as compared to the conventional PEHCB. The idle time between each motion cycle is also effectively reduced. The efficiency of the PEH is thus significantly increased.

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT -symmetric dynamical models in complex phase space exhibit strong qualitative similarities.

In the paper we show the possibilities of physical modeling in Matlab/SimMechanics on a simple mechanical model of two link manipulator. We deal with its direct and inverse dynamics. Considering direct problem we investigate mechanical movement of the robot under the action of given forces and moments. As regards the issue of inverse motion we identify forces which cause a prescribed motion of the effector. Both problems are solved using block diagrams in Simulink and SimMechanics. Results are presented graphically.

Real-time demonstration of the main char. of chaos in the motion of a real double pendulum 1 Abstract. Several studies came to the conclusion that chaotic phenomena are worth including in high school and undergraduate education. The double pendulum is one of the simplest systems which are chaotic, therefore, the numerical simulations and theoretical studies of it have been given large publicity, and thanks to its spectacular motion, it has become one of the most famous demonstration tools of chaos, either through simulations or in real experiments. Although several attempts have been made to use the experiment in laboratory exercises, as the friction in the real experiment changes the nature of the motion and the values of characteristic parameters during the motion, examining the measured (dissipative) motion and to compare with theoretical results raise several questions. In our review, we are presenting a measurement system which is able to analyse these questions. The system, which consists of simple yet precise data acquisition electronics, easily attainable sensors, a Bluetooth module (to the communication with the PC), and an open-source software, demonstrates on-line the main characteristics of chaos and the methods of its study and allows to analyse the dissipative motion. Further information (including downloadable software) is provided on a dedicated page, http://www.inf.u-szeged.hu/noise/Research/DoublePendulum/.

Many activities present in the offshore technology are affected by sea waves and their safety strongly depends on the sea state. The fundamental question in operation risk analysis is the limit sea state which enables the safe operation controlled in all phases: from the sea surface to the sea bottom. The safe limit sea state is especially important when some lifting operation is performed in sea waves. This paper presents a dynamical model of a floating crane in sea waves with a hanging load at a high altitude above sea level. The model is defined as a linearized coupled double pendulum where the usual 6 DOF of the floating crane oscillatory motions in waves are extended by additional 3 DOF of the swinging load. The numerical model of the floating crane is calibrated and tuned according to the measured model in a towing tank. The significant values of the crane boom top accelerations were estimated for the given design sea state with different vertical load positions. The problem is illustrated by the example of a floating crane consisting of a simple single pontoon with an ordinary land crane mounted on the deck. The reliability of the proposed method is evaluated on the basis of correlation between the calculated and measured data.