Flexible Legs Research Articles

Impact modelling and analysis of the compliant legged robots

The dynamics of the compliant legged robots are commonly characterized by the spring loaded inverted pendulum model. In this article, a new model is presented for the impact of the compliant legged robots. Compared with the spring loaded inverted pendulum model, the new model provides a means to take into account the factors such as the sliding of the terminal, the vibrations of the leg with distributed compliance and variation of the nonlinear contact force. The effectiveness of the model is validated by the finite element program LS-DYNA from the velocity and energy point of view. Based on the method used, the influences of the parameters, such as the incident angle, width, thickness and Young’s modulus of the flexible leg on the dynamic characteristics of the robot, are analysed. It is found that the post-impact vertical velocity of the robot decreases with the increasing incident angles, and increases approximately linearly with the width and thickness, while the variation of Young’s modulus of the flexible leg has little effects on it. The same is true of the energy loss ratio during the impact. All the parameters investigated are more intuitive than the stiffness described in the spring loaded inverted pendulum model and can be utilized directly for the optimization design and locomotion control of the compliant legged robots. In addition, the vibrations and multiple impacts can be predicted by the proposed model to reduce the energy loss.

Role of flexibility in the water repellency of water strider legs: Theory and experiment

Water striders enjoy an intriguing ability to stand and walk freely on water surfaces, which is mainly attributed to the superior water repellency of their slender legs. In previous theoretical analyses, the legs are usually treated as rigid beams and the results show that a tremendously deep dimple and a large supporting force can be achieved when the leg descends into water. In this paper, the effect of the flexibility of water strider legs on their water-repellent ability is investigated, both theoretically and experimentally. We analyze a hydrophobic and flexible leg pressing obliquely on water. The leg may undergo a large deformation and assume different geometric configurations. It is shown that the flexible leg can float easily on a water surface, inducing only a shallow water puddle and a moderate supporting force as observed in real water striders. When the long leg is sufficiently compliant, the water surface will never be pierced and the leg will never sink. The findings are experimentally testified by using flexible fibers to represent water strider legs pressing on water.

Dynamic Modeling of Continuum Flexible Leg System for Micro Robot

The micro robot that based on resonant principle can get high speed and high precision. However its leg is usually a flexible continuum with complex shapes, and its dynamic modeling is a key problem during researching this kind of robot. A method combining finite element with modal coordinates is presented, and is used to build Finite Degree Of Freedom (FDOF) model of Multi Rigid Bodies (MRD) for flexible leg of micro robot. Modal analysis of continuum model and FDOF model of MRD for flexible leg is conducted in ANSYS and ADAMS software environment respectively. Analysis results show that the two model have similar lower nature frequency and vibration modes, which verified the correctness of the FDOF model and its establish method. Based on FDOF model, the equivalent drive model of piezoelectric bimorph and system dynamic model of micro robot are build, which provides a theoretical basis for dynamic analysis of the micro robot.

The Finite Element Analysis and Optimization for the Steel Structure of Gantry Bucket Wheel Stacker-Reclaimer

Gantry bucket wheel stacker-reclaimer belongs to large complex steel structure. Once it is instability at the working time that will make a large accident. So we have to calculate its strength and stiffness. But its connection and the working condition are very complex. And the size of the model is so large which leads to debase the calculation efficiency. This paper use Pro/E software to create the model. And use Pro/Mechanical to make a finite element analysis. Through the properly simplified the model, we can increase the calculation efficiency. During the calculation result we find that the Pulley yoke, Rigid leg and Flexible leg appear big stress areas. We will give an optimization design for the irrational place and high stress areas. So that to improve the Gantry bucket wheel stacker-reclaimer on-site safety. And provide a certain reference for the subsequent design and improvement.

Unique Centipede Mechanism of Mycoplasma Gliding

Mycoplasma, a genus of pathogenic bacteria, forms a membrane protrusion at a cell pole. It binds to solid surfaces with this protrusion and then glides. The mechanism is not related to known bacterial motility systems, such as flagella or pili, or to conventional motor proteins, including myosin. We have studied the fastest species, Mycoplasma mobile, and have proposed a working model as follows. The gliding machinery is composed of four huge proteins at the base of the membrane protrusion and supported by a cytoskeletal architecture from the cell inside. Many flexible legs approximately 50 nm long are sticking out from the machinery. The movements generated by the ATP hydrolysis cell inside are transmitted to the "leg" protein through a "gear" protein, resulting in repeated binding, pull, and release of the sialylgalactose fixed on the surface by the legs. The gliding of Mycoplasma pneumoniae, a species distantly related to M. mobile, is also discussed.

Bending of floating flexible legs

When long thin flexible solid objects, such as the legs of water striders, disposable spoons and human hairs, are pressed against a liquid surface, they bend due to interfacial and hydrostatic forces. To understand the phenomenon, we study the bending of a sheet touching the liquid surface at an angle while clamped at the other end, to find its deflection and the load that the sheet can support before sinking. The theoretically predicted shapes of the sheet and the meniscus match well with experiments. Our theory shows that flexible sheets can support more load than rigid ones before sinking when the sheets are highly hydrophobic.

Generating continuous free crab gaits for quadruped robots on irregular terrain

This paper presents a method for generating free gaits for quadruped robots capable of performing statically stable, omnidirectional locomotion on irregular terrain containing forbidden areas. The rule-based deliberative algorithm can generate flexible sequences of leg transferences while maintaining constant vehicle speed. The foothold planning method is compatible with the use of these flexible leg sequences, and is designed to maintain a minimum absolute stability margin despite the terrain height uncertainty. The integration of exteroceptive terrain profile data has been considered to improve adaptability. Experimental results are presented to show the gait's efficiency in adapting to an irregular terrain containing forbidden areas.

A biofidelic birthing simulator

The design, testing, and implementation of a novel birthing simulator (patent pending, 6 September 2005) developed specifically to research the delivery process and improve clinical training in uncommon but inevitable complicated human births is reported on. The simulator consists of a maternal model and an instrumented fetal model that are used in conjunction with an existing force-sensing system and a data-acquisition system. The maternal model includes a bony, rotatable pelvis, flexible legs, and an optional uterine expulsive system. The fetal model, which can be delivered repeatedly through the maternal model, is instrumented with potentiometers to measure neck extension, rotation, and flexion during delivery. Simulation of the brachial plexus within the model fetal neck allows measurement of stretch in those nerves at risk for injury during difficult deliveries. Elements mimic the range-of-motion properties of neonate. Two methods for measuring clinician-applied force during simulated deliveries provide trainees with the real-time assessment of their own traction force and allow researchers to correlate fetal neck motion and nerve stretch parameters with clinician-applied traction. Preliminary testing indicates the system is biofidelic for the final stages of the birthing process and can be used for training and research in obstetrics.

A Trotting Horse Model

A new control strategy is used to stabilize numerical simulations of a horse model in the trotting quadrupedal gait. Several well-established experimental findings are predicted by the model, including how stride frequency and stride length change with forward running speed. Mass is distributed throughout the model's legs, trunk, and head in a realistic manner. Leg and trunk flexion is modeled using four flexible legs, a back joint, and a neck joint. In the control model, pitch stabilization is achieved without directly controlling body pitch, but rather by controlling both the aerial time and the foot speed of each stance leg. The legs behave as ideal springs while in contact with the ground, enabling the model to rebound from the ground with each trotting step. Numerical experiments are conducted to test the model's capacity to overcome a change in ground impedance. Model stability is maximized and the metabolic cost of trotting is minimized within a narrow range of leg stiffness where trotting horses of similar body size have been observed to operate. This work suggests that a horselike robot will exhibit behavior that is mechanically similar to that of a trotting horse if it operates in a narrow range of leg stiffness and employs simple control strategies where postural stabilization is an emergent property of the system.

Stability and Postbuckling of a Platform with Flexible Legs Resting on a Slippery Surface*

ABSTRACT A rigid platform is supported by thin elastic legs. The legs are able to slide on the ground as they deform. The governing equations for large deformations are formulated and solved numerically by homotopy and quasi Newton methods. Nonlinear phenomena such as nonuniqueness are found. A global critical load for nonlinear stability is presented.

MMAE/MMAC control for bending with multiple uncertain parameters

A moving-bank multiple model estimator/controller (MMAE/MMAC) based on linear system, quadratic cost, and Gaussian noise (LQG) assumptions is used to quell unwanted vibrations in a simulated large flexible space structure. The structure, known as the Space Integrated Controls Experiment (SPICE), exists at Phillips Laboratory, Kirtland Air Force Base, New Mexico. The structure consists of a large platform and a smaller platform connected by a tripod of flexible legs. The purpose of the control system is to maintain a very precise line-of-sight (LOS) vector through the center of the spacecraft. Kalman filtering, used to estimate the position and velocity of the bending modes of the structure, and LQG control techniques are the primary design tools used in the MMAE/MMAC algorithms. Implementing a parallel bank of filters increases robustness when uncertainties exist in the system model, here specifically allowing adaptation to uncertain and changing undamped natural frequencies of the bending modes of the structure. A moving-bank algorithm is utilized to reduce the computational loading. The MMAE/MMAC design provides a well-suited method of estimating variations in the vector of undamped natural frequencies and quelling vibrations in the structure. The MMAE/MMAC was able to track numerous parameter changes and jumps while providing adequate control for the structure.

Numerical Investigation of an Improved Gas and Steam Turbine Seal

A numerical study has been conducted to assess the viability of a new sealing mechanism for gas and steam turbines. This new static-to-rotating sealing mechanism is mounted on flexible legs which permit radial movement and is designed to take advantage of the hydro-dynamic pressure forces, which result from fluid leaking around the seal, to maintain an ideally small and constant clearance. Relatively simple seal geometries have been numerically tested to find an optimal shape. These results indicate that a substantial sealing improvement (between two and four times less leakage) relative to a labyrinth seal is possible. Although these results show that a brush seal is more effective than the present seal, the present seal is designed to operate in high-speed and high-temperature environments in which the brush seal would degrade.

Pengana robertbolesi, a peculiar bird of prey from the Tertiary of Riversleigh, northwestern Queensland, Australia

Pengana robertbolesi, a fossil raptor from the Tertiary of Riversleigh, northwestern Queensland, shares with the living genera Polyboroides and Geranospiza a distinctive morphology of the distal tibiotarsus. The modified structure of the intertarsal joint permits a much greater degree of both anterioposterior and mediolateral flexion than in other species of the Accipitridae. Living species employ acrobatic foraging methods, using the flexible leg to probe hollows and recesses. It is considered that P. robertbolesi used similar foraging techniques. Because it was approximately twice the size of living taxa, it probably was capable of predating substantially larger prey.

Sensor for detecting vibrations in a plane, particularly in a stringed musical instrument

An improved sensor for detecting vibrations uses a flexible moving beam supported by two flexible leg members. The flexible moving beam can be moved in two directions. A protrusion extends from near one end of the flexible moving beam. The protrusion is placed against a transducer element 22 which is against a rest element 24 . When the moving beam is moved parallel to its length, the protrusion is pushed against the transducer element 22 and against the rest element 24, thereby generating electrical signals. When the moving beam detects vibrations in a direction perpendicular to its length, the protrusion is rotated upward and outward and pushes against the transducer element 22, causing the generation of electrical signal. The improved sensor is particularly adapted for detecting vibrations from a stringed musical instrument.

協調制御を必要としない歩行機械に関する研究

Legged locomotion over irregular terrain is composed of body propelling motion and terrain adapting motion. Although conventional walking machines with three active degrees of freedom (d.o.f) for each leg can adapt their feet on irregular ground using flexible leg freedom, such machines generally require a tremendously complex control scheme for the body propelling motion, because cooperational control of leg freedoms in stance is required for a system with several closed kinematic chains between the body and the ground. To cope with this problem, a walking machine with decoupled freedoms, described in this paper, is based on the idea that body propelling motion is realized by only one degree of freedom and can be perfectly decoupled from the freedoms for terrain adaptability. In this type walking machine, the control system is perfectly released from the control of closed kinematic chains. Therefore it can be expected that the control algorithm will become much easier than that of conventional walking machines having three active d.o.f. per each leg. First, the authors discuss such walking machines and make clear the quadruped walking model with minimum active d.o.f. through basic considerations of freedoms of walking machines. Next, according to observations of animal locomotion, a hexapod walking machine (MELWALK) with decoupled freedoms using an approximate straight line mechanism is developed in order to realize faster and simpler walking machines than the quadruped one. As the foot pattern of this walking machine is limited to only one pattern, other kinds of freedoms are established to implement a body direction changing motion and a terrain adapting motion. Rotational freedom other than propulsion is added to implement the body direction changing motion, and extension and contraction freedom to the legs are also added to implement the terrain adapting motion. Although more than two active d.o.f. for each leg are desirable for terrain adaptability, the proposed walking machine has only one active d.o.f. for simplicity. Experiments are carried out to certify the body propelling motion, terrain adapting motion and body direction changing motion. It can be recognized from the trajectory of LED that the body proceeds along an approximate straight line close to an exact one. Body direction changing motion is implemented with relatively high speed. Furthermore in order to check energetic efficiency, the power consumed by DC motor is also measured using MELWALK MARK-I. Several features of the proposed hexapod walking machine are revealed through these experiments.

A hexapod walking machine with decoupled freedoms

Legged locomotion over irregular terrain is composed of body-propelling motion and terrain-adapting motion. Although conventional walking machines with three degrees-of-freedom for each leg can adapt their feet on irregular ground using flexible leg freedom, such machines generally require a tremendously complex control scheme for the body-propelling motion. A walking machine with decoupled freedoms is based on the idea that body-propelling motion is realized by only one degree-of-freedom, and this freedom can be perfectly decoupled from the freedoms for terrain adaptability. As an application of such a walking machine, a hexapod walking machine using an approximate straight line mechanism was developed and several basic experiments were performed to demonstrate the properties of this type of walking machine.

Assembly units of clathrin coats.

Clathrin, a polypeptide of molecular weight (MW) 180,000, is the main constituent of the polygonal network that forms the coat of coated pits and vesicles; these vesicles play a part in intracellular transport between membranous organelles. This function involves specific recognition of target membranes as well as fusion and fission events that must be coordinated with the assembly, partial disassembly or reorganization of the clathrin coats. To understand these interactions on a molecular level, information about the structure of clathrin and the interactions of clathrin with itself and other proteins is required. Here we show that purified clathrin coats dissociate reversibly into triskelions, structures composed of three usually bent, rather flexible legs irradiated from a centre. We have determined the molecular weight of these triskelions and conclude that they contain trimers of clathrin together with about three light molecular weight polypeptide chains.

Dynamics of a Drifting Buoy-Cable-Array Assembly Used in Submarine Detection

The paper investigates the dynamics of a drifting buoy-cable-array assembly used in submarine detection. The steady-state configurations of the three-dimensional cable and flexible legs are determined. A perturbation analysis around the steady state is carried out, and the frequencies for both lateral and longitudinal motions of the system obtained by analyzing the resulting eigenvalue problem. A study of the decay of the disturbances applied to the system suggests the use of an optimum arm diameter for given cable and arm lengths.

Ultrastructure of gamma-M immunoglobulin and alpha macroglobulin: electron-microscopic study.

Electron microscopy of purified Waldenström macroglobulins and normal human and rabbit gammaM immunoglobulins revealed spider-like structures with five legs varying in length and often joining a central ring. Usually only the central more rigid part of this structure (about 150 by 170 angstroms) was clearly visible, but occasionally particles were seen with longer very flexible legs having a total span of about 350 angstroms. Molecules of gammaM antibody retained antibody activity during preparation for electron microscopy. Human and rabbit alpha macroglobulins revealed more rigid symmetric structures (100 by 200 angstroms) which resembled the Russian letter .