The Hexapodopter: A Hybrid Flying Hexapod—Holonomic Flying Analysis

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Daniel Soto-Guerrero ◽  
José Gabriel Ramírez-Torres
Keyword(s):  
Degrees Of Freedom ◽  
The Body ◽  
Design Criteria ◽  
Control Law ◽  
Two Degrees Of Freedom ◽  
Main Design ◽  
Walking Machine ◽  
Six Degrees Of Freedom ◽  
Thrust Vector ◽  
Thrust Forces

This document introduces the holonomic flying capabilities of the Hexapodopter, a six-legged walking machine capable of vertical take-off and landing. For ground locomotion, each limb has two degrees-of-freedom (2DoF); while the thrust required for flying is provided by six motors mounted close to every knee, so the thrust vector can be reoriented depending on the configuration of each limb. The capacity of reorienting the thrust forces makes the Hexapodopter a true holonomic vehicle, capable of individually controlling its six degrees-of-freedom (6DoF) on the air without reorienting any of the thrust motors nor the body. The main design criteria and validation will be discussed on this paper, as well as a control law for the vehicle.

Reflections and Conclusions

2017 ◽  
pp. 626-653
Keyword(s):  
Mode Coupling ◽  
Degrees Of Freedom ◽  
Subsequent Development ◽  
Eyewitness Testimony ◽  
Design Criteria ◽  
Dynamic Design ◽  
Two Degrees Of Freedom ◽  
Long Span ◽  
Gate Design

In this chapter, reflection on the discovery of gate instability mechanisms is provided. Stemming from Ishii's encounter as an undergraduate with the Wachi gate failure and his subsequent development of the theory for eccentricity instability, a framework for future analyses of other gate instabilities was established. The study of two degrees-of-freedom instabilities of long-span gates created a paradigm for mode coupling in hydraulic gate vibrations. The Folsom failure occurred with eyewitness testimony claiming to have heard and felt vibration. The path to understanding the mechanism that could produce vibration of the Folsom gate was the realization that the skinplate can be easily excited to undergo streamwise vibration. To counteract such vibration, dynamic design criteria for Tainter gates are needed. A draft formulation of dynamic guidelines for Tainter gate design is developed. We hope for feedback from those who use the guidelines to provide for the continuing improvement of the guidelines.

A Numerical Investigation of the Response of an Elastically Mounted Rigid Cylinder With Two Degrees of Freedom

2010 ◽  
Author(s):  
Bruno C. Ferreira ◽  
Marcelo A. Vitola ◽  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos A. Levi
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Two Degrees Of Freedom ◽  
Conservative Scheme ◽  
Rigid Cylinder

The vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the Reynolds average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k–ε turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse and in-line directions. In previous work, numerical results for the amplitude of oscillation, vortex shedding frequency, and phase angle between lift and displacement were compared to experimental data obtained from Khalak and Williamson (1996) to validate the code for VIV simulations in the transverse direction. In the present work, results are obtained for phase angle, amplitude, frequency, and lift coefficient and compared to experimental data from Jauvtis and Williamson (2003) for an elastically mounted rigid cylinder with two degrees of freedom. Differences in the amplitude of oscillation between experimental and numerical data were observed for both direction. It seems that the fluid flow memory effect is an important aspect that should be taken in consideration on numerical simulation to reproduce the experimental results for VIV with 2DOF as pointed out by Moe and Wu [1].

Study on the Control Law for Water Trajectory of Unpowered Carrier under Wave Force

2013 ◽  
Vol 401-403 ◽  
pp. 525-530
Author(s):  
Guang Pan ◽  
Yao Shi ◽  
Peng Wang ◽  
Xiao Xu Du
Keyword(s):  
Degrees Of Freedom ◽  
Reference Value ◽  
Wave Theory ◽  
Wave Force ◽  
Calculation Model ◽  
Two Dimensions ◽  
Control Law ◽  
Engineering Research ◽  
Six Degrees Of Freedom ◽  
Movement Stability

During the process of exiting from water, the unpowered carrier launched by submarine will be disturbed by the wave force. It will have impact on the trajectory of carrier. Based on carrier vehicle exiting water requirement the six degrees of freedom mathematical model of carrier was established. The calculation model for wave force was built based on the two dimensions wave theory. The steering sequence of carrier was designed and the process of the carrier out of water was simulated under the influence of wave force. The results show that the vehicle movement stability, the control law is reasonable and the simulation methods and results of engineering research had a certain reference value.

Power Extraction from Water Waves

1976 ◽  
Vol 20 (02) ◽  
pp. 63-66 ◽  
Author(s):  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Degrees Of Freedom ◽  
Vertical Axis ◽  
Horizontal Cylinder ◽  
The Body ◽  
Floating Body ◽  
Maximum Efficiency ◽  
Viscous Effects ◽  
Two Degrees Of Freedom ◽  
Power Extraction

Salter has demonstrated experimentally that a horizontal cylinder in the free surface of water can be a device to extract energy from the incident waves. This paper proposes a design which is based on the idea of a tethered-float breakwater, and gives the theoretical design criteria for maximum power extraction from a general floating cylinder with one or two degrees of freedom. It is shown that the rate of energy extraction must be equal to the rate of radiation damping and that the floating body must be made to resonate then for a body with one degree of freedom, the maximum efficiency at a given frequency can be at leastone half if the body is symmetrical about a vertical axis, and greater for an asymmetrical body. For a body with two degrees of freedom, all the wave power can be extracted. Hydrodynamical aspects of the controlled motion are examined. Viscous effects are ignored.

Optimal Preview Semiactive Suspension

1996 ◽  
Vol 118 (1) ◽  
pp. 99-105 ◽  
Author(s):  
L. Jezequel ◽  
V. Roberti
Keyword(s):  
Degrees Of Freedom ◽  
Active Suspension ◽  
Control Law ◽  
Semiactive Control ◽  
Active System ◽  
Two Degrees Of Freedom ◽  
Suspension Control ◽  
Computer Controlled ◽  
Track Irregularities ◽  
Semiactive Suspension

This paper examines an optimal preview semiactive suspension of a quarter-coach model moving along randomly profiled track. This optimal computer-controlled suspension is designed only to dissipate energy, and is able to use knowledge of track irregularities over a distance L in front of the train. Thus the deformation of the track can be taken into account when calculating the semi-active suspension control law. First, the expression of the optimal preview semiactive control law is established. Then, using a two-degrees-of-freedom quarter-coach model, preview information is shown to improve the behavior of an optimal non-preview semi-active system, which can come close to the performance of an active system.

Design of a Simple Electronic Flutter Simulator

1953 ◽  
Vol 57 (505) ◽  
pp. 29-38 ◽  
Author(s):  
F. Smith ◽  
W. D. T. Hicks
Keyword(s):  
Degrees Of Freedom ◽  
Successful Operation ◽  
Two Degrees Of Freedom ◽  
Six Degrees Of Freedom ◽  
Electronic Simulator

SummaryThis paper describes the construction of a simple electronic simulator for the solution of flutter problems in two degrees of freedom. It was intended as a prototype for a much larger machine to solve problems in six degrees of freedom.Details of the construction and circuits are given, together with some typical solutions obtained on the machine. As a result of the successful operation of this prototype a larger machine in six degrees of freedom has now been built.

Vibration of a Spring-Supported Body

1965 ◽  
Vol 7 (2) ◽  
pp. 185-192 ◽  
Author(s):  
P. Grootenhuis ◽  
D. J. Ewins
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Vertical Axis ◽  
The Body ◽  
Stiffness Ratio ◽  
Six Degrees Of Freedom ◽  
Centre Of Gravity ◽  
Longitudinal Stiffness ◽  
The Matrix

The equations of motion for a rigid body supported on four springs are derived for the general case of the centre-of-gravity being anywhere within the body and allowing for the sideways as well as the longitudinal stiffnesses of the springs. This constitutes a six-degrees-of-freedom case with three degrees of asymmetry. Coupling between motions in all directions occurs even when the centre-of-gravity is at the geometric centre with the exception then of vertical oscillations and rotation about the vertical axis. Any number of additional springs can be allowed for by adding terms to the expression for the potential energy stored in the springs. Allowance is made in the expression for kinetic energy for the products of inertia which arise with an offset centre-of-gravity. The real case is simulated for purposes of analysis by replacing the rigid body by a rectangular box with a light framework and all the mass concentrated at the eight corners. The matrix solution is changed into dimensionless parameters and the effect of an offset centre-of-gravity upon the eigenvalues and eigenvectors studied. Only the proportions of the box and the stiffness ratio between sideways to longitudinal stiffness of the springs remain as factors. The numerical example given is for proportions of height to width to length of 3/4/5 and for a stiffness ratio of 5. Small amounts of offset of the centre-of-gravity from the geometric centre do not alter the dynamic behaviour of the system much but displacing the total mass towards either a lower or an upper corner has marked effects. Some of the natural frequencies associated with motion in rotation when the system is symmetric become less than the frequencies connected with motion in translation for the centre-of-gravity being close to a corner connected to a spring. A large region free from any natural frequency arises when the centre-of-gravity is moved towards a corner furthest removed from the plane containing the springs. The asymptotic conditions for the position of the centre-of-gravity are also considered.

Spatial Mechanism-Environment Contact Geometric Models

2021 ◽  
Author(s):  
Nina Robson ◽  
Aaron Lee
Keyword(s):  
Degrees Of Freedom ◽  
Theoretical Foundation ◽  
Kinematic Chain ◽  
The Body ◽  
Order Effects ◽  
Six Degrees Of Freedom ◽  
Spatial Mechanism ◽  
Motion Constraints ◽  
Spherical Surfaces ◽  
Proposed Model

Abstract This work proposes a theoretical foundation for a general spatial geometric mechanism-environment contact model. In the proposed model the curvature of the environment in the vicinity of the contact is approximated by a number of spherical surfaces with known radii of curvature that constrain/define the movement of the body. We show how the modeled body-environment contact and curvature constraints can be transformed into conditions on spatial velocity and acceleration (i.e. first and second order effects) of certain points of the moving body that can be incorporated in the kinematic task for designing spatial mechanisms. Further, we explore the exact synthesis of a spatial six degrees-of-freedom TPS kinematic chain which end-effector maintains contact with objects in the environment and varies orientation in the vicinity of a contact location. It is discussed how the higher order motion constraints allow for the introduction of kinematic task variations in the vicinity of a contact, resulting in different behaviors of the designed spatial mechanism. The theoretical foundation presented in this paper is crucial in gaining understanding of the constraints in describing mechanism-environment interactions in the vicinity of a contact and is a new contribution.

scholarly journals ON INERTIAL MOTION OF AN ABSOLUTELY RIGID BODY ON A THREE-DEGREE SUSPENSION WITH LINKS OF FINITE LENGTH

2020 ◽  
Vol 2 (2) ◽  
pp. 6-17
Author(s):  
L Akulenko ◽  
◽  
N Bolotnik ◽  
D Leshchenko ◽  
E Palii ◽  
...  
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Exact Analytical Solution ◽  
Rigid Bodies ◽  
The Body ◽  
Theoretical Research ◽  
Double Pendulum ◽  
Two Degrees Of Freedom ◽  
Practical Applications ◽  
Wide Range

Papers on the dynamics of an absolutely rigid body with a fixed point generally assume that the mechanical system has three degrees of freedom. This is the situation when the body is attached to a fixed base by a ball-and-socket joint. On engineering systems one often encounters rigid bodies attached to a base by a two-degrees-of-freedom joint, consisting of a fixed axis and a movable one, which are mutually perpendicular. Such systems have two degrees of freedom, but the set of kinematically possible motions is quite rich. Dynamic analysis of the motion of a rigid body with a two-degree hinge in a force field is an integral part of the description of the action of mechanical actions of robotic systems. In recent decades, an increasingly closed role in the dynamics of rigid body systems has been played by manipulation robots consisting of a sequential chain of rigid links and controlled by means of torque drives in articulated joints. The same class of objects can be attributed to many biological systems that imitate, for example, the movements of a person or animal (walking, running, jumping). Two-link systems have a variety of practical applications and an almost equally wide range of areas of theoretical research. We note, in particular, the analysis of free and forced plane-parallel motion of a bundle of two rigid bodies connected by an ideal cylindrical hinge and simulating a composite satellite in outer space, a two-link manipulator, and an element of a crushing machine. The dynamic behavior of a rigid body in the gimbal suspension is a system, which can be interpreted as two-degree manipulator and used an element of more complex robotic structures. The linear mathematical model of two-link manipulator free oscillations with viscous friction in both its joints is a system, which reduces to the calculation scheme of double pendulum and allows the construction of exact analytical solution in the partial case. According to the research methodology, the proposed paper is close to works, where the motion by inertia of a plane two–rigid body hinged system was studied and devoted to the study of the motion of an absolutely rigid body on a power-to-power joint.

scholarly journals Maneuvering Hydrodynamics of Ellipsoidal Forms

1979 ◽  
Vol 23 (01) ◽  
pp. 66-75
Author(s):  
Touvia Miloh
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Major Axis ◽  
The Body ◽  
Time Dependent ◽  
Triaxial Ellipsoid ◽  
Inviscid Fluid ◽  
Six Degrees Of Freedom ◽  
Ellipsoidal Harmonics ◽  
Unbounded Medium

The hydrodynamical forces and moments acting on a triaxial ellipsoid moving in an incompressible and inviscid fluid are analyzed. The rigid ellipsoid is allowed to move in the most general manner with time-dependent velocity and six degrees of freedom. The force and moment expressions are obtained by applying the Lagally theorem to the image singularities system representing the body in the presence of exterior disturbances. First, expressions for the Lagally force and moment acting on a maneuvering ellipsoid in an unbounded medium are derived and then these expressions are generalized to include the effect of an exterior source moving in an arbitrary manner. It is also shown how the Lagally expressions for an exterior source can be used to obtain closed-form expressions for the hydrodynamical forces and moments acting on a maneuvering ellipsoid in the presence of an arbitrary exterior disturbance. The analysis, which is based on the application of ellipsoidal harmonics, is demonstrated in a simple case of propeller-hull interaction. Here the motion of the ellipsoid is restricted to the major axis, and the propeller at the stern is represented by an isolated sink in accordance with Dickmann's model. 'Practical expressions for the thrust-deduction coefficient, wake fraction, and propeller-induced vibration are then derived for ellipsoidal, spheroidal and spherical hulls..

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