scholarly journals Correction of the Koenig Formula for the Kinetic Energy of a Rotating Solid

2021 ◽  
Author(s):  
Yuriy Alyushin
Keyword(s):  
Kinetic Energy ◽  
Degrees Of Freedom ◽  
Superposition Principle ◽  
Initial Position ◽  
The Body ◽  
Moments Of Inertia ◽  
Lagrange Form ◽  
Joint Plane ◽  
Integral Characteristics ◽  
Joint Motions

An exact solution is obtained for the kinetic energy in the general case of the spatial motion of solids with arbitrary rotation, which differs from the Koenig formula by three additional terms that take into account the change in the centrifugal moments of inertia when the body rotates. The description of motion in the Lagrange form and the superposition principle are used, which provides a geometric summation of the velocities and accelerations of the joint motions in the Lagrange form for any particle at any time. The integrand function in the equation for kinetic energy is represented as the sum of the identical velocity components of the joint plane-parallel motions. In the general case of motion with 6 degrees of freedom, the energy of rotational motion is determined by three axial moments of inertia, as in the Koenig formula, and three additional centrifugal moments, which take into account the rotation of the body. They can be calculated through 6 integral characteristics of the density distribution, determined for the initial position of the body.

scholarly journals Correction of the Koenig Formula for the Kinetic Energy of a Rotating Solid

2021 ◽  
Author(s):  
Yuriy Alyushin
Keyword(s):  
Kinetic Energy ◽  
Degrees Of Freedom ◽  
Superposition Principle ◽  
Initial Position ◽  
The Body ◽  
Moments Of Inertia ◽  
Lagrange Form ◽  
Joint Plane ◽  
Integral Characteristics ◽  
Joint Motions

An exact solution is obtained for the kinetic energy in the general case of the spatial motion of solids with arbitrary rotation, which differs from the Koenig formula by three additional terms that take into account the change in the centrifugal moments of inertia when the body rotates. The description of motion in the Lagrange form and the superposition principle are used, which provides a geometric summation of the velocities and accelerations of the joint motions in the Lagrange form for any particle at any time. The integrand function in the equation for kinetic energy is represented as the sum of the identical velocity components of the joint plane-parallel motions. In the general case of motion with 6 degrees of freedom, the energy of rotational motion is determined by three axial moments of inertia, as in the Koenig formula, and three additional centrifugal moments, which take into account the rotation of the body. They can be calculated through 6 integral characteristics of the density distribution, determined for the initial position of the body.

scholarly journals Correction of the Koenig Formula for the Kinetic Energy of a Rotating Solid

2021 ◽  
Author(s):  
Yuriy Alyushin
Keyword(s):  
Kinetic Energy ◽  
Superposition Principle ◽  
The Body ◽  
Initial State ◽  
Moments Of Inertia ◽  
Lagrange Form ◽  
Joint Plane ◽  
Angular Velocities ◽  
The Difference ◽  
Cyclic Changes

An exact solution is obtained for the kinetic energy in the general case of the spatial motion of solids with arbitrary rotation, which differs from the Koenig formula by three additional terms with centrifugal moments of inertia. The description of motion in the Lagrange form and the superposition principle are used, which provides a geometric summation of the velocities and accelerations of the joint motions in the Lagrange form for any particle at any time. The integrand function in the equation for kinetic energy is represented by the sum of the identical velocity components of the joint plane-parallel motions. The moments of inertia in the Koenig formula do not change during movement and can be calculated from the current or initial state of the body. The centrifugal moments change and turn to 0 when rotating relative to the main central axes only for bodies with equal main moments of inertia, for example, for a ball. In other cases, the difference in the main moments of inertia leads to cyclic changes in the kinetic energy with the possible manifestation of precession and nutation, the amplitude of which depends on the angular velocities of rotation of the body. An example of using equations for a robot with one helical and two rotational kinematic pairs is given.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

scholarly journals Motion Planning for a Mobile Humanoid Manipulator Working in an Industrial Environment

2021 ◽  
Vol 11 (13) ◽  
pp. 6209
Author(s):  
Iwona Pajak ◽  
Grzegorz Pajak
Keyword(s):  
Kinetic Energy ◽  
Collision Avoidance ◽  
Industry 4.0 ◽  
Degrees Of Freedom ◽  
Industrial Environment ◽  
Acceleration Level ◽  
Different Types ◽  
Manipulability Measure ◽  
Robotic Tasks ◽  
Primary Problem

This paper presents the usage of holonomic mobile humanoid manipulators to carry out autonomous tasks in industrial environments, according to the smart factory concept and the Industry 4.0 philosophy. The problem of transporting lengthy objects, taking into account mechanical limitations, the conditions for avoiding collisions, as well as the dexterity of the manipulator arms was considered. The primary problem was divided into three phases, leading to three different types of robotic tasks. In the proposed approach, the pseudoinverse Jacobian method at the acceleration level to solve each of the tasks was used. The redundant degrees of freedom were used to satisfy secondary objectives such as robot kinetic energy, the maximization of the manipulability measure, and the fulfillment mechanical and collision-avoidance limitations. A computer example involving a mobile humanoid manipulator, operating in an industrial environment, illustrated the effectiveness of the proposed method.

scholarly journals Finite-Horizon Kinetic Energy Optimization of a Redundant Space Manipulator

2021 ◽  
Vol 11 (5) ◽  
pp. 2346
Author(s):  
Alessandro Tringali ◽  
Silvio Cocuzza
Keyword(s):  
Kinetic Energy ◽  
Real Time ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Computational Time ◽  
Redundant Manipulators ◽  
Space Robotics ◽  
Optimal Method ◽  
End Effector ◽  
Global Optimal

The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On the one hand, these methods are suitable for real-time implementation; nevertheless, on the other hand, they often provide solutions quite far from the globally optimal one and, moreover, are prone to singularities. In this paper, a novel inverse kinematics method for redundant manipulators is presented, which overcomes the above mentioned issues and is suitable for real-time implementation. The proposed method is based on the optimization of the kinetic energy integral on a limited subset of future end-effector path points, making the manipulator joints to move in the direction of minimum kinetic energy. The proposed method is tested by simulation of a three degrees of freedom (DOF) planar manipulator in a number of test cases, and its performance is compared to the classical pseudoinverse solution and to a global optimal method. The proposed method outperforms the pseudoinverse-based one and proves to be able to avoid singularities. Furthermore, it provides a solution very close to the global optimal one with a much lower computational time, which is compatible for real-time implementation.

scholarly journals Designing of Drive Systems in the Aspect of the Desired Spectrum of Operation

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2562
Author(s):  
Tomasz Dzitkowski ◽  
Andrzej Dymarek ◽  
Jerzy Margielewicz ◽  
Damian Gąska ◽  
Lukasz Orzech ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Dynamic Parameters ◽  
Synthesis Algorithm ◽  
Moments Of Inertia ◽  
Driving System ◽  
Six Degrees Of Freedom ◽  
Resonance Frequencies ◽  
Drive Systems ◽  
Power Component

A method for selecting dynamic parameters and structures of drive systems using the synthesis algorithm is presented. The dynamic parameters of the system with six degrees of freedom, consisting of a power component (motor) and a two-speed gearbox, were determined, based on a formalized methodology. The required gearbox is to work in specific resonance zones, i.e., meet the required dynamic properties such as the required resonance frequencies. In the result of the tests, a series of parameters of the drive system, defining the required dynamic properties such as the resonance and anti-resonance frequencies were recorded. Mass moments of inertia of the wheels and elastic components, contained in the required structure of the driving system, were determined for the selected parameters obtained during the synthesis.

Moving Cage: Vibration, Sonification and the Quanta of Time

2021 ◽  
Vol 46 (2) ◽  
pp. 169-183
Author(s):  
MARCUS CHENG CHYE TAN
Keyword(s):  
Kinetic Energy ◽  
The Body ◽  
Dance Movements ◽  
Politics Of The Body

Dear John is an experimental choreomusical work that reinterprets Cage's works while advancing his ideas of sound as sonic events and embodied choreography. In this episodic work, improvised movement unfolds to a soundscape of defamiliarized instruments, sound devices and sonicities of macro- and micro-movements. The correspondence and (in)congruence between dance movements and music's kinetic energy become the means to examine a politics of the body and sound, of music on movement. Additionally, in this ‘auditory architecture’ the quanta of time, its relations and (lack of) unity are exposed. This article then examines the intersubjective interplay of movement and music, body and sonicity; it considers the resonance of the performing body as intermaterial vibration and how this invites a sonic politics of relational possibility. The article will then also investigate the ways in which the interaction of motion and music, movement and stillness engenders experiences of time's indeterminacy and elasticity.

scholarly journals Estimation of the Abduction/Adduction Movement of the Metacarpophalangeal Joint of the Thumb

2021 ◽  
Vol 11 (7) ◽  
pp. 3158
Author(s):  
Néstor J. Jarque-Bou ◽  
Margarita Vergara ◽  
Joaquín L. Sancho-Bru
Keyword(s):  
3D Modeling ◽  
Daily Living ◽  
Degrees Of Freedom ◽  
Estimation Error ◽  
Metacarpophalangeal Joint ◽  
Joint Movement ◽  
Carpometacarpal Joint ◽  
Small Space ◽  
Joint Motions

Thumb opposition is essential for grasping, and involves the flexion and abduction of the carpometacarpal and metacarpophalangeal joints of the thumb. The high number of degrees of freedom of the thumb in a fairly small space makes the in vivo recording of its kinematics a challenging task. For this reason, along with the very limited independence of the abduction movement of the metacarpophalangeal joint, many devices do not implement sensors to measure such movement, which may lead to important implications in terms of the accuracy of thumb models. The aims of this work are to examine the correlation between thumb joints and to obtain an equation that allows thumb metacarpophalangeal abduction/adduction movement to be estimated from the other joint motions of the thumb, during the commonest grasps used during activities of daily living and in free movement. The correlation analysis shows that metacarpophalangeal abduction/adduction movement can be expressed mainly from carpometacarpal joint movements. The model thus obtained presents a low estimation error (6.29°), with no significant differences between grasps. The results could benefit most fields that do not typically include this joint movement, such as virtual reality, teleoperation, 3D modeling, prostheses, and exoskeletons.

scholarly journals The Analysis with Finite Elements of the Elasto-plastic Behaviour of the Spinal Immobilizers - in the Case of Comminutive Fractures

2019 ◽  
Vol 57 (2) ◽  
pp. 253-264
Author(s):  
Bogdan Florin Toma ◽  
Constantin Nanu ◽  
Cezar Popescu ◽  
Razvan Vladimir Socolov ◽  
Vasile-Eduard Rosu ◽  
...  
Keyword(s):  
Theoretical Study ◽  
Initial Position ◽  
The Body ◽  
Elastic Behaviour ◽  
Element Analysis ◽  
Clinical Observations ◽  
Clinical Investigations ◽  
Extension Force ◽  
Bone Fragments ◽  
Tension State

In this paper it is presented a comparative theoretical study - performed by finite element analysis (FEA), of the tension state that appears at the level of the spine, as well as in the areas adjacent to it, under the following conditions: a) the existence of a comminutive fracture at the level of the vertebra T11; b) of the external immobilization of the body through a Lombax orthesis (LO) or of the internal immobilization of the column by means of a spinal fixator (SF); c) of performing some basic flexion or extension movements. In this study, both flexural force and extension force varied on three levels. The results of the comparative theoretical study were supplemented with the clinical observations obtained from a number of 52 patients who had suffered comminutive fractures in the T11 vertebra and who were treated - by external immobilization, in the Lombax orthesis or were surgically treated - by applying a trapped spinal fixator on the T10-T12 vertebrae. The study had demonstrated that, by immobilizing the body in the Lombax orthesis, following the application of the flexion or extension movement, the mobility of the body is low, the bone fragments move less distances by about 12% against to their displacement under the condition of immobilizing the column by a spinal fixator. Although, in the latter case, the displacements of the bone fragments are greater, the elastic behaviour of the spinal fixator determines the returning of the fragments and of the spine to the initial position as well as the distance between the vertebrae. Clinical investigations on patients treated by external immobilization of the body in the Lombax orthesis show that the values of the local kyphosis angle (LKA) are about 30% lower than the values of the same parameter obtained under the surgical treatment.

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