Manipulator Kinematics and Dynamics On Differentiable Manifolds: Part II Dynamics

2021 ◽  
Author(s):  
Edward J. Haug
Keyword(s):  
Inverse Kinematics ◽  
Ad Hoc ◽  
Equations Of Motion ◽  
Differentiable Manifold ◽  
Differentiable Manifolds ◽  
Manipulator Dynamics ◽  
On Line ◽  
Forward And Inverse Kinematics ◽  
Path Connected ◽  
Manipulator Control

Abstract The manipulator differentiable manifold formulation presented in Part I of this paper is used to create algorithms for forward and inverse kinematics on maximal, singularity free, path connected manifold components. Existence of forward and inverse configuration mappings in manifold components is extended to obtain forward and inverse velocity mappings. Computational algorithms for forward and inverse configuration and velocity analysis on a time grid are derived for each of the four categories of manipulator treated. Manifold parameterizations derived in Part I are used to transform variational equations of motion in Cartesian generalized coordinates to second order ordinary differential equations of manipulator dynamics, in terms of both input and output coordinates, avoiding ad-hoc derivation of equations of motion. This process is illustrated in evaluating terms required for equations of motion of the four model manipulators analyzed in Part I. It is shown that computation involved in forward and inverse kinematics and in evaluation of equations of manipulator dynamics can be carried out in real-time on modern microprocessors, supporting on-line implementation of modern methods of manipulator control.

Multibody Dynamics on Differentiable Manifolds

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Edward J. Haug
Keyword(s):  
Euclidean Space ◽  
Differential Equations ◽  
Vector Space ◽  
Ordinary Differential Equations ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differentiable Manifold ◽  
Kinematics And Dynamics ◽  
Variational Equations ◽  
Differentiable Manifolds

Abstract Topological and vector space attributes of Euclidean space are consolidated from the mathematical literature and employed to create a differentiable manifold structure for holonomic multibody kinematics and dynamics. Using vector space properties of Euclidean space and multivariable calculus, a local kinematic parameterization is presented that establishes the regular configuration space of a multibody system as a differentiable manifold. Topological properties of Euclidean space show that this manifold is naturally partitioned into disjoint, maximal, path connected, singularity free domains of kinematic and dynamic functionality. Using the manifold parameterization, the d'Alembert variational equations of multibody dynamics yield well-posed ordinary differential equations of motion on these domains, without introducing Lagrange multipliers. Solutions of the differential equations satisfy configuration, velocity, and acceleration constraint equations and the variational equations of dynamics, i.e., multibody kinematics and dynamics are embedded in these ordinary differential equations. Two examples, one planar and one spatial, are treated using the formulation presented. Solutions obtained are shown to satisfy all three forms of kinematic constraint to within specified error tolerances, using fourth-order Runge–Kutta numerical integration methods.

Kinematics Analysis and Simulation of a 4-DOF Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 656-660
Author(s):  
Yu Jie Cui ◽  
Jian Ning Hua
Keyword(s):  
Detailed Analysis ◽  
Inverse Kinematics ◽  
Kinematics Analysis ◽  
Forward And Inverse Kinematics ◽  
Manipulator Control

Detailed analysis is given to kinematics of a 4-DOF manipulator. Forward and inverse kinematics of the manipulator is performed through Denevit and Hartenberg method. Kinematics equations are obtained, whereupon mathematic formulas are provided for the manipulator control. The effectiveness of kinematics equations is verified by the Robotics Toolbox simulation of the Matlab.

A Hybrid Self-Stressed Cable-Driven Mechanism

2008 ◽  
Author(s):  
Saeed Behzadipour
Keyword(s):  
Static Loading ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Tensile Force ◽  
Cable System ◽  
End Effector ◽  
Stiffness Analysis ◽  
Cable Length ◽  
Cable Drive ◽  
Forward And Inverse Kinematics

A new hybrid cable-driven manipulator is introduced. The manipulator is composed of a Cartesian mechanism to provide three translational degrees of freedom and a cable system to drive the mechanism. The end-effector is driven by three rotational motors through the cables. The cable drive system in this mechanism is self-stressed meaning that the pre-tension of the cables which keep them taut is provided internally. In other words, no redundant actuator or external force is required to maintain the tensile force in the cables. This simplifies the operation of the mechanism by reducing the number of actuators and also avoids their continuous static loading. It also eliminates the redundant work of the actuators which is usually present in cable-driven mechanisms. Forward and inverse kinematics problems are solved and shown to have explicit solutions. Static and stiffness analysis are also performed. The effects of the cable’s compliance on the stiffness of the mechanism is modeled and presented by a characteristic cable length. The characteristic cable length is calculated and analyzed in representative locations of the workspace.

A Model of the Human Spine: Forward and Inverse Kinematics

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
Siyan Li ◽  
Glen Desmier
Keyword(s):  
Range Of Motion ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Joint Angles ◽  
Human Spine ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degrees Of Freedom ◽  
Adjacent Vertebra

Abstract The human spine is a sophisticated mechanism consisting of 24 vertebrae which are arranged in a series-chain between the pelvis and the skull. By careful articulation of these vertebrae, a human being achieves fine motion of the skull. The spine can be modeled as a series-chain with 24 rigid links, the vertebrae, where each vertebra has three degrees-of-freedom relative to an adjacent vertebra. From the studies in the literature, the vertebral geometry and the range of motion between adjacent vertebrae are well-known. The objectives of this paper are to present a kinematic model of the spine using the available data in the literature and an algorithm to compute the inter vertebral joint angles given the position and orientation of the skull. This algorithm is based on the observation that the backbone can be described analytically by a space curve which is used to find the joint solutions..

A Concept for Rapidly-Deployable Cable Robot Search and Rescue Systems

2005 ◽  
Author(s):  
Paul Bosscher ◽  
Robert L. Williams ◽  
Melissa Tummino
Keyword(s):  
Mobile Robots ◽  
Inverse Kinematics ◽  
Search And Rescue ◽  
Kinematic Structure ◽  
Rescue Workers ◽  
Cable Robot ◽  
System Concept ◽  
Moment Resisting ◽  
Calibration Algorithm ◽  
Forward And Inverse Kinematics

This paper introduces a new concept for robotic search and rescue systems. This system uses a rapidly deployable cable robot to augment existing search and rescue mobile robots. This system can greatly increase the range of mobile robots as well as provide overhead views of the disaster site, allowing rescue workers to reach survivors as quickly as possible while minimizing the danger posed to rescue workers. In addition to the system concept, this paper presents a novel kinematic structure for the cable robot, allowing simple translation-only motion (with moment-resisting capability) and easy forward and inverse kinematics for a 3-DOF spatial manipulator. Also, a deployment sequence is described, a rapid calibration algorithm is presented and the workspace of the manipulator is investigated.

scholarly journals Stability and Gait Planning of 3-UPU Hexapod Walking Robot

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Ruiqin Li ◽  
Hongwei Meng ◽  
Shaoping Bai ◽  
Yinyin Yao ◽  
Jianwei Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Step Length ◽  
Parallel Robot ◽  
Search Method ◽  
Walking Robot ◽  
Gait Control ◽  
Gait Planning ◽  
Forward And Inverse Kinematics ◽  
Passing Ability

The paper presents an innovative hexapod walking robot built with 3-UPU parallel mechanism. In the robot, the parallel mechanism is used as both an actuator to generate walking and also a connecting body to connect two groups of three legs, thus enabling the robot to walk with simple gait by very few motors. In this paper, forward and inverse kinematics solutions are obtained. The workspace of the parallel mechanism is analyzed using limit boundary search method. The walking stability of the robot is analyzed, which yields the robot’s maximum step length. The gait planning of the hexapod walking robot is studied for walking on both flat and uneven terrains. The new robot, combining the advantages of parallel robot and walking robot, has a large carrying capacity, strong passing ability, flexible turning ability, and simple gait control for its deployment for uneven terrains.

The Effects of Harmonic Drive Gears on Robot Dynamics

1991 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Robot Dynamics ◽  
Harmonic Drive ◽  
Dynamic Coupling ◽  
Manipulator Dynamics ◽  
Dynamic Formulation ◽  
System Equations ◽  
Modelling Assumptions

Abstract Mathematical models of the harmonic drive have been developed, and their effects on manipulator dynamics have been examined. The harmonic drive is modelled as a flexible gear with a high gear reduction ratio. The recursive Newton-Euler dynamic formulation is applied to deriving the system equations of motion that include the effects of the geared actuation. The equations include not only the nonlinear dynamic coupling between rotors and links but the gyroscopic effect due to the spinning rotors. Different modelling assumptions creates four models and their time responses are compared. As an example, a seven degree of freedom robot was chosen to make comparisons in time responses.

Autonomously Evolving Communication Protocols

2012 ◽  
pp. 183-204
Author(s):  
Endre Sándor Varga ◽  
Bernát Wiandt ◽  
Borbála Katalin Benko ◽  
Vilmos Simon
Keyword(s):  
Natural Selection ◽  
Genetic Programming ◽  
Programming Language ◽  
Ad Hoc ◽  
Communication Protocols ◽  
Machine Intelligence ◽  
On Line ◽  
Hoc Networks ◽  
Autonomous Machine ◽  
Delay Tolerant

While traditional telecommunication still relies on rigid, highly regulated, and highly controlled communication protocols, with the emergence of new forms of networks (mobile ad hoc and delay-tolerant networks, lacking central infrastructure and strict regulations) bio-inspired communication protocols have also found their way to success. In this chapter we introduce a nontraditional way of creating and shaping communication protocols, through an autonomous machine intelligence model, built upon on-line evolutionary methods such as natural selection and genetic programming. Creating a genetic programming language and a selection mechanism for multi-hop broadcast protocols in ad hoc networks, we show that this kind of approach can outperform traditional ones under given circumstances, offering a powerful alternative in the future.

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