scholarly journals A Novel, Oriented to Graphs Model of Robot Arm Dynamics

Robotics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 128
Author(s):  
George Boiadjiev ◽  
Evgeniy Krastev ◽  
Ivan Chavdarov ◽  
Lyubomira Miteva
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computer Experiments ◽  
Kinematic Chain ◽  
Robot Arm ◽  
Conservation Of Energy ◽  
Interdisciplinary Field ◽  
Novel Approach ◽  
Robot Arm Control

Robotics is an interdisciplinary field and there exist several well-known approaches to represent the dynamics model of a robot arm. The robot arm is an open kinematic chain of links connected through rotational and translational joints. In the general case, it is very difficult to obtain explicit expressions for the forces and the torques in the equations where the driving torques of the actuators produce desired motion of the gripper. The robot arm control depends significantly on the accuracy of the dynamic model. In the existing literature, the complexity of the dynamic model is reduced by linearization techniques or techniques like machine learning for the identification of unmodelled dynamics. This paper proposes a novel approach for deriving the equations of motion and the actuator torques of a robot arm with an arbitrary number of joints. The proposed approach for obtaining the dynamic model in closed form employs graph theory and the orthogonality principle, a powerful concept that serves as a generalization for the law of conservation of energy. The application of this approach is demonstrated using a 3D-printed planar robot arm with three degrees of freedom. Computer experiments for this robot are executed to validate the dynamic characteristics of the mathematical model of motion obtained by the application of the proposed approach. The results from the experiments are visualized and discussed in detail.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

A Three-Dimensional Dynamic Model for Determining the Equilibrium Configurations of Buoyantly Unstable Icebergs

1990 ◽  
Vol 112 (3) ◽  
pp. 253-262
Author(s):  
R. G. Jessup ◽  
S. Venkatesh
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Static Potential ◽  
Initial State ◽  
Model Simulations ◽  
Six Degrees Of Freedom ◽  
Equilibrium Configurations ◽  
Variation Range

This paper describes a dynamic model developed for the purpose of determining the final equilibrium configurations of buoyantly unstable icebergs. The model places no restrictions on the size, shape, or dimensionality of the iceberg, or on the variation range of the configuration coordinates. Furthermore, it includes all six degrees of freedom and is based on a Lagrangian formulation of the dynamic equations of motion. It can be used to advantage in those situations in which the iceberg has a complicated potential function and can acquire enough momentum and kinetic energy in the initial phase of its motion to make its final configuration uncertain on the basis of a static potential analysis. The behavior of the model is examined through several model simulations. The sensitivity of the final equilibrium position to the initial orientation and shape of the iceberg is clearly evident in the model simulations. Model simulations also show that when an iceberg is released from a nonequilibrium initial state, the time taken for it to settle down varies from about 40 s for a growler to nearly 400 s for a large iceberg. While these absolute times may change with better parameterization of the forces, the relative variations with iceberg size are likely to be preserved.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

scholarly journals Energy Optimization of Functionally Redundant Robots through Motion Design

2020 ◽  
Vol 10 (9) ◽  
pp. 3022
Author(s):  
Paolo Boscariol ◽  
Roberto Caracciolo ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Energy Efficiency ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Energy Savings ◽  
Robot Arm ◽  
Redundant Robots ◽  
Performance Metric ◽  
Serial Robot ◽  
Motion Profile ◽  
Motion Design

This work proposes to exploit functional redundancy as a tool to enhance the energy efficiency of a robotic system. In a functionally redundant system, i.e., one in which the number of degrees of freedom required to complete the task is smaller than the number of available degrees of freedom, the motion of the extra degrees of freedom can be tailored to enhance a performance metric. This work showcases a method that can be used to effectively enhance the energy efficiency through motion design, using a detailed dynamic model of the UR5 serial robot arm. The method is based on an optimization of the motion profile, using a parametrized description of the end-effector orientation: the results showcase an increased efficiency that allows energy savings up to 20.8%, according to the energy consumption results according to the electro-mechanical dynamic model of the robot.

A New Approach to Modeling Surface Defects in Bearing Dynamics Simulations

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Ankur Ashtekar ◽  
Farshid Sadeghi ◽  
Lars-Erik Stacke
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Surface Defects ◽  
Equations Of Motion ◽  
Infinite Domain ◽  
Step Size ◽  
Deep Groove ◽  
Dynamics Simulations ◽  
Bearing Dynamics

A dynamic model for deep groove and angular contact ball bearings was developed to investigate the influence of race defects on the motions of bearing components (i.e., inner and outer races, cage, and balls). In order to determine the effects of dents on the bearing dynamics, a model was developed to determine the force-deflection relationship between an ellipsoid and a dented semi-infinite domain. The force-deflection relationship for dented surfaces was then incorporated in the bearing dynamic model by replacing the well-known Hertzian force-deflection relationship whenever a ball/dent interaction occurs. In this investigation, all bearing components have six degrees-of-freedom. Newton’s laws are used to determine the motions of all bearing elements, and an explicit fourth-order Runge–Kutta algorithm with a variable or constant step size was used to integrate the equations of motion. A model was used to study the effect of dent size, dent location, and inner race speed on bearing components. The results indicate that surface defects and irregularities like dent have a severe effect on bearing motion and forces. Furthermore, these effects are even more severe for high-speed applications. The results also demonstrate that a single dent can affect the forces and motion throughout the entire bearing and on all bearing components. However, the location of the dent dictates the magnitude of its influence on each bearing component.

DYNAMIC SIMULATION OF A SPATIAL 3-DOF TENSEGRITY MECHANISM

2005 ◽  
Vol 29 (4) ◽  
pp. 491-505 ◽  
Author(s):  
Marc Arsenault ◽  
Clément M. Gosselin
Keyword(s):  
Dynamic Model ◽  
Dynamic Simulation ◽  
Dynamic Problem ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Equations Of Motion ◽  
Attractive Alternative ◽  
Equilibrium Configurations ◽  
Geometrical Constraints ◽  
Three Degree Of Freedom

Tensegrity mechanisms have the advantage of being relatively lightweight due to. their extensive use of cables and springs. As such, they have the potential of being an attractive alternative to conventional mechanisms in certain application environments. However, the presence of unconstrained degrees of freedom in tensegrity mechanisms leads to a dynamic behaviour that cannot be directly controlled with the actuators. In this work, the dynamic model of a novel spatial three-degree-of-freedom (3-DOF) tensegrity mechanism is developed using the Lagrangian formulation. The resulting equations of motion are then solved to simulate the mechanism's motion between equilibrium configurations. Since the mechanism is subjected to holonomic nonlinear geometrical constraints, these must be considered during the solution of its forward dynamic problem. It is seen that the use of damping in the springs is not very efficient in dissipating the mechanism's energy during motion.

scholarly journals Reaction on a Rink: Kondo-Enhanced Heterogeneous Single-Atom Catalysis

2021 ◽  
Author(s):  
Xiangyang Li ◽  
Hong Gong ◽  
Qingfeng Zhuang ◽  
Bing Wang ◽  
Xiao Zheng ◽  
...  
Keyword(s):  
Density Functional ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Single Atom ◽  
Spin Interaction ◽  
Free Energy Barrier ◽  
Free Electrons ◽  
Atomic Spin ◽  
Novel Approach ◽  
Metal Support

<p></p><p>Boosting the efficiency of heterogeneous single-atom catalysts (SACs) by adjusting the microenvironment of the active atom has recently attracted enormous attention. However, attempts to tune the spin-spin interaction between the SAC and its microenvironment have remained rather scarce. Some interesting questions can be raised, among which a fundamental one is: can the surrounding environment influence the local spin state of an SAC, and if so, can such influence be utilized to enhance the catalytic activity?</p> <p> </p> <p>In this work, we explore such a possibility by investigating the thermochemical effect of Kondo screening of a local atomic spin by free electrons in the metal support. Inspired by the exothermicity of the spin-screening interaction, a novel approach to heterogeneous catalysis -- reaction on a rink (ROAR) -- is proposed. In contrast to the conventional notion of thermal catalytic reaction, lowering the temperature of metal support is predicted to result in a reduced reaction barrier. As a proof of concept, CO oxidation catalyzed by the Co@CoPc/Au(111) composite is scrutinized. By combining the density functional theory and a hierarchical equations of motion approach, it predicts that the existing <i>s-d</i> hybridization between the magnetic <i>d</i> orbital of Co adatom and the substrate metallic states in the transition state will lower the free energy barrier and accelerate the reaction rate. Furthermore, if the strength of <i>s-d</i> hybridization is enlarged, a more appreciable speedup will be achieved.</p> <p> </p> <p>This work highlights the potential usefulness of the spin degrees of freedom to heterogeneous single-atom catalysis, and our proposed ROAR approach could open up a new horizon for exploiting the role of atomic spin in chemical reactions.</p><br><p></p>

Dynamic Analysis of Mechanical Systems With Elastic Telescopic Members

1994 ◽  
Author(s):  
B. O. Al-Bedoor ◽  
Y. A. Khulief
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Vibrational Motion ◽  
Dynamic Coupling ◽  
Gravitational Effects ◽  
Coupling Terms ◽  
Tip Mass ◽  
Stiffening Effect

Abstract A dynamic model for the vibrational motion of an elastic beam-like telescopic member is presented. In addition to translation, the elastic member is allowed to execute large reference rotation. The Lagrangian approach in conjunction with the assumed modes technique are employed in deriving the equations of motion. The developed model accounts for all the dynamic coupling terms, as well as the stiffening effect due to the beam reference rotation. The tip mass dynamics is included together with the associated dynamic coupling between the modal degrees of freedom. In addition, the devised dynamic model takes into account the gravitational effects, thus permitting motions in either vertical or horizontal planes. Numerical simulation of a mechanical system with an elastic telescopic member is presented.

Efficient Loads Analyses of Shuttle-Payloads Using Dynamic Models With Linear Or Nonlinear Interfaces

1990 ◽  
Vol 112 (3) ◽  
pp. 366-373 ◽  
Author(s):  
P. D. Spanos ◽  
T. T. Cao ◽  
D. A. R. Nelson ◽  
D. A. Hamilton
Keyword(s):  
Dynamic Model ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Space Shuttle ◽  
Equations Of Motion ◽  
Combined System ◽  
Time Step ◽  
Upper Stage ◽  
Loads Analysis

A technique is presented for conducting efficient loads analyses of Shuttle-payloads systems with linear or nonlinear attachment interfaces. The technique relies on representing the Space Shuttle and the payloads with physical and modal coordinates. Further, by invoking a standard algorithm of numerical integration of equations of motion, the kinematics of the interface degrees of freedom at a given time are determined without calculating the modes of the combined system involving the Space Shuttle and the payload. If the Shuttle-payloads interface coupling induces a linear dynamic model for the loads analysis, the equations of motion of the Shuttle and the payload are integrated separately step-by-step in time. If the dynamic model is nonlinear, the equations of motion of the Shuttle and the payload are again integrated separately. However, in the latter case an iterative procedure is used within a time step to converge to reliable values of the nonlinear terms of the equations of motion. The usefulness of the proposed technique is demonstrated by conducting a loads analysis for the Shuttle abort landing event with the Inertia Upper Stage (IUS) booster carrying a Tracking and Data Relay Satellite (TDRS) in the payload bay. This combined system has at its interface dry friction and hydraulic nonlinear dampers. For the analysis of this system, the discontinuous signum function used traditionally in modeling dry friction is replaced by an expeditious continuous approximation. Because of its efficiency and versatility, the new technique deserves serious consideration for becoming a standard tool for linear or nonlinear analysis of combined systems, in general, and of Shuttle-payloads systems, in particular.

scholarly journals Reaction on a Rink: Kondo-Enhanced Heterogeneous Single-atom Catalysis

2021 ◽  
Author(s):  
Xiangyang Li ◽  
Hong Gong ◽  
Qingfeng Zhuang ◽  
Bing Wang ◽  
Xiao Zheng ◽  
...  
Keyword(s):  
Density Functional ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Single Atom ◽  
Spin Interaction ◽  
Free Energy Barrier ◽  
Free Electrons ◽  
Atomic Spin ◽  
Novel Approach ◽  
Metal Support

Boosting the efficiency of heterogeneous single-atom catalysts (SACs) by adjusting the microenvironment of the active atom has recently attracted enormous attention. However, attempts to tune the spin-spin interaction between the SAC and its microenvironment have remained rather scarce. Some interesting questions can be raised, among which a fundamental one is: can the surrounding environment influence the local spin state of an SAC, and if so, can such influence be utilized to enhance the catalytic activity? In this work, we explore such a possibility by investigating the thermochemical effect of Kondo screening of a local atomic spin by free electrons in the metal support. Inspired by the exothermicity of the spin-screening interaction, a novel approach to heterogeneous catalysis -- reaction on a rink (ROAR) -- is proposed. In contrast to the conventional notion of thermal catalytic reaction, lowering the temperature of metal support is predicted to result in a reduced reaction barrier. As a proof of concept, CO oxidation catalyzed by the Co@CoPc/Au(111) composite is scrutinized. By combining the density functional theory and a hierarchical equations of motion approach, it predicts that the existing s-d hybridization between the magnetic d orbital of Co adatom and the substrate metallic states in the transition state will lower the free energy barrier and accelerate the reaction rate. Furthermore, if the strength of s-d hybridization is enlarged, a more appreciable speedup will be achieved. This work highlights the potential usefulness of the spin degrees of freedom to heterogeneous single-atom catalysis, and our proposed ROAR approach could open up a new horizon for exploiting the role of atomic spin in chemical reactions.

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