A systematic formulation of dynamic equations for robot manipulators with elastic links

2011 IEEE 9th International Symposium on Intelligent Systems and Informatics

2011

For many years our contemporaries have been using the original form of the Euler-Bernoulli equation in inappropriate way, and thus, as a matter of fact, the information about the complexity of the observed mechanism motion has being lost. In the new form of the Euler-Bernoulli equation the value of elastic deformation and its frequency change depend on the present moments and they also depend on the mechanism configuration, mass, segment length of the reference trajectory selection, dynamic characteristics of motor motions, selection of control laws etc.

Section: Introductionmentioning

confidence: 99%

The procedure for the application of a new form of Euler-Bernoulli equation and its solutions

2011 IEEE 9th International Symposium on Intelligent Systems and Informatics

2011

“…In paper [15] the authors extend the integral manifold approach for the control of flexible joint robot manipulators from the known parameter case to the adaptive case. The author of paper [13] designed a control law for local regulation of contact force and position vectors to desired constant vectors.…”

mentioning

confidence: 99%

“…In paper [14] different from conventional approaches, authors focus on the design of rigid part motion control and the selection of bandwidth of rigid subsystem. Work [15] presents the derivation of the equations of motion for application mechanical manipulators with flexible links. In [16] the equations are derived using Hamilton's principle, and are nonlinear integro-differential equations.…”

mentioning

confidence: 99%

New interpretation of the Euler-Bernoulli equation

2008 6th International Symposium on Intelligent Systems and Informatics

Vukobratović

2008

A new notion of joint, defined in terms of the state of motor (active or locked) and type of the elastic or rigid element, gear and/or link that follows after the motor, is introduced. Special attention is paid to the motion of the flexible links in the robotic configuration. The article is concerned with the relationship between the Euler-Bernoulli equation, the "Euler-Bernoulli approach" (EBA), and equation of equilibrium at the point of elastic line tip, the "Lumped-mass approach" (LMA). The Euler-Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler-Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.

“…In paper [6] differently from conventional approaches, authors focus on the design of rigid part motion control and the selection of bandwidth of rigid subsystem. Paper [20] presents the derivation of the equations of motion for application to mechanical manipulators with flexible links. In [21] the equations are derived using Hamilton's principle, and are nonlinear integro-differential equations.…”

mentioning

confidence: 99%

Complement of Source Equation of Elastic Line

Vukobratović

2008

J Intell Robot Syst

A new notion of joint, defined in terms of the state of motor (active or locked) and type of the elastic or rigid element, gear and/or link that follows after the motor, is introduced. Special attention is paid to the motion of the flexible links in the robotic configuration. The paper deals with the relationship between the equation of elastic line equilibrium, the "Euler-Bernoulli approach" (EBA), and equation of motion at the point of elastic line tip, the "Lumped-mass approach" (LMA). The Euler-Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the elasticity moment of the considered mode. This yields the difference in the structure of Euler-Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and cannot be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. The choice of reference trajectory is analyzed. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the gear and of the link (two modes), as well as the environment force dynamics.