Complement of Source Equation of Elastic Line |
| |
Authors: | Mirjana Filipovic Miomir Vukobratovic |
| |
Affiliation: | (1) Mihajlo Pupin Institute, Belgrade, Serbia |
| |
Abstract: | 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. |
| |
Keywords: | Robot Modeling Elastic deformation Gear Link Coupling Dynamics Kinematics Trajectory planning |
本文献已被 SpringerLink 等数据库收录! |
|