ROBOT DYNAMICS
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T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 ROBOT DYNAMICS T. Bajd and M. Mihelj
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ROBOT DYNAMICS. T. Bajd and M. Mihelj. Robot dynamics. In contrast to kinematics, dynamics represents the part of mechanics, which is interested into the forces and torques which are producing the motion of a mechanism. The analysis of robot dynamics enables us to consider - PowerPoint PPT Presentation
Transcript of ROBOT DYNAMICS
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
ROBOT DYNAMICS
T. Bajd and M. Mihelj
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• In contrast to kinematics, dynamics represents the part of mechanics, which is interested into the forces and torques which are producing the motion of a mechanism.
• The analysis of robot dynamics enables us to consider– the torques necessary to compensate the gravity forces of robot
segments,– the differences in moments of inertia occurring during the robot
motion,– dynamic couplings caused by simultaneous movements of all
robot segments.
Robot dynamics
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
Forward and inverse dynamics
Applied torques Joint motions
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• The dynamic analysis of a robot is based on a two-segment robot mechanism.
• The motion of the robot manipulator with two rotational joints occurs in the vertical plane.
• Both segments are of equal length. • The dynamic model is simplified by assuming that
the whole mass of each segment is concentrated in its center of mass.
• Such a pair of segments appears both in the anthropomorphic and in the SCARA robot structures.
• The robot trajectory is denoted by the two joint angles.
• The robot is placed into the fixed reference frame with z axis aligned with the axis of the first joint.
Two-segment robot mechanism
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Position, velocity and acceleration of the center of mass of the second segment
Torque in the second joint
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• The motion of the second segment mass is given by Newton’s law
• In addition to the force of gravity, the mass is acted upon by the force , transmitted by the massless segment
Torque in the second joint
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Robot segments and are rigid, thus
Center of mass acceleration
Centripetal acceleration Tangential acceleration
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• The torque in the second joint is
• or
Torque in the second joint
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Considering
• the torque in the second joint is
• With
Torque in the second joint
Inertial coupling Inertial Centrifugal Gravitational
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Relation between the total torque of external forces and the time derivative of the angular momentum
• The sum of the torques produced by the external forces
Torque in the first joint
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• The angular momentum of the mass equals
• with
• The angular momentum of the mass equals
• with
Angular momentum
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• With
Torque in the first joint
Inertial coupling
Inertial
Centrifugal
Gravitational
Coriolis
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• The torques in the robot joints can be written in the following general form
• where
Dynamic model in matrix form
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Inertial matrix
Inertial matrixb11 b12
b21 b22
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Coriolis and centrifugal terms
Coriolis and centrifugal terms
c11 c12
c21
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Gravitational terms
Gravitational terms
g1
g2
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
• Inverse dynamic model with friction (diagonal matrix of the joint friction coefficients )
• Forward dynamic model with friction
Forward and inverse dynamic model
T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010
Forward dynamic model block scheme
