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ROBOT DYNAMICS

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

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ROBOT DYNAMICS

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  1. ROBOT DYNAMICS T. Bajd and M. Mihelj

  2. 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 • 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.

  3. Forward and inverse dynamics Applied torques Joint motions

  4. Two-segment robot mechanism • 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.

  5. Torque in the second joint • Position, velocity and acceleration of the center of mass of the second segment

  6. Torque in the second joint • 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

  7. Center of mass acceleration • Robot segments and are rigid, thus Centripetal acceleration Tangential acceleration

  8. Torque in the second joint • The torque in the second joint is • or

  9. Torque in the second joint • Considering • the torque in the second joint is • With Inertial coupling Inertial Centrifugal Gravitational

  10. Torque in the first joint • 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

  11. Angular momentum • The angular momentum of the mass equals • with • The angular momentum of the mass equals • with

  12. Torque in the first joint • With Inertial Inertial coupling Centrifugal Coriolis Gravitational

  13. Dynamic model in matrix form • The torques in the robot joints can be written in the following general form • where

  14. Inertial matrix b11 b12 • Inertial matrix b22 b21

  15. Coriolis and centrifugal terms • Coriolis and centrifugal terms c12 c11 c21

  16. Gravitational terms • Gravitational terms g1 g2

  17. Forward and inverse dynamic model • Inverse dynamic model with friction (diagonal matrix of the joint friction coefficients ) • Forward dynamic model with friction

  18. Forward dynamic model block scheme

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