Modelling and Simulation of Arm-Type Robot Dynamics

Dynamic Model is the mathematical relationship between. Robot spatial localization (end-effector coordinates), time derivatives, forces and torques (end-effector) and adimensional parameters: lengths, masses, inertia. Robot spatial localization (joint coordinates), time derivatives, forces and torques (joints) and adimensional parameters: lengths, masses, inertia. Robot spatial localization (joint or end-effector coordinates), time derivatives, forces or torques (joints or end-effector) and dimensional parameters: lengths, masses, inertia. Robot spatial localization (joint or end-effector coordinates), time derivatives, forces and torques (joints or end-effector) and adimensional parameters: lengths, masses, inertia. Robot spatial localization (joint or end-effector coordinates), time derivatives, forces and torques (joints or end-effector) and adimensional parameters: lengths, masses, inertia.

Dynamic model is necessary to. -Simulate the robot motion -Design and assess the mechanical structure -Size and select actuators -Design and assess the dynamic control. -Simulate the robot motion -Design and assess the digital structure -Size and select sensors -Design and assess the dynamic control. -Simulate the robot motion -Design and assess the mechanical structure -Size and select sensors -Design and assess the dynamic control. -Simulate the robot motion -Design and assess the digital structure -Size and select actuators -Design and assess the kinematic control.

The equations of motion of the dynamic model are based on. Newton's 2nd Law Y Euler's Law. Newton's 2nd Law. Euler's Law.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. q,qdot, qdotdot= Coriolis and centripetal coupling matrix. q,qdot, qdotdot= Friction force. q,qdot, qdotdot= Joint coordinates, velocities, and accelerations. q,qdot, qdotdot= Wrench applied at the end effector.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. M(q) = Coriolis and centripetal coupling matrix. M(q) = Friction force. M(q) = Gravity loading. M(q) = Joint-space inertia matrix.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. C(q, qdot) = Joint-space inertia matrix. C(q, qdot) = Coriolis and centripetal coupling matrix. C(q, qdot) = Gravity loading. C(q, qdot) = Friction force.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. F(qdot) = Joint-space inertia matrix. F(qdot) = Coriolis and centripetal coupling matrix. F(qdot) = Gravity loading. F(qdot) = Friction force.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. G(q) = Joint-space inertia matrix. G(q) = Coriolis and centripetal coupling matrix. G(q) = Gravity loading. G(q) = Jacobian matrix.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. Q = Joint-space inertia matrix. Q = Generalized actuator forces/torques. Q = Friction force. Q = Coriolis and centripetal coupling matrix.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. J(q) = Joint-space inertia matrix. J(q) = Jacobian matrix. J(q) = Coriolis and centripetal coupling matrix. J(q) = Friction force.

Differential Vector equations 1 row per dof is: Q=M(q)*qdotdot+C(q,qdot)*qdot+F(qdot)+G(q)+J(q)^T*g. g = wrench applied at the end-effector. g = Gravity loading. g = Coriolis and centripetal coupling matrix. g = Jacobian matrix.

Dynamic model: Dynamic matrices depend on kinematic parameters. VERDADERO. FALSO.

Dynamic model: Every link has 10 independent inertial parameters. -Mass(1) -Position of the centre of mass (COM) wrt link CF (6) -Second moments representing the inertia about the COM but wrt axes aligned with the link CF (3). -Mass(1) -Position of the centre of mass (COM) wrt link CF (4) -Second moments representing the inertia about the COM but wrt axes aligned with the link CF (5). -Mass(1) -Position of the centre of mass (COM) wrt link CF (5) -Second moments representing the inertia about the COM but wrt axes aligned with the link CF (4). -Mass(1) -Position of the centre of mass (COM) wrt link CF (3) -Second moments representing the inertia about the COM but wrt axes aligned with the link CF (6).

G(q) Gravity term. Dominating term when robot is stationary or slow and depends strongly on the robot pose. Dominating term when robot is dynamic or fast and depends strongly on the robot pose. Dominating term when robot is stationary or slow and depends not strongly on the robot pose.

G(q) Gravity term helps only for robot design. VERDADERO. FALSO.

M(q,qdot) Inertia matrix. Depends on the robot pose. VERDADERO. FALSO.

M(q). Inertia matrix. Diagonal terms (Mjj) are. Coupling of acceleration from joint j to the generalized force on joint i. Inertia seen by joint j.

M(q). Inertia matrix. Off-diagonal terms (Mij, with i=/=j). Inertia seen by joint j. Coupling of acceleration from joint j to the generalized force on joint i.

C(q,qdot). Coriolis Matrix. Depends on the robot pose. VERDADERO. FALSO.

C(q,qdot). Coriolis terms. Proportional to qidotqjdot represent the coupling of joint j velocity to the generalized force action on joint i. Proportional to qi^2.

C(q, qdot). Centripetal terms. Proportional to qidotqjdot represent the coupling of joint j velocity to the generalized force action on joint i. Proportional to qidot^2.

F(q). Friction matrix. Electric motors: Wide use of. Reduction gearboxes. Gearmotors.

F(q). Friction matrix. Electric motors use reduction gearboxes. Advantages: Decreased torque and inertia seen by the motor is reduced Disadvantages: Increased friction. Advantages: Multiplied torque and inertia seen by the motor is reduced Disadvantages: Decreased friction. Advantages: Multiplied torque and inertia seen by the motor is reduced Disadvantages: Increased friction.

Friction is the least dominant force. TRUE. FALSE.

J(q)^Tg. Wrench. Forces and torques applied at the end effector. Forces and torques applied at the base.

J(q)^Tg. Wrench. Influence on. Inertia. Joint torques.

Forward dynamics. Forward dynamics: From joint torques/forces (Q1,Q2,...,Qn) TO joint accelerations (qdotdot1, qdotdot2,...,qdotdotn). Forward dynamics: From joint accelerations (qdotdot1, qdotdot2,...,qdotdotn) TO joint torques/forces (Q1,Q2,...,Qn).

Inversed dynamics. inverse dynamics: From joint accelerations (qdotdot1, qdotdot2,...,qdotdotn) TO joint torques/forces (Q1,Q2,...,Qn). inverse dynamics: From joint torques/forces (Q1,Q2,...,Qn) TO joint accelerations (qdotdot1, qdotdot2,...,qdotdotn).

Forward Kinematics. Forward Kinematics: From End-effector positions TO Joint positions (q1,q2,...,qn). Forward Kinematics: From Joint positions (q1,q2,...,qn) TO End-effector positions.

Inverse Kinematics. Inverse Kinematics: From End-effector positions TO Joint positions (q1,q2,...,qn). Inverse Kinematics: From Joint positions (q1,q2,...,qn) TO End-effector positions.

M(q). Inertia Matrix is important for. robot design. For a fixed minimum motor torque, inertia sets an upper bound on acceleration. robot design. For a fixed maximum motor torque, inertia sets a lower bound on acceleration. robot design. For a fixed maximum motor torque, inertia sets an upper bound on speed. robot design. For a fixed maximum motor torque, inertia sets an upper bound on acceleration.

Forward dynamics provide. joint accelerations: integrate to obtain joint velocities and coordinates. joint velocities and coordinates: integrate to obtain joint accelerations.

Characteristics of Lagrangian energy-based approach to obtain the Dynamic Model. It starts at the base and, by working outwards, adds the velocity and acceleration of each joint to determine the velocity and acceleration of each link Final well-structured equations Computationally inefficient. Makes use of HTMs defined in the forward kinematics Final well-structured equations Computationally efficient. Makes use of HTMs defined in the forward kinematics Final well-structured equations Computationally inefficient. Makes use of HTMs defined in the forward kinematics Then, working from the tool back to the base, it computes the forces and moments acting on each link, and thus the joint torques Computationally inefficient.

Characteristics of Newton-Euler's recursive formulation to obtain the Dynamic Model. It starts at the base and, by working outwards, adds the velocity and acceleration of each joint to determine the velocity and acceleration of each link Final well-structured equations Computationally inefficient. It starts at the base and, by working outwards, adds the velocity and acceleration of each joint to determine the velocity and acceleration of each link Then, working from the tool back to the base, it computes the forces and moments acting on each link, and thus the joint torques Computationally efficient. Makes use of HTMs defined in the forward kinematics Final well-structured equations Computationally efficient. Makes use of HTMs defined in the forward kinematics Then, working from the tool back to the base, it computes the forces and moments acting on each link, and thus the joint torques Computationally inefficient.

Actuator dynamics. Dynamic model of a robot made up of: -Dynamic model of the mechanical structure: Relates motion and forces/torques applied to joints -Dynamic model of the actuation system: Relates control actions and forces/torques applied to joints. Dynamic model of a robot made up of: -Dynamic model of the mechanical structure: Relates control actions and forces/torques applied to joints -Dynamic model of the actuation system: Relates motion and forces/torques applied to joints.

Actuator dynamics. Most robots are drive by. Hydraulic motors. Electrical motors.