Dynamics of Parallel Robots

1 Introduction.- 1.1 Robotic systems.- 1.2 Historical development.- 1.3 Mechanics of robots.- 2 Matrix kinematics of the rigid body.- 2.1 Position and orientation of a rigid body.- 2.2 Velocity field.- 2.3 Acceleration field.- 2.4 Twist of velocity field of a rigid body.- 2.5 Types of rigid body motions.- 3 Matrix kinematics of composed motion.- 3.1 Kinematics of composed motion of a point.- 3.2 Kinematics of composed motion of a rigid body.- 3.3 Application to kinematics analysis of mechanisms.- 4 Kinetics of the rigid body.- 4.1 Centre of mass and tensor of static moments of a rigid body.- 4.2 Moments of inertia of a rigid body.- 4.3 Kinetic impulse of a system of particles.- 4.4 Kinetic moment of a rigid body.- 4.5 Kinetic energy of a rigid body.- 4.6 Power and work of the forces acting on a system of particles.- 4.7 Power and work of the forces acting on a rigid body.- 5 Dynamics of the rigid body.- 5.1 Fundamental system of differential equations of motion for a system of particles.- 5.2 Theorem of kinetic impulse.- 5.3 Theorem of kinetic moment.- 5.4 Theorem of kinetic moment with respect to a translating frame.- 5.5 Theorem of kinetic energy.- 5.6 Conservation of mechanical energy.- 5.7 Theorem of kinetic energy with respect to a translating frame.- 5.8 Equations of motion in dynamics of the rigid body.- 6 Analytical Mechanics.- 6.1 Principle of virtual work.- 6.2 D'Alembert principle.- 6.3 Lagrange equations.- 6.4 Canonical Hamiltonian equations.- 7 Dynamics of constrained robotic systems.- 7.1 Geometric model of the robot.- 7.2 Velocities and accelerations.- 7.3 Equations of motion.- 7.4 Advantages of the present method.- 7.5 Application to dynamics analysis of mechanisms.- 8 Planar parallel robots.- 8.1 Power requirement comparison in dynamics of the 3-PRR planar parallel robot.- 8.2 Internal reaction joint forces in dynamics of the 3-RRR planar parallel robot.- 8.3 Inverse kinematics and dynamics of a 3-PRP planar parallel robot.- 9 Spatial parallel