Dynamics of Constrained Robotic Systems

Abstract

Serial manipulators are mechanisms which consist of a series of single-DOF active revolute or prismatic joints connecting the fixed base to the end-effectors. These robots have good operating characteristics, such as a large workspace and high flexibility, but have some disadvantages, such as low precision, low stiffness and high vibrations and deflections. To overcome the aforementioned drawbacks of the serial architectures, there have been considerable developments in the field of manipulating structures, now known as the parallel manipulators. Constrained systems differ from free systems in that the freedom of motion of one or more position variables is limited by mechanical constraints. Parallel robots are closed chains consisting of a fixed base and a moving platform that are connected to each other by a set of serial legs. These legs, which typically have the same kinematical structure, are connected to both the platforms at points that are distributed in a geometrically symmetric fashion. In engineering, holonomic constraints are achieved by means of inflexible guides, joints, levers, bearings, rods and other connections. For an industrial robot, for example, each degree of freedom is normally assigned one rigid body and a drive motor. As the mechanical complexity of new robotic devices increases, it is becoming more important to have good formal procedures for representing kinematics and dynamics relationships. Based on the matrix mechanics of a rigid body, recursive relations about the kinematics and the dynamics of the constrained robotic systems schematized by kinematical chains are developed in this chapter. By using a set of successive mobile frames, we will first analyze the geometrical properties and the kinematics of the vector system of velocities and accelerations for each element of the robot. Expressed for every independent loop of a parallel mechanism, useful conditions of connectivity regarding the relative velocities and the relative accelerations will be determined for the direct or the inverse kinematics problem. With known positions, velocities and accelerations for a given trajectory of the end-effectors, the required actuation forces or torques, the internal reaction joint forces and, finally, the dimensions of the robot can easily be determined by solving the inverse dynamic problem. Dynamics modelling of parallel robots has been a subject of great research interest, because the dynamics models are also needed for control purposes. The dynamics problem is solved in two efficient ways: using an approach based on the general Principle of virtual work and sometimes applying sometimes the formalism of Lagrange equations of second kind. Final matrix relations written in a recursive compact form express only the explicit dynamics equations of the constrained robotic systems. When establishing the expressions for the active forces and the active torques in an inverse dynamics problem, these equations are in fact useful for real-time control of the robot's evolution. This methodology might be serviceable for the kinematics analysis and the nonlinear dynamics of a multi-body system consisting of interconnected rigid or, possibly, deformable bodies. Examples of mechanical structures that can be modeled as constrained robotic systems are: mechanisms, planar and spatial parallel robots, mobile robots, parallel kinematics machines, gear trains for robotics and robotic hybrid architectures.