Đang chuẩn bị liên kết để tải về tài liệu:
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 5

Tham khảo tài liệu 'multi-arm cooperating robots- dynamics and control - zivanovic and vukobratovic part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Mathematical Models of Cooperative Systems 67 the close neighborhood of the unloaded state 0. To form the equations of motion in this field it is necessary to know the accumulated potential energy in the system of bodies. If the potential gravitational forces they constantly act in the direction of the Oz axis of the absolute coordinate frame in Lagrange s equations are associated with non-potential forces and are considered as a system of unknown external forces then it remains only to determine the potential energy of the elastic forces deformation energy . The purpose of the introduced assumptions and proposed modeling procedure is to avoid solving a system of equations that describes the deformation of the elastic system and using approximate methods derive the model of the cooperative system only on the basis of known absolute coordinates of the MCs and their derivatives along with gripping points at the initial moment i.e. the contact points tips of the manipulators and the MC of the manipulated object. The idea of modeling in the system of absolute coordinates is based on the following. As it is assumed that all the mass is concentrated at the elastic system nodes inertial and external forces represented by gravitational and contact forces act at these nodes. The links between particular nodes are massless so that the dissipation forces of the elastic system are also associated with the forces at other nodes. As we do not deal with manipulation in a resistive environment there are no surface resistance forces. Hence the forces acting at each node can be replaced with one resulting force. These resulting forces act at the nodes of the elastic system. To each deformed state corresponds only one system of node forces. The instantaneous deformed state can be obtained by static deformation of the unloaded state 0 involving the same system of forces which enables one to calculate deformation energy by using static procedures. The work of the external forces is .