Tham khảo tài liệu 'dynamics of mechanical systems 2009 part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 682 Dynamics of Mechanical Systems Then by substituting from Eqs. and we obtain mkvklm vkpmqp vkpmtfp kmn klm kpntfp kpntfp E -hsn klmersm - mịgVịl1 Mk3 Fl 0 l 1 . n 1 k l - 1 Equation may be written in the compact matrix form as Aq f F where A is a symmetrical n 1 X n 1 generalized mass array q is an n 1 X 1 column array of generalized coordinates f is an n 1 X 1 column array of inertia forces and F is an n 1 X 1 column array of generalized applied forces. The elements app of A are a ro lp k klm kpm kmn klm kn The elements fp of f are f - mv jv ji L. Wt 0u q. e I wt. w w q q l k klm kpm p kmn klm kpn p rsm ksn klm kqr kpn p q The elements f of F are E Fl -mgVjl1 Mi-h3 Fl E where the F are given by Eq. . Redundant Robots Redundant robots have more degrees of freedom than are needed to accomplish a given task. These extra degrees of freedom pose special problems for dynamics analysis. Decisions need to be made as to how the superfluous degrees of freedom are to be used. Expressed another way constraints need to be imposed upon redundant robots for the robots to accomplish a given task. These constraints may take a variety of forms such as minimum joint torques minimum energy consumption obstacle avoidance minimum jerk or least time of operation. Methods of analysis to accommodate such constraints are still being developed. Difficulties of these analyses have not all been resolved. To avoid these difficulties early manufacturers of robots have restricted their machines to at most six degrees of freedom however without redundancy the machines cannot accomplish their given tasks in an optimal manner. In this and the following section we will explore some of the issues in the dynamics and control of redundant robot systems. Consider the general system of Figure . Suppose we have a desired movement of the end effector E. For simplicity and without loss of .
