Tham khảo tài liệu 'mechatronic systems, simulation, modeling and control part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 128 Mechatronic Systems Simulation Modelling and Control Fig. 5. a Inverse kinematic singularities if Ỡ21 n- b Inverse kinematic singularities where Ỡ2Í 0 V i. 1 2 3. c Direct kinematic singularity if 3u Ỡ2Í V i. 1 2 3. d Combined kinematic singularity if Ỡ21 n 32 0 O33 0 ỡ12 Ỡ22 13 23 0 and 02 03 0orn. Note that the robot presents a combined singularity if three angles Ỡ3Í n V I 1 2 3 consequently case c is a combined singularity Ỡ32 0 ỡ33 0 . Note that the design of the robot plays a very important role because singularities can even avoid. For example in figure c the singularity is present because lengths of the forearm allows to be in the same plane that the end effector platform and in the figure d a combined singularity is present because 02 03 0. In all figures we suppose that the limb I 1 is the limb situated to the left of the images. Note that collisions between mechanical elements are not taken into account. d By considering 27 to 30 direct kinematic singularities present when the end effector platform is in the same plane as the parallelograms of the 3 limbs in this configuration the robot cannot resist any load in the Z direction see Fig. 5 c . Note that singularities like above depend on the lengths and angles of the robot when it was designed Fig. 5 c such is the case of the above configuration where singularity can present when a H b other singularities can present in special values of Fig. 5 d . Analysis of singularities of the work space is important for Visual controller in order to bound the workspace an avoid robot injures. Above analysis is useful because some singularities are given analytically. Different views of the work space of the CAD model of the Robotenis system is shown in Fig. 6 a b c Fig. 6 Work space of the Robotenis system. a Work space is seen from bottom part of the robot b it shows the workspace from side. c The isometric view of the robot is shown. New visual Servoing control strategies in tracking tasks using a PKM 129 As .
