tailieunhanh - Industrial Robotics Theory Modelling and Control Part 10

Tham khảo tài liệu 'industrial robotics theory modelling and control part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Model-Based Control for Industrial Robots Uniform Approaches. 529 s vE x z. This formal property has also an important impact in the practice. The symbolic derivation of the Lagrangian equations of motions becomes very messy for parallel robots such that its implementation in real-time control systems is very restrictive Tsai 1999 . The last fundamental step of our revised kinematic analysis is the definition of limb s jacobians JT and Jr that relate its translational and its angular velocities to the generalized velocities of the robot respectively J 9 . v J Ti ds and J Ri d a ds The use of the modified DENAVIT-HARTENBERG-notation allows also a recursive calculation of the limb s jacobians J T R-1 j i-iT k . dd. i-1 r JRi-1 ez ds 11 JR. Ri-1 JRi-1 ez s Ỉ-1 12 The next subsection demonstrates the efficiency and uniformity of the proposed method for deriving the kinematics of a serial and a parallel industrial robot. Application of the Kinematic Analysis of Industrial Robots Serial Manipulators Case Study KUKA KR15 The direct kinematics of serial-chain robots is straight forward. The transformation matrix can be calculated by starting from the base and evaluating the single T-l. By solving T q. n 0 T fa. T x we obtain the pose vector x. The jacobian is also joint-wise simple to obtain J q J1 I J2 I- with J. J n 0 ez x 0 rE 0 e lz 13 530 Industrial Robotics Theory Modelling and Control This can be deduced by using the MDH-notation and the recursive formulae given above. Although the solution of the inverse kinematics is generally hard to obtain for open-chain mechanisms industrial robots are characterized by simple geometry such that a closed-form solution exists. This is the case here where the three last revolute joint axes intersect at a common point spherical wrist Sciavicco Siciliano 2000 . Parallel Manipulators Case Study PaLiDA The general method of calculating the inverse kinematics of parallel robots is given by splitting the system into