Đang chuẩn bị liên kết để tải về tài liệu:
Advances in Robot Manipulators Part 17

Tham khảo tài liệu 'advances in robot manipulators part 17', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 632 Advances in Robot Manipulators Similar to the those established in De Silva 1976 Sooraksa Chen 1998 equation 16 is the fifth order TB homogeneous linear PDE with internal and external damping effects expressing the deflection w x t . We have added to this equation the following initial and pinned clamped -mass boundary conditions Loudini et al. 2007a Loudini et al. 2006 Initial conditions w x 0 w0 õw x t at w 0 t 0 Pinned end w 0 t 0 M x t - Jh a3w x t õxõt2 Jx 0 Clamped end w 0 t 0 aw x t Õx x 0 aM x t - M a2w x t ax p at2 Free end with payload mass 18 19 20 21 M x t Jp a3w x t axat2 0 0 0 The classical fourth order TB PDE is retrieved if the damping effects terms are suppressed _a4w x t E a4w x t p21 a4w x t . a2w x t EI------- - pll 1 ----I - ------------- - pA------- - 0 ax4 KG ax2at2 KG at4 at2 22 If the effect due to the rotary inertia is neglected we are led to the shear beam SB model Morris 1996 Han et al. 1999 a4w x t piE a4w x t a2w x t EI -A pA - 0 23 ax4 KG ax2at2 at2 but if the one due to shear distortion is the neglected one the Rayleigh beam equation Han et al. 1999 Rayleigh 2003 arises r ri w x t a4w x t a2w x t E s - p S T pA TT 0 24 ax4 ax2at2 at2 Moreover if both the rotary inertia and shear deformation are neglected then the governing equation of motion reduces to that based on the classical EBT Meirovitch 1986 given by Timoshenko Beam Theory based Dynamic Modeling of Lightweight Flexible Link Robotic Manipulators 633 __a4w x t a2 w x t El 77 pA 77 0 25 ax4 at2 If the above included damping effects are associated to the EBB the corresponding PDE is a5w x t a4w x t a2w x t aw x t KdI ax4at EI ax4 pA at2 Ad at 0 26 The resolution of the PDE with mixed derivative terms 16 is a complex mathematical problem. Among the few methods existing in the literature we cite the following approaches with some representative works the finite element method Kapur 1966 Hoa 1979 Kolberg 1987 the Galerkin method Wang and Chou 1998 Dadfarnia et al. 2005 the .