Tham khảo tài liệu 'climbing and walking robots part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Mathematical Modelling and Simulation of Combined Trajectory Paths of a Seven Link Biped Robot 173 Fig. 5. The link s angles and configuration. Now the kinematic parameters will be obtained with respect to the above mentioned combined trajectory paths combined with the domain of the nonlinear equations see Fig. 5 . The nonlinear equations can be obtained as follows For support legs 11 cos -01 12 cos -02 a 11 sin -01 12 sin - 02 b For swing legs 13 cos 03 14 cos 04 c 13 sin 03 14 sin 04 d 23 24 where a xa sup xhip b zhip-za sup c xhip xa swing d zhip za swing With the aid of the written programs and designed software the above nonlinear equations based on the gait parameters are solved and also the link s angles are obtained. The kinematic parameters of the robot for single phase of the walking can be found in Mousavi Bagheri 2007 Mousavi 2006 . 174 Climbing and Walking Robots 3. Dynamic investigations With the biped s motion an important stability criteria in similarities to the human gait is defined using the zero moment point ZMP . The ZMP is a point on the ground about which the sum of all the moments around is equal to zero. The ZMP formula is written as follows Huang et al. 2001 Xzmp x x x i X1 mi g COSẰ Zi xi m g sinZ xi zi- 1 Ifii 25 Y mi g cosẰ z i where xi z i are the vertical and horizontal acceleration of the mass center of link i with respect to the fixed coordinate system which is on the support foot . 0t is the angular acceleration of link i obtained from the interpolation process and k denotes the slope of the surface. Principally two types of ZMP are defined a moving ZMP and b fixed ZMP. The moving ZMP of the robot is similar to that for the human gait Mousavi Bagheri 2007 . In the fixed type the ZMP position is restricted through the support feet or the user s selected areas. Consequently the significant torso s modified motion is required for stable walking of the robot. For the process here the software has been designed to find the target angle
