tailieunhanh - Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 9

Tham khảo tài liệu 'multi-arm cooperating robots- dynamics and control - zivanovic and vukobratovic part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Synthesis ofNominals 147 c i I d G R6x6m and cv c1 G R6x6. For the given yv and Fsec the position vector of the other nodes yj0 is calculated from 223 as ysS0 yss y0s A l Fs - A 1 M us 0r ec 71 us0n uvyv 224 and consequently the force at the manipulated object MC at the end of the gripping phase will be s 1 s 1 Fe0 cs0Aus0Fec cv cs0 Aus0Auv yv. 225 It should be noticed that in the case of nominal gripping it is not necessary to give the overall vector of elasticity force FS but only the part associated to the contact points Fsec which is equivalent to prescribing the vector of contact forces Fsc. Expressions 224 and 225 can be interpreted in the following way to determine all the characteristics of the elastic system at the end of gripping phase it suffices to know the position of one contact point and forces at the other contact points. In other words it is not necessary to know the properties of the manipulated object in order to be able to reach a conclusion about the elastic system position. Moreover on the basis of knowing the position of one contact point and forces at the other contact points it is possible to determine the displacement and forces at the manipulated object MC. Namely 224 determines ys0 yT yT T. In this way the object MC y0 is uniquely determined and by replacing it into 223 one can calculate the force Fes0 at the object s MC. If however exact elasticity force at the object MC Fes0 G0 is required then as in the previous case of nominal gripping the displacement of another node different from the contact point of the leader must be in agreement with the preset force requirement leader s displacement generally different from zero and with the state at other contact points. Namely as det K 0 then according to 197 det cv cs0A S0Auv 0 so that on the basis of the known forces Fes0 and F c. from 225 one cannot calculate the necessary leader s displacement ysv. It is necessary to first fix the elastic system in space by giving . the .