Tham khảo tài liệu 'fundamentals_of_robotic_mechanical_systems part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 146 4. Kinetostatics of Simple Robotic Manipulators and hence a simple algorithm follows p. - Q. For i 2 to n do Pj Pj . Qj enddo Now since p. is identical to Q. the first product appearing in the do-loop p. Q. is identical to Q. Q. whose two factors have a special structure. The computation of this product then requires special treatment which warrants further discussion because of its particular features. From the structure of matrices Qj as displayed in eq. we have cos Ớ. p. sinớ. 0 A. sinớ. A. cos 6. V- J sinớ. p. cos 6. A. cos Ớ. A. sinớ. p. sinớ. sinớ. A. cos 6. fl. cos 6. 0 p. A. The foregoing product is calculated now by first computing the products A. A. A. p. p. p. and A. p. which involve only constant quantities these terms thus being posture-independent. Thus in tracking a prescribed Cartesian trajectory the manipulator posture changes continuously and hence its joint variables also change. However its DH parameters those defining its architecture remain constant. Therefore the four above products remain constant and are computed prior to tracking a trajectory . off-line. In computing these products we store them as A. A. A. p. A. p. p. p. p. A. A. p. Next we perform the on-line computations. First let 7 A. sinớ. T sinớ. cos 6. V cos 6. cos 6. u cos 6. sin 6. A. T V sin 6. sin 6. and hence V ơ sin Ớ. p. T Ơ COS 6. p. sinớ. A. u p. sinớ. A. V p. cos 6. A. cos 6. p. p. w A. sin Ớ. p. V A. cos 0. fl. cos 6. A. 1Although V and V look similar they should not be confused with each other the former being the lowercase Greek letter upsilon. As a matter of fact no confusion should arise because upsilon is used only once and does not appear further in the book. Velocity Analysis of Serial Manipulators 147 As the reader can verify the foregoing calculations consume 20 multiplications and 10 additions. Now we proceed to compute the remaining products in the foregoing do-loop. Here notice that the product Pj . Qj for 3 i n can be computed recursively
