TAILIEUCHUNG - Industrial Robotics Theory Modelling and Control Part 5

Tham khảo tài liệu 'industrial robotics theory modelling and control part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Cable-based Robot Manipulators with Translational Degrees of Freedom 229 Tensionability of DishBot For the tensionability of DishBot Theorem 1 given in Section 3 is not sufficient. The reason is that the spine force only affects the tension of drive cables and has no influence on the passive ones. As a result it cannot leverage all the tensions. However it should be noted that each passive cable has a pre-tensioning spring to maintain the tension. Therefore the tensionability can be still proved based on its definition in Section 2. For the proof of tensionability we use the idea of Theorem 1 not the theorem itself . tension can be generated in the cables to any extent while the static equilibrium is satisfied. The free body diagram of the end-effector is shown in Fig. 8. The passive cables are in parallel with the spine and their tensions are shown by a superscript p while for the tension of drive cables a superscript d is used. The static equilibrium equations are found to be EF Tdú. TdÌ1 TdIK f -Td -Td - rd w 0 34 T1 u1 t2 u2 t3 u3 fs T t2 t3 w M -T r1 X w -Tp r2 X w ũ1 -Tp r1 X w 0 35 where TdÌÌị s are drive cable forces i 1 2 3 Tjw s are passive cable forces Ij s are the position vectors of the anchor points of the passive cables j 1 2 3 and fsw is the spine force. Figure 8. Free body diagram of DishBot s end-effector 230 Industrial Robotics Theory Modelling and Control A quick inspection of the above equations shows that Eq. 35 which is the equilibrium of the moments is a set of homogenous equations independent from the spine force which in general results in zero tension for passive cables. The tension of the drive cables are found from Eq. 34 . Note that the drive cables form a cone which contains the spine and hence using Lemma 4 the drive cable tensions are positive as long as the equivalent spine force fs -t1 -t2-t3 is positive compressive . As a conclusion tension in the drive cables can be generated to any desired level by choosing a large .

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