TAILIEUCHUNG - Advances in Robot Kinematics - Jadran Lenarcic and Bernard Roth (Eds) Part 15

Tham khảo tài liệu 'advances in robot kinematics - jadran lenarcic and bernard roth (eds) part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 418 P. Boning and S. Dubowsky When there are two unknown forces such as in Fig. 7 c the forces and torques cannot be calculated directly. This situation can often be solved by starting at several points in the chain and propagating the known forces and moments to a common point. In other cases additional information such as provided by an additional force torque sensor is needed to permit a solution. When all of the links in the system have been visited it is possible to determine if the given set of sensors is sufficient or if additional sensors are required. Analysis of Canonical Elements The above analysis can be applied case by case to the canonical elements in Fig. 3. First consider the chain with known loads Fig. 3 a . Starting with the link on the far left it is possible to find the actuator torques on the first joint. Continuing with the links from left to right it is possible to find forces and torques on all joints in this system. Hence there are enough sensors to completely identify all actuation efforts for this case. The canonical element chain with one unknown load also has enough sensors but it is necessary to work inward from both ends of the chain simultaneously so that the single unknown load at the middle link can be determined. However for any chain that has more than one unknown load as in Fig. 3 c all actuator efforts cannot be determined without adding more sensors. Loops can be resolved into two chains joined by two branching links. Loops are analysed by starting with a link that has only known applied loads and propagating the loads in both directions around the loop until the chain rejoins. It can be shown that there are not enough sensors to determine all actuation efforts for any of the three canonical elements with loops. However inserting a sensor in a loop converts this problem into the case of the chain with known loads Fig. 3 a . To summarize for all the canonical elements only a chain with known loads Fig. 3 a and a chain with

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