A comparative study on the manipulability index of RRR planar manipulators

This paper presents a comparative study on the dexterity and manipulability of three planar 1-RRR, 2-RRR and 3-RRR manipulators.After derivation of the Jacobian matrix of three manipulators, they are transformed to a homogeneous form to include components with homogenous physical units. The condition number of each Jacobian matrix is calculated. Since the condition number changes in general between 1 to ∞, its inverse is used for definition of the local condition index.A zero value for this index indicates that the Jacobian matrix is singular and consequently, the robot has the worse manipulability. On the other hand, the robot indicates the best manipulability and dexterity when this index is close to one. Furthermore, the effect of changing the platform angle on the local condition index is investigated. The manipulability of three manipulators is then compared to each other for the platform angle for which the maximum local condition index is resulted. The results show that the 3-RRR manipulator has a better dexterity than other manipulators at the platform angles less than 90 degree.For the angles greater than 90 degree, the 1-RRR manipulator has a greater local condition index which indicates more dexterity. Finally, the maximum local condition index is compared for each robot at its own workspace and common workspace of three robots.The results verify that this index has almost identical values for the already mentioned workspaces for each robot.Based on the manipulability distribution, the global condition index of theses robots are checked.The results confirm the superiority of the 3-RRR robot.