Embedded Files
To obtain the desired torques by plugging the joint angle parameters is not straight forward as it ought to be. We need to ensure where the robot can move smoothly and safely around the workspace. There are many configurations of the robot where it falls under the singularity positions. That is the positions in the workspace or the configuration of the robot for which joint velocities are infinite or the robot may not be able to reconfigure to any other position by itself in the workspace, which is just like a gimbal lock in a gyroscope or that tragedy happened in Apollo 11 moon mission.
Understanding the singularities of the mechanism is necessary and important to ensure the manipulator works smoothly in the work environment. To derive the singularities we make use of jacobian matrix that had mentioned in Jacobian. It is found that the determinant of this jacobian matrix will give those joint angular parameters for which the robot takes this singular configuration.
The final results after decomposition (for deriving the results refer to the text by [1]) are presented below
The figures on the left show the singularity curves when plotted for q2 and q3 angles only. Since the joint space is in 6D. It is difficult to view the 6D cube (because of joint limits of RALS. Otherwise it will be an n-D torus). The curve divides the joint space into two regions (more about this will be posted later) as seen from this graph. In the next figure, the impact of this singularity is shown. It tells when the condition in the above equation involving q2 and q3 is met, whatever values of rest joint angles, the wrist centre meets the z-axis.
Page updated
Google Sites
Report abuse