Question

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A 3DOF spherical manipulator (RRP) has the following DH parameters and forward kinematics. L10e0-90 C2d3 3 a) Is each joint revolute or prismatic? [1st Joint 2nd Joint 3rd Joint 30° b) Ifd2 -2, find the position of the end-effector for a set of joint variable to be: q -45° c) The Jacobian matrix has been found to be: d3S2C2 10% Determine if q -0°is a singularity

Answer 1

a) s each joint is revolute or prismatic? Ans 1st joint Revolute joint with Joint variable8 2nd Joint Revolute joint with Joint variable 3rd Joint Prismatic joint with Joint variabled b) If d2 - 2,find the position of the end- effectorfor a set of joint variables to be 30° -45° Ans. The position of end effector is given by | dpC1-d3SS- d3C2 -2 sin30 3 cos30 sin(-45°) -2.8371 2 * cos30° + 3 * sin30° * sin(-450) | Ξ | 0.6714 | m 3 cos(-45°) 2.1213 or 10° 2 cos10cos0cos10sin0 -2 sin102 cos10°sin0 2sin10 cos0° sin10 sinoo -2cos10° -2sin 10° -2 sin0 cos0o -1.9696 1.9696 0 -0.3473 0.3473 0 thefore the determinate of J(q) 0, which is the condition for the singulairity so, it is the singularity condition