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In direct kinematics of the RSMG, the angular displace- ments of the rotor are obtained by the given angular displacements of the active joints. It is desired to set up encoders to monitor the angles between upper links and lower links, the passive joints (y%;), which is required in direct kinematics.

Figure 8 In direct kinematics of the RSMG, the angular displace- ments of the rotor are obtained by the given angular displacements of the active joints. It is desired to set up encoders to monitor the angles between upper links and lower links, the passive joints (y%;), which is required in direct kinematics.

Related Figures (14)

Figure 1: CAD outlook of RSMG
Figure 1: CAD outlook of RSMG
Figure 3: Vectors attached on the arm
Figure 3: Vectors attached on the arm
Figure 2: Overview of RSMG with one arm
Figure 2: Overview of RSMG with one arm
Figure 4: Virtual Tetrahedron
Figure 4: Virtual Tetrahedron
Figure 5: Frame F’, M and M; vectors Pu;, “vj, and Fw; intersect on the centre of the spherical rotor. Angles a is defined between Fu; and Fu; and 3 between “'w; and 'v;. Angles a and ( represents the angular length of the upper and lower links of the arms, respectively.
Figure 5: Frame F’, M and M; vectors Pu;, “vj, and Fw; intersect on the centre of the spherical rotor. Angles a is defined between Fu; and Fu; and 3 between “'w; and 'v;. Angles a and ( represents the angular length of the upper and lower links of the arms, respectively.
Figure 6: u, v and w in the fixed frame F
Figure 6: u, v and w in the fixed frame F
Figure 7: Frame F’, F; and M;
Figure 7: Frame F’, F; and M;
Finally, the Euler angles can be found by the above equations based on the active joints 0; and passive joints For “vu; and “y;, they can be written in matix forms so that K and LF are defined, where K is a matrix of all My, and L is a matrix of all “vu; from (27).
Finally, the Euler angles can be found by the above equations based on the active joints 0; and passive joints For “vu; and “y;, they can be written in matix forms so that K and LF are defined, where K is a matrix of all My, and L is a matrix of all “vu; from (27).
As mentioned in Section 2, parallel manipulator has singularities. There are two types of singularities, workspace-boundary singularity, workspace-interior sin- gularity and simultaneous singularity [Gosselin and An- geles, 1990]. The kinematic relationship between the ac- tive joints and the orientation of the rotor is given by: As described above, the workspace-interior singularity, type A singularity, occurs when det(A) = 0 and the workspace-boundary singularity, type B singularity, oc- curs when det(B) = 0.
As mentioned in Section 2, parallel manipulator has singularities. There are two types of singularities, workspace-boundary singularity, workspace-interior sin- gularity and simultaneous singularity [Gosselin and An- geles, 1990]. The kinematic relationship between the ac- tive joints and the orientation of the rotor is given by: As described above, the workspace-interior singularity, type A singularity, occurs when det(A) = 0 and the workspace-boundary singularity, type B singularity, oc- curs when det(B) = 0.
A is rank-deficient only when A, and Ag are both sin- vular. ie: Assume rl and r2 are independent. Then, we make two sub-matrices to determine when it is singular be- cause A is a 4 by 3 matrix.
A is rank-deficient only when A, and Ag are both sin- vular. ie: Assume rl and r2 are independent. Then, we make two sub-matrices to determine when it is singular be- cause A is a 4 by 3 matrix.
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