Fig. 1. Model parameters of parallel mechanisms

Fig. 2. Definition of rotation direction of coaxial 3-RRR spherical parallel mechanism

Fig. 3. Inverse kinematics vector projection method

Fig. 4. Passive linkage fully extended or folded at singularity

Fig. 5. Vector relationship in CSPM forward kinematics

Fig. 6. Two types of collisions

Fig. 7. Flowchart of cartesian space solution

Fig. 8. Flowchart of configuration space solution

Fig. 9. Configuration space and cartesian space. （a） The configuration space without linkage collision constraints；（b） The actual configuration space with linkage collision constraints；（c） and （d） The actual Cartesian space of the mechanism with linkage collision constraints； （e） and （f） The Cartesian spaces. The range of motion without linkage collision constraints for pitch from 30° to 150° and azimuth from -180° to 180°

Fig. 10. Actual mechanism model

Fig. 11. Orientation trajectory planning of moving platform

Fig. 12. Driving axes angular velocity

Fig. 13. Variation of actuated joint angle with time