Kinematics Of Lower-Mobility Parallel Maniulator And Theory On 5-DOF Parallel Manipuator

Recently, the lower-mobility parallel mechanisms have been one of hot topics in fields of international mechanics and robotics. Hence, kinematics of lower-mobility parallel mechanisms received more and more attention. In the kinematics analysis, Jacobian plays as an important role. However, for a lower-mobility parallel mechanism, there is no unify and practical method to build Jacobian matrix only with structure and configuration parameters. This paper proposed a method to build N×N Jacobian matrix and N×N×N Hessian matrix for a class of lower-mobility parallel mechanism whose mobility of limb equals the mobility of mechanism is also given. Meanwhile, the method is developed to be valid for all 14 classes of lower-mobility parallel mechanisms. A build N×N Jacobian matrix is adopted to show the mapping relationship between N input velocity elements and N independent output velocity elements. Furthermore, the 6×N Jacobian is given by transforming the square Jacobian matrix.Among the existing lower-mobility parallel mechanisms, the history of 5-DoF parallel mechanism with symmetrical structure is short. Most of them are 3R2T. People realized the existence of this class of mechanisms after some novel mechanism types are synthesized by Prof. Huang and co-workers with the synthesis theory based on constraint screw. However, the essence of one thing cannot be recognized just by inventing. To deepen the cognition on the 5-DoF parallel mechanisms with symmetrical structure, this paper summarized 11 types from more than 70 ones and also proposed 7 ones. The actuators of these 18 mechanisms are symmetrical. Furthermore, they can adopt base-mount-actuator structure or prismatic-actuator-adjacent-to-the-base structure. Symmetrical structure and actuators will be convenient to achieve nearly isotropic kinematics performance. The base-mount-actuator structure could reduce the extra-burden of a mechanism to improve work speed. The prismatic-actuator-adjacent-to- the-base structure will improve the capacity of load and accuracy. Moreover, this paper also synthesized the first 5-DoF 3T2R (three translational and two independent rotational degrees of freedom) with symmetrical structure and assembly condition.Recently, the lower-mobility parallel mechanisms have been one of hot topics in fields of international mechanics and robotics. Hence, kinematics of lower-mobility parallel mechanisms received more and more attention. In the kinematics analysis, Jacobian plays as an important role. However, for a lower-mobility parallel mechanism, there is no unify and practical method to build Jacobian matrix only with structure and configuration parameters. This paper proposed a method to build N×N Jacobian matrix and N×N×N Hessian matrix for a class of lower-mobility parallel mechanism whose mobility of limb equals the mobility of mechanism is also given. Meanwhile, the method is developed to be valid for all 14 classes of lower-mobility parallel mechanisms. A build N×N Jacobian matrix is adopted to show the mapping relationship between N input velocity elements and N independent output velocity elements. Furthermore, the 6×N Jacobian is given by transforming the square Jacobian matrix.Among the existing lower-mobility parallel mechanisms, the history of 5-DoF parallel mechanism with symmetrical structure is short. Most of them are 3R2T. People realized the existence of this class of mechanisms after some novel mechanism types are synthesized by Prof. Huang and co-workers with the synthesis theory based on constraint screw. However, the essence of one thing cannot be recognized just by inventing. To deepen the cognition on the 5-DoF parallel mechanisms with symmetrical structure, this paper summarized 11 types from more than 70 ones and also proposed 7 ones. The actuators of these 18 mechanisms are symmetrical. Furthermore, they can adopt base-mount-actuator structure or prismatic-actuator-adjacent-to-the-base structure. Symmetrical structure and actuators will be convenient to achieve nearly isotropic kinematics performance. The base-mount-actuator structure could reduce the extra-burden of a mechanism to improve work speed. The prismatic-actuator-adjacent-to- the-base structure will improve the capacity of load and accuracy. Moreover, this paper also synthesized the first 5-DoF 3T2R (three translational and two independent rotational degrees of freedom) with symmetrical structure and assembly condition.