Kinematics, stiffness and natural frequency of a redundantly actuated masticatory robot constrained by two point-contact higher kinematic pairs

This paper presents kinematics and two dynamic characteristics including stiffness and natural frequency of a four degrees-of-freedom (DOFs) masticatory robot. Based on the biological architecture of human masticatory system, this robot is modeled in the form of a redundantly actuated parallel mechanism constrained by two point-contact higher kinematic pairs (HKPs). The aim of this robot is to chew samples of newly developed foods in a human way while the food textures can be characterized. The kinematics including inverse kinematics, workspace and singularity are studied systematically. The inverse kinematics is given in closed-form solutions. The workspace is generated by a numerical search method. In virtue of the Jacobian matrix derived from differential kinematics, the singularity and the stiffness are investigated. Via the derived stiffness matrix and mass matrix, natural frequency is also computed. Finally, simulation is carried out, one real incisor trajectory of a healthy human subject is reproduced, illustrating the robot is able to reproduce kinematic behaviors of the human masticatory system, and it owns a satisfactory performance in terms of stiffness and natural frequency. Comparison between the redundantly actuated masticatory robot and its two non-redundantly actuated counterparts also exhibits that the former owns better performance, in terms of a similar incisor's workspace as the Posselt envelope, no singularity, larger stiffness and higher natural frequency.