The analytical expression of driving force is helpful to quickly plan the kinematic trajectory of parallel mechanism for automatic drilling and riveting. For parallel posture alignment mechanism, because of its closed-loop characteristics, the inverse dynamic solution is more complex, especially for parallel bracket with actuation redundancy. Considering that the telescopic rods are actually flexible parts, the dynamic analytical modeling is carried out with deformation supplementary equation. Taking the force at the spherical joint as the intermediate variable and the driving force of each active prismatic pair are analytically analyzed by vector cross-product. The modeling was verified by experiment. Compared with previous research methods, the analytical method proposed improves the solution accuracy of driving force slightly and reduces the driving force solution time by 56.28%, which is high efficiency. The maximum error percentage is 1.61%, and the experimental results show that the method of inverse dynamics modeling is practical. This paper can be used for driving force analysis of parallel posture alignment mechanism based on positioner in the field of aircraft assembly.

PMs with two rotations and one translation (2R1T) have been used as skeletons in various advanced manufacturing equipment where high accuracy and stiffness are basic requirements. Considering the advantages of redundant actuation and overconstrained structure, such as reduced singularities and improved stiffness, a new 2R1T overconstrained PM with actuation redundancy, called Hex4, is proposed in this paper. This is a 2-PUR/2-RPU PM (where P denotes an actuated prismatic joint, U a universal joint, and R a revolute joint) that is actuated by four prismatic joints. Compared with some existing 2R1T overconstrained PMs with actuation redundancy, the main advantage of the proposed PM is that the heavy motors of two limbs are mounted on the base to reduce the movable mass and improve dynamic response. First, mobility analysis, inverse kinematics, and velocity analysis are presented. Then, the local transmission index and good transmission workspace are used to evaluate the motion/force transmissibility of the Hex4 PM. The variation tendencies of the two indices with different link parameters are investigated. The singularity is then discussed by considering the motion/force transmissibility. Finally, link parameters are optimized to obtain an improved good transmission workspace. It is shown that the proposed PM has a good potential for high precision applications.

This paper discusses a planar 2-DOF (degrees of freedom) parallel kinematic machine with actuation redundancy. Its inverse dynamic model is constructed by utilizing the Newton–Euler method based on the kinematic analysis. However, the dynamic model cannot be solved directly because the number of equations is less than the number of unknowns, which is due to the redundant force. In order to solve this problem, the relationship between the deformations of the links and the position errors of the moving platform are further explored. Then a novel method, which aims at minimizing the position errors of the machine, is proposed to optimize the redundant force. It also enables to solve the dynamic model. Finally, the dynamic performance analyses of this machine and its non-redundant counterpart are provided by numerical examples. Besides, another optimization method proposed for minimizing the constraint forces is also applied for comparison. The results show the effectiveness of the novel methods in improving the position precision of the machine.

Parallel kinematics machines (PKMs) can exhibit kinematics as well as actuation redundancy. While the meaning of kinematic redundancy has been already clarified for serial manipulators, actuation redundancy, which is only possible in PKMs, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM, a nonlinear control system is introduced whose dynamics evolves on c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKMs are classified as full-actuated and underactuated machines. Relating this DOA to degree of freedom allows to classify the actuation redundancy.

In this work, accuracy enhancement through backlash elimination is considered. When a nonredundantly actuated parallel manipulator is subjected to a wrench while following a trajectory, required actuator torque switching (going from positive to negative or vice versa) may occur. If backlash is present in the actuation hardware for a manipulator, torque switching compromises accuracy. When in-branch redundant actuation is added, a pseudoinverse torque solution requires smaller joint torques, but torque switching may still occur. A method is presented where concepts of exploiting a nullspace basis of the joint torques are used to ensure that single sense joint torques can be achieved for the actuated joints. The same sense torque solutions are obtained using nonlinear optimization. The methodology is applied to several examples simulating parallel manipulators in machining applications.

The global trajectory control of walking machines is addressed here with particular attention paid to the consequences of actuator redundancy for control and to the inclusion of actuator dynamics in trajectory controller design. Redundancy of actuation, typical of walking machines, results in the trajectory control problem being formulated perforce in a global coordinate frame, instead of the joint space, as in nonredundant manipulators. This lack of one-to-one correspondence between the degrees of freedom of motion in the global coordinate frame and the actuators results in coupling between the different trajectory control loops. A mechanism for reducing this coupling effect is proposed here, along with a procedure to take into account approximately the effect of actuator dynamics in designing the trajectory controllers. The proposed methods are evaluated by simulation for an example problem in legged locomotion and are shown to be effective.

This paper deals with the position workspace, orientation workspace, and singularity of a 3-degree-of-freedom (DOF) planar parallel manipulator with actuation redundancy, which is created by introducing a redundant link with active actuator to a 3-DOF nonredundant parallel manipulator. Based on the kinematic analysis, the position workspace and orientation workspace of the redundantly actuated parallel manipulator and its corresponding nonredundant parallel manipulator are analyzed, respectively. In the singularity analysis phase, the relationship between the generalized input velocity and the generalized output velocity is researched on the basis of the theory of singular value decomposition. Then a method to investigate the singularity of parallel manipulators is presented, which is used to determine the singularity of the redundantly actuated parallel manipulator. In contrast to the corresponding nonredundant parallel manipulator, the redundant one has larger orientation workspace and less singular configurations. The redundantly actuated parallel manipulator is incorporated into a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

This paper analyses the concept of velocity isotropy for Parallel Mechanisms with Actuation Redundancy (PMAR). The limits of classical indices based on the Jacobean matrix condition number are shown. It is proposed to use either the largest ellipsoid included in the operational polytop, or the operational polytop itself, as better representations of a PMAR capabilities. The polytop is studied because it is actually the accurate representation of a machine capability, while the largest ellipsoid remains similar to the classical tool roboticists are dealing with for decades. Velocity performance indices are proposed, and the ways to compute them efficiently are given.