In this paper, a systematic approach is developed for the structural synthesis of a class of four-degrees-of-freedom (4-DoF) and 5-DoF overconstrained parallel manipulators with identical serial limbs. The theory of screws and reciprocal screws is employed for the analysis of the geometric conditions that must be met by the limbs of such parallel manipulators. Limb structures that can be used for constructing 4-DoF or 5-DoF parallel manipulators are enumerated according to the reciprocity of the twist and wrench systems. The assembly conditions of a parallel manipulator built by using identical C- or F-limbs are discussed. Several 4-DoF and 5-DoF parallel manipulators are sketched as examples.

Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators with Identical Limb Structures

A systematic theory for topology synthesis of parallel manipulators considering basic requirements such as kinematics, dynamics, control, and actuation is built. The kernel part of the theory is its proper application of a new mobility formula, output character equation of parallel manipulators, and units for single-opened-chains that have topological features. A feasible methodology for synthesizing parallel manipulators is also given, by which a detailed application is focused on the synthesis of three-dimension-translation parallel manipulators. The result synthesized encompasses not only most known mechanisms, but also some novel mechanisms with fine performances, such as simple forward/ inverse kinematics and decoupling of input-output parameters that especially benefit control of theses structures.

Theory for Topology Synthesis of Parallel Manipulators and Its Application to Three-Dimension-Translation Parallel Manipulators

The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.

Dynamic formulation and performance evaluation of the redundant parallel manipulator

In this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0263574708004657

Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

The kinematics decoupling for parallel manipulators is studied in this paper. Based on the topological structure characteristics of parallel mechanisms, the internal relationship between kinematics decoupling and basic kinematics chains is revealed, and the basic principle for structural synthesis of topologically decoupled mechanisms is put forward. Using this theory, a group of 3 degree-of-freedom (DOF) partially decoupled manipulators are synthesized. The expected kinematic outputs of these manipulators are 1-DOF translation and 2-DOF rotation, and motions along or about undesired directions do not exist. The kinematics analysis of a newly synthesized manipulator is discussed and the results indicate that the decoupling property of these architectures makes possible reaching real time control and path planning of parallel manipulators.

Synthesis and Analysis of a Group of 3-Degree-of-Freedom Partially Decoupled Parallel Manipulators

For enlarging workspace and avoiding singularities, a double parallel manipulator has been designed by combining two parallel mechanisms with a central axis The motion of the device is decoupled and constrained by the central axis This leads to simplicity in geometric constraints but needs a novel strategy for the mechanism analysis Based on the geometric constraints, the paper develops the formulation for inverse/forward kinematics and Jacobian to be implemented in real time position and velocity controls These are used for propeller grinding to measure the surface of a casting blade and to grind the removal depth A dynamic formulation for the parallel mechanism composed of one passive and n-active link trains is derived from motor algebra and a virtual coefficient The formulation can compute the forces and moments acting at the passive joints as well as the active ones Workspace and singularities are also analyzed to prove the advantage of the device

Kinematic and dynamic analysis of a double parallel manipulator for enlarging workspace and avoiding singularities

Industrial robot has played a central role in the production automation such as welding, assembling, and painting. There has been however, little effort to the application of robots in machining works (grinding, cutting, milling, etc.) which are typical 3D works. The machining automation requires a high stiffness robot arm to reduce deformation and vibration. Conventional articulated robots serially connected links from the base to the gripper. So they have very weak structure for the machining work. Stewart platform is a typical parallel robotic mechanism with a very high stiffness but it has a small work space and a large installation space. This research proposes a new machining robot arm with a double parallel mechanism. It is composed of two platforms and a central axis. The central axis will connect the motions between the fist and the second platforms. Therefore, the robot has a large work space as well as a high stiffness. This paper will introduce the machining automation with a robot and design a machining robot arm using the double parallel mechanism.

Min Ki Lee

Papers

Kinematic and dynamic analysis of a double parallel manipulator for enlarging workspace and avoiding singularities

Design of a high stiffness machining robot arm using double parallel mechanisms