On the terminology and geometric aspects of redundant parallel manipulators

Robotica ◽  
2012 ◽  
Vol 31 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Andreas Müller

SUMMARYParallel 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.

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 379-388 ◽  
Author(s):  
Roger Boudreau ◽  
Xu Mao ◽  
Ron Podhorodeski

SUMMARYIn 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.


Author(s):  
Andreas Mu¨ller

Different types of redundancy in parallel kinematics machines (PKM) can be used to improve their kinematic and dynamic properties. The meaning of redundancy of PKM is often differently understood in the literature. In this paper a terminology for redundant PKM is proposed. The basis for this classification is a general mathematical model. With the help of this model PKM are regarded as non-linear control systems. The different types of redundancy are clearly distinguished, and their potential applications are discussed. Redundancy is considered from a geometric point of view. Redundancy is a means to deal with singularities of PKM. The different types of singular configurations are considered in the paper, and the potential of redundancy to cope with such situations is discussed. Again singularities are considered from a geometric point of view.


2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Long Kang ◽  
Wheekuk Kim ◽  
Byung-Ju Yi

Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.


10.14311/710 ◽  
2005 ◽  
Vol 45 (3) ◽  
Author(s):  
M. Valášek ◽  
V. Bauma ◽  
Z. Šika

This paper deals with possible new concepts for machine tools based on parallel kinematics for advanced manufacturing. Parallel kinematics machines (PKM) enable the mechanical properties of manufacturing machines to be improved. This has been proven by several new machine tool concepts. However, this potential can be and must be increased by applying the principle of redundant actuation. This paper deals with the extension of the concepts of redundantly actuated parallel kinematics structures for five-sided five-axis machine tools and for a free-forming sheet metal forming machine. The design principles of previous successful PKMs are summarized and new concepts are proposed. The most important requirement criteria are summarized. The proposed concepts are qualitatively and initially quantitatively evaluated according to these criteria. 


2021 ◽  
Author(s):  
Amin Moosavian

The ability to vary the geometry of a wing to adapt to different flight conditions can significantly improve the performance of an aircraft. However, the realization of any morphing concept will typically be accompanied by major challenges. Specifically, the geometrical constraints that are imposed by the shape of the wing and the magnitude of the air and inertia loads make the usage of conventional mechanisms inefficient for morphing applications. Such restrictions have served as inspirations for the design of a modular morphing concept, referred to as the Variable Geometry Wing-box (VGW). The design for the VGW is based on a novel class of reconfigurable robots referred to as Parallel Robots with Enhanced Stiffness (PRES) which are presented in this dissertation. The underlying feature of these robots is the efficient exploitation of redundancies in parallel manipulators. There have been three categories identified in the literature to classify redundancies in parallel manipulators: 1) actuation redundancy, 2) kinematic redundancy, and 3) sensor redundancy. A fourth category is introduced here, referred to as 4) static redundancy. The latter entails several advantages traditionally associated only with actuation redundancy, most significant of which is enhanced stiffness and static characteristics, without any form of actuation redundancy. Additionally, the PRES uses the available redundancies to 1) control more Degrees of Freedom (DOFs) than there are actuators in the system, that is, under-actuate, and 2) provide multiple degrees of fault tolerance. Although the majority of the presented work has been tailored to accommodate the VGW, it can be applied to any comparable system, where enhanced stiffness or static characteristics may be desired without actuation redundancy. In addition to the kinematic and the kinetostatic analyses of the PRES, which are developed and presented in this dissertation along with several case-studies, an optimal motion control algorithm for minimum energy actuation is proposed. Furthermore, the optimal configuration design for the VGW is studied. The optimal configuration design problem is posed in two parts: 1) the optimal limb configuration, and 2) the optimal topological configuration. The former seeks the optimal design of the kinematic joints and links, while the latter seeks the minimal compliance solution to their placement within the design space. In addition to the static and kinematic criteria required for reconfigurability, practical design considerations such as fail-safe requirements and design for minimal aeroelastic impact have been included as constraints in the optimization process. The effectiveness of the proposed design, analysis, and optimization is demonstrated through simulation and a multi-module reconfigurable prototype.


2021 ◽  
pp. 019-029
Author(s):  
Lahoud Marcel ◽  
Melendez Leonardo ◽  
Gil Arturo

The additive manufacture is a fabrication process that has taken huge steps in the last decade, even though the first researches and prototypes are around since almost forty years ago. In this article, a design method for a Parallel Kinematics Robot for Additive Manufacturing Applications is proposed. A numerical model is obtained from the kinematics of the robot for which the design, construction and assembly are planned using recycled materials and equipment. The control of the robot is done using open source software, allowing the planning of trajectories in the Cartesian space on a maximum designed cylindrical workspace of 300mm in diameter by 300mm high. At the end of the work the robot was identified, the kinematic model was validated and considerations for future works were given.


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