Parallel Mechanism

Constrained multibody systems typically feature multiple closed kinematic loops that constrain the relative motions and forces within the system. Typically, such systems possess far more articulated degrees-of-freedom (within the chains) than overall end-effector degrees-of-freedom.Thus, actuation of a subset of the articulations creates mixture of active and passive joints within the chain.The presence of such passive joints interferes with the effective modular formulation of the dynamic equations-of-motion in terms of a minimal set of actuator coordinates as well the subsequent recursivesolution for both forward and inverse dynamics applications. Thus, in this paper, we examine the development of modular and recursive formulations of equations-of-motion in terms of a minimal set of actuated-joint-coordinates for an exactly-actuated parallel manipulators. The 3 RRR planar parallel manipulator, selected to serve as a case-study, is an illustrative example of a multi-loop, multi-degree-of-freedom system with mixtures of active/passive joints. The concept of decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism inherent in parallel mechanisms to develop a dynamics formulation that is both recursive and modular. An algorithmic approach to the development of both forward and inverse dynamics is highlighted. The presented simulation studies highlight the overall good numerical behavior of the developed formulation, both in terms of accuracy and lack of formulation stiffness.

The avian wing possesses the ability to synchronize flexion or extension of the elbow and wrist joints automatically. Skeletal and muscular mechanisms are involved in generating this phenomenon. The “drawing-parallels” action of the radius and ulna coordinates the movements of the forearm with the carpus. Movement of the radius along the length of the forearm isnot dependent on the shape disparity between the dorsal and ventral condyles of the humerus, nor is it generated by the shape of the dorsal condyle itself. Instead, shifting of the radius toward the wrist occurs during humeroulnar flexion when the radius, being pushed by muscles toward the ulna, is deflected off theIncisura radialis toward the wrist. Movement of the radius toward the elbow occurs during the latter stages of humeroulnar extension when, as the dorsal condyle of the humerus and the articular surface of the ulna's dorsal cup roll apart, the radius gets pulled by the humerus and its ligaments away from the wrist. Synchronization of the forearm with the manus is accomplished by twojoint muscles and tendons.M. extensor metacarpi radialis and the propatagial tendons act to extend the manus in unison with the forearm, whileM. extensor metacarpi ulnaris helps these limb segments flex simultaneously.M. flexor carpi ulnaris, in collaboration with the “drawing-parallels” mechanisms, flexes the carpus automatically when the elbow is flexed, thereby circumducting the manus from the plane of the wing toward the body. In a living bird, these skeletal and muscular coordinating mechanisms may function to automate the internal kinematics of the wing during flapping flight. A mechanized wing may also greatly facilitate the initial flight of fledgling birds. The coordinating mechanisms of the wing can be detected in a bird's osteology, thereby providing researchers with a new avenue by which to gauge the flight capabilities of avian fossil taxa.

Recursive matrix relations for kinematics and dynamics analysis of a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) are performed in this paper. Knowing the translational motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot’s elements. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work and the results in the framework of the Lagrange equations with their multipliers can be verified. Finally, compact matrix equations and graphs of simulation for input force and power of each of three actuators are obtained. The investigation of the dynamics of this parallel mechanism is made mainly to solve successfully the control of the motion of such robotic system.

The paper describes the architecture of a novel parallel kinematics machine that is characterized by motions of pure translation. It is shown that the Cartesian arrangement of the 3 limbs assures simple kinematic relations and an isotropic workspace, without any rotation or translation singularity. Such good features should allow the design of parallel robots that are characterized by simple controllers

This paper deals with the problem of optimal geometry design of parallel manipulators. In order to reduce the main drawbacks of parallel manipulators, relatively small workspace and more singularities, two requirements, workspace and condition number, are considered. The design problem is thus formulated to find a parallel mechanism such that its Cartesian workspace contains a prescribed workspaces with good condition numbers in it. By observing that those requirements can be locally cast into Linear Matrix Inequalities (LMIs), we formulate the design problem locally as a convex optimization problem subject to LMIs with a max-det function as its objective function. Hence, at each node of discretized space of design parameters, there is an LMI-based convex optimization problem. A two-level algorithm can be applied to solve for a set of optimal design parameters: (1) Discretize the space of design parameters into a set of discrete nodes; (2) At each node the Newton algorithm is applied to solve the max-det optimization problem. By comparing all the locally optimal costs, we can obtain a corresponding set of globally optimal design parameters correspondingly. Simulation results verify the effectiveness of the proposed approach.

Abstract Parallel kinematic machines (PKM) are still a research-and-development topic in many laboratories although many of them, unfortunately, have no PKM at all. Therefore, the use of a desktop educational 3-axis parallel kinematic milling machine is suggested as a ...

The wrench-closure workspace of parallel cable-driven mechanisms is the set of poses of their mobile platform for which the cables can balance any external wrench. The determination of this workspace is an important issue since the cables can only pull and not push on the mobile platform. This paper deals with the wrench-closure workspace of six-degrees-of-freedom (DOF) parallel mechanisms driven by m cables, m≥ 7.

A hexapod robotic test system has been developed to enable complex six degree of freedom (6-DOF) testing of bones, joints, soft tissues, artificial joints and other medical and surgical devices. The device employs six permanent-magnet servomotor driven ballscrews to actuate the system, and measures the displacement response using incremental encoders and loads using a six axis load-cell. The mechanism incorporates a unique design which mitigates many of the issues arising from load-cell compliance, common to most other serial and parallel mechanisms for material testing. This was achieved through a non-collocated design which raises additional challenges. Achieving high bandwidth control of the hexapod also presents challenges, and was achieved using a combination of LabVIEW real-time running on a floating-point Intel processor, along with LabVIEW FPGA running on 16bit Xilinx FPGAs. In this paper the following unique aspects of this hexapod are discussed: the mitigation of load-cell compliance, non-collocated control, implementation of the controller on a real-time platform, and finally technical solutions to solve the complex forward-kinematics solution in real-time. Finally, the results from testing a high-density polymer cylindrical specimen are presented.