This paper examines the symbolic kinematic modeling of a general 6-P-U-S (prismatic-universal-spherical) parallel kinematic manipulator (PKM). The base location of actuators has been previously shown to lead to: (i) reduction of the (motor) weight carried by the legs; (ii) elimination of the actuation transmission requirement (through intermediary joints as in the case of the Stewart-Gough platform); and (iii) most-importantly absorption of reaction-forces by the ground. We focus on using the symbolic equations to derive the conditions for type I and II singularities of this class of parallel manipulators. Based on these conditions, this system of equations is specialized to a specific configuration of the platform that has superior structural design and comparatively minimal singularities within its workspace. A series of studies were conducted to investigate the quality of workspace as well as estimate the actuation requirements for a unit payload carried over their workspace using the symbolic Jacobian model for this specialized configuration.
The challenges of workspace determination of parallel manipulators (PMs) arise principally from the lack of analytical solutions of the forward kinematics. The inverseposition kinematics based approach for determining workspace tends to be inefficient, time consuming and unsophisticated. In this paper, we present a geometry-based method for accurate and computationally effective calculation of the workspace of a constrained parallel manipulator. We illustrate how boolean geometric operations can simplify the process of finding the workspace and optimizing the designs. Comparative performance studies, in terms of accuracy and computational performance, are performed to benchmark the approach against more conventional methods. Finally, we examine ways to further automate the process using a CAD package.
In recent years there has been a significant increase in the variety and complexity of Articulated-Multi-Body-Systems (AMBS) used in various applications. There is also increased interest in the model-based design-refinement and controller-development, which is critically dependent upon availability of underlying plant-models. Kinematic and dynamic plant-models for AMBSs can be formulated by systematic application of physics postulates. This process, in its various variants, forms the basis of various mechanisms/robotics courses. However, the type and complexity of the example systems is often limited by the tractability of first generating and subsequently analyzing complex equations-of-motion. Nevertheless, using simpler examples alone may sometimes fail to capture important physical phenomena (e.g. gyroscopic, coriolis). Hence, we examine the use of some contemporary symbolic- and numeric-computation tools to assist with the automated symbolic equation generation and subsequent analysis. We examine a host of examples beginning with simple pendulum, double pendulum; building up to intermediate examples like the four-bar mechanism and finally examine the implementation of 3-PRR and 3-RRR planar parallel platform mechanisms. The principal underlying philosophy of our effort is to establish linkage between traditional modeling approaches and use of these contemporary tools. We also try to make a case for use of automatic symbolic computation and manipulation as a means for enhancing understanding of both basic and advanced AMBS concepts. Lastly, we document our efforts towards creation of self-paced tutorials and case-studies that serve to showcase the benefits.
A critical precursor to deployment of model-based controllers for articulated-mechanical-systems is availability of a systematic means for generating plant-model-equations. However, the complexity and tractability of generating and analyzing models serves to limit the size of the chosen examples. Hence, we examine the use of contemporary symbolic-computation tools to assist with the automated symbolic equation generation and subsequent analysis to support control systems course work. In particular, we seek to establish linkage between traditional-approach and block-diagram-based symbolic-modeling and controller-development. The Furuta Pendulum example allows us to showcase the emergence of model-complexity, even in relatively-simple two-jointed mechanical system, while studying various aspects of model-creation, model-linearization and model-based controller development in a timely manner.
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