کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
804665 1467752 2014 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nonholonomic dynamical reduction of open-chain multi-body systems: A geometric approach
ترجمه فارسی عنوان
کاهش دینامیکی غیرخالص سیستمهای چند زنجیره باز: یک رویکرد هندسی
کلمات کلیدی
سیستم چند منظوره بدون زنجیر باز، کاهش چپلیگین، تقریبا تقریبا سمپلکتیک، سیستم مکانیکی همیلتونین غیرخولومونی
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی صنعتی و تولید
چکیده انگلیسی


• Two-step dynamical reduction of Hamiltonian mechanical systems.
• Application to nonholonomic open-chain multi-body systems with multi-d.o.f. joints.
• A case study of a four-wheel mobile manipulator.

This paper studies the geometry behind nonholonomic Hamilton's equation to present a two-stage reduction procedure for the dynamical equations of nonholonomic open-chain multi-body systems with multi-degree-of-freedom joints. In this process, we use the Chaplygin reduction and an almost symplectic reduction theorem. We first restate the Chaplygin reduction theorem on cotangent bundle for nonholonomic Hamiltonian mechanical systems with symmetry. Then, under some conditions we extend this theorem to include a second reduction stage using an extended version of the symplectic reduction theorem for almost symplectic manifolds. We briefly introduce the displacement subgroups and accordingly open-chain multi-body systems consisting of such joints. For a holonomic open-chain multi-body system, the relative configuration manifold corresponding to the first joint is a symmetry group. Hence, we focus on a class of nonholonomic distributions on the configuration manifold of an open-chain multi-body system that is invariant under the action of this group. As the first stage of reduction procedure, we perform the Chaplygin reduction for such systems. We then introduce a number of sufficient conditions for a reduced system to admit more symmetry due to the action of the relative configuration manifolds of other joints. Under these conditions, we present the second stage of the reduction process for nonholonomic open-chain multi-body systems with multi-degree-of-freedom joints. Finally, we explicitly derive the reduced dynamical equations in the local coordinates for an example of a two degree-of-freedom crane mounted on a four-wheel car to illustrate the results of this paper.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mechanism and Machine Theory - Volume 82, December 2014, Pages 231–255
نویسندگان
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