Planar Stewart Gough platforms with a type II DM self-motion

نویسنده

  • Georg Nawratil
چکیده

Due to previous publications of the author, it is already known that one-parametric self-motions of general planar Stewart Gough platforms can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, the author also proved the necessity of three conditions for obtaining a type II DM self-motion. Based on this result we determine in the article at hand, all general planar Stewart Gough platforms with a type II DM self-motion. This is an important step in the solution of the famous Borel Bricard problem. Mathematics Subject Classification (2010). 53A17; 70B15.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Necessary conditions for type II DM self-motions of planar Stewart Gough platforms

Due to a previous publication of the author, it is already known that oneparametric self-motions of Stewart Gough platforms with planar base and planar platform can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, the author also presented a method for computing the set of equations yielding a type II DM self-motion explicitly. Based on these equations we prove...

متن کامل

Types of self-motions of planar Stewart Gough platforms

With this talk, which is based on reference [1], we want to continue the series of contributions about selfmotions of Stewart Gough platforms given by Karger [2, 3] in the previous conferences on geometry – theory and applications, held in Vorau 2007 and Plzen 2009. We show that the self-motions of the general planar Stewart Gough platforms can be characterized in the complex extension of the E...

متن کامل

Basic result on type II DM self-motions of planar Stewart Gough platforms

In a recent publication [10] the author showed that self-motions of general planar Stewart Gough platforms can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, in [10] the author was able to compute the set of equations yielding a type II DM selfmotion explicitly. Based on these equations we present a basic result for this class of self-motions.

متن کامل

Review and recent results on Stewart Gough platforms with self-motions

In Section 1, we give a review on Stewart Gough (SG) platforms with self-motions and the related Borel Bricard problem. Moreover, in Section 2, we report about recent results achieved by the author on this topic (SG platforms with type II DM self-motions). In context of these results, we also present two new theorems in Section 3, which open the way for addressed future work. In Section 4, we g...

متن کامل

Non-existence of planar projective Stewart Gough platforms with elliptic self-motions

In this paper, we close the study on the self-motional behavior of nonarchitecturally singular parallel manipulators of Stewart Gough (SG) type, where the planar platform and the planar base are related by a projectivity κ , by showing that planar projective SG platforms with elliptic self-motions do not exist. The proof of this result demonstrates the power of geometric and computational inter...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012