A survey of instantaneous poles for a class of two-degree-of-freedom spherical mechanisms

doi:10.1007/s11465-014-0320-z

Front. Mech. Eng.

2014, Vol. 9

Issue (4) : 344-353 https://doi.org/10.1007/s11465-014-0320-z

RESEARCH ARTICLE

A survey of instantaneous poles for a class of two-degree-of-freedom spherical mechanisms

Soheil ZARKANDI(

)

Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

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Abstract

This paper is a detailed exploration of instantaneous poles for a class of two-degree-of-freedom (two-DOF) spherical mechanisms (SMs) with seven links or bars. For two-DOF SMs, the secondary instantaneous poles (the ones which cannot be found by direct inspection) must lie on the specified great circles. For many of these mechanisms, however, some of these great circles cannot be obtained by a direct application of Aronhold-Kennedy theorem. This paper presents geometrical and analytical techniques to locate these unknown great circles for three topologies of seven-bar two-DOF SMs.

Keywords spherical mechanisms instantaneous poles Aronhold-Kennedy theorem great circles pencil of meridian

Corresponding Author(s): Soheil ZARKANDI

Issue Date: 19 December 2014

Cite this article:

Soheil ZARKANDI. A survey of instantaneous poles for a class of two-degree-of-freedom spherical mechanisms[J]. Front. Mech. Eng., 2014, 9(4): 344-353.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0320-z
https://academic.hep.com.cn/fme/EN/Y2014/V9/I4/344

Fig.1 Three topologies of seven-bar SMs. (a) The first seven-bar SM; (b) the second seven-bar SM; (c) the third seven-bar SM

Fig.2 Unit sphere and a pencil of meridians with slope angle ?

Fig.3 Ten instant poles of the seven bar spherical mechanism

Fig.4 The point of concurrency

Fig.5 The GCs of p₂₆ and p₄₆. (a) The GC of p₂₆; (b) the GC of p₄₆

Fig.6 The known instant poles of the second two-DOF spherical mechanism

Fig.7 The locations of p_im and p_jm. (a) Common reference point S; (b) different reference point for p_jm

Fig.8 The third seven-bar Spherical mechanism with no four-bar chain

Fig.9 Finding points on the GC of p₁₄. (a) The first choice of p₃₆; (b) the second choice of p₃₆

Fig.10 The GC of p₁₄

Fig.11 The GC of p₂₅

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[1]	Soheil ZARKANDI. On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms[J]. Front. Mech. Eng., 2014, 9(1): 34-40.

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