Indexed by:期刊论文

Date of Publication:2014-11-01

Journal:CHINESE JOURNAL OF MECHANICAL ENGINEERING

Included Journals:SCIE、EI、Scopus

Volume:27

Issue:6

Page Number:1157-1168

ISSN No.:1000-9345

Key Words:spherical motion; centrode; axode; curvature theory; spherical four-bar linkage

Abstract:Planar kinematics has been studied systematically based on centrodes, however axodes are underutilized to set up the curvature theories in spherical and spatial kinematics. Through a spherical adjoint approach, an axode-based theoretical system of spherical kinematics is established. The spherical motion is re-described by the adjoint approach and vector equation of spherical instant center is concisely derived. The moving and fixed axodes for spherical motion are mapped onto a unit sphere to obtain spherical centrodes, whose kinematic invariants totally reflect the intrinsic property of spherical motion. Based on the spherical centrodes, the curvature theories for a point and a plane of a rigid body in spherical motion are revealed by spherical fixed point and plane conditions. The Euler-Savary analogue for point-path is presented. Tracing points with higher order curvature features are located in the moving body by means of algebraic equations. For plane-envelope, the construction parameters are obtained. The osculating conditions for plane-envelope and circular cylindrical surface or circular conical surface are given. A spherical four-bar linkage is taken as an example to demonstrate the spherical adjoint approach and the curvature theories. The research proposes systematic spherical curvature theories with the axode as logical starting-point, and sets up a bridge from the centrode-based planar kinematics to the axode-based spatial kinematics.