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• Planar Cesaro's adjoint approach is expanded to spherical motion to establish the spherical adjoint approach. • Both local and global geometric properties of coupler curves can be studied based on the unified description method. • Spherical fixed point condition is derived to make full use of the kinematic invariants of the centrodes. • The evolution rules of the geometric characteristics of the coupler curves with double points are firstly presented. • The moving centrode acts as a bridge between local and global properties of coupler curves. The local and global geometric properties of spherical coupler curves constitute spherical kinematics of spherical four-bar linkages, which can be adopted to reveal distribution characteristics of spherical coupler curves. New unified spherical adjoint approach is established in the paper to study both the local and global geometric properties in order to enrich the atlas of spherical coupler curves with geometric characteristics. Since the constraint curve of spherical four-bar linkage is a simple spherical circle and the spherical centrodes imply intrinsic properties of spherical motion of the coupler link, they are in their turn taken as the original curves in spherical adjoint approach to derive the geodesic curvature and analyze the local geometric characteristics of the spherical coupler curves. The conditions for different spherical double points, such as spherical crunodes, tacnodes and cusps of the spherical coupler curve are derived through the spherical adjoint approach. The spherical surface of the coupler link can be divided into several areas by the spherical moving centrode and the spherical tacnode's tracer curve. The points in each area trace spherical coupler curves with a specific shape. The characteristic points, which trace spherical coupler curves with cusp, geodesic inflection point, spherical Ball point, spherical Burmester point, crunode and tacnode can be readily located in the coupler link by the modelling procedure and the derived condition equations. In the end the distribution of spherical coupler curves with both local and global characteristics is elaborated. The research proposes systematic geometric properties of spherical coupler curves based on the new established approach, and provides a solid theoretical basis for the kinematic analysis and synthesis of the spherical four-bar linkages. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on some notions of the lightlike rectifying curves and the centrodes in Minkowski 3-space. Some geometrical characteristics of the three types of lightlike curves are obtained. In addition, we obtain the conditions of the centrodes of the lightlike curves are the lightlike rectifying curves. Meanwhile, a detailed analysis between the N-type lightlike slant helices and the centrodes of lightlike curves is provided in this paper. We give the projections of the lightlike rectifying curves to the timelike planes.

First, we study rectifying curves via the dilation of unit speed curves on the unit sphere S² in the Euclidean space E³. Then we obtain a necessary and sufficient condition for which the centrode d(s) of a unit speed curve α(s) in E3 is a rectifying curve to improve a main result of [4]. Finally, we prove that if a unit speed curve α(s) in E3 is neither a planar curve nor a helix, then its dilated centrode β(s) = ρ(s)d(s), with dilation factor ρ, is always a rectifying curve, where ρ is the radius of curvature of &#945. [ABSTRACT FROM AUTHOR]

Although many methods have been proposed in the literature for rigid-body guidance synthesis none of them establishes the position of the instant center (IC) and the centrode as a design requirement. In many cases, practical designs of mechanisms need to accurately establish the position of the IC and the centrode. Due to the lack of methods tackling this problem directly, designers try to approach it indirectly. In other words, they establish the position of the desired rigid-body to obtain the desired position of the IC. However, small errors in the position of the rigid-body may lead to significant errors in the position of the IC and a trial-and-error process is necessary to achieve accuracy. The main difficulty in implementing the centrode in a synthesis approach is how to formulate the IC conditions in an optimization method. This paper presents a synthesis approach based on optimization in which the location of the centrode is included in the objective function. The formulation developed in the paper uses exact differentiation to obtain the descent direction and can be applied to any type of planar mechanism. Multi-objective optimization is also possible, including different design criteria in the target function. Several examples are provided to demonstrate the robustness, accuracy and efficiency of the new approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a finger mechanism that mimics human finger motion with contact aided compliant mechanisms. The motion mimicking is done through well-known linkage synthesis theories, and is converted to a compliant mechanism to reduce the number of actuators and to achieve compactness. To achieve these goals, the design procedures, modeling methods and design criteria of the contact aided compliant mechanism are presented. [Copyright &y& Elsevier]

This paper mainly focuses on some notions of the lightlike rectifying curves and the centrodes in Minkowski 3-space. Some geometrical characteristics of the three types of lightlike curves are obtained. In addition, we obtain the conditions of the centrodes of the lightlike curves are the lightlike rectifying curves. Meanwhile, a detailed analysis between the N-type lightlike slant helices and the centrodes of lightlike curves is provided in this paper. We give the projections of the lightlike rectifying curves to the timelike planes. [ABSTRACT FROM AUTHOR]