Spherical and Spatial Linkages

2021 ◽  
pp. 375-441
Author(s):  
Asok Kumar Mallik ◽  
Amitabha Ghosh ◽  
Günter Dittrich
Keyword(s):  
1980 ◽  
Vol 15 (1) ◽  
pp. 47-60 ◽  
Author(s):  
M.S Konstantinov ◽  
M.D Markov
Keyword(s):  

Author(s):  
L. T. Wang

Abstract A new method of formulating the generalized equations of motion for simple-closed (single loop) spatial linkages is presented in this paper. This method is based on the generalized principle of D’Alembert and the use of the transformation Jacobian matrices. The number of the differential equations of motion is minimized by performing the method of generalized coordinate partitioning in the joint space. Based on this formulation, a computational algorithm for computer simulation the dynamic motions of the linkage is developed, this algorithm is not only numerically stable but also fully exploits the efficient recursive computational schemes developed earlier for open kinematic chains. Two numerical examples are presented to demonstrate the stability and efficiency of the algorithm.


Author(s):  
Xian-Wen Kong ◽  
Ting-Li Yang

Abstract This paper presents systematically a new method for the displacement analysis (DA) of multi-loop spatial linkages (MLSLs) based on ordered simple-opened-chains (SOCs). In performing DA, a MLSL is converted into not a set of base points, a set of isolated links or a tree with/without isolated links in common use, but a weakly coupled MLSL in this paper. The characteristics of the proposed method are: (a) The number of unknowns in the set of equations for displacement analysis (EDA) of a MLSL is reduced to the minimum; (b) All the possible configurations corresponding to a given set of inputs of a weakly coupled MLSL or a strongly coupled MLSL with the coupled degree k = 1 can be obtained quickly. As compared with the other two methods available to find all the solutions to the DA in the case of MLSL with k = 1, the proposed method is superior to the resultant method in that it is applicable to more complex MLSLs and superior to the continuation method in that it takes much less CPU time to find all the solutions; (c) The set of EDA can be formulated and solved automatically; and (d) The new approach makes it possible to perform the kinematic and kineto-static analyses in a unified and simplified way.


Author(s):  
Maria Koinova

Chapter 2 is the first theoretical chapter developing the contours of the theory of socio-spatial positionality and how it applies to the four types of diaspora entrepreneurs—Broker, Local, Distant, and Reserved. They operate in transnational social fields, simultaneously embedded in different global contexts. The chapter builds on diaspora-, host-land-, and home-land-centric theories and further integrates three streams of thought that have not been in conversation with one another. First, it reimagines transnational social fields from a socio-spatial positionality perspective, considering earlier work in International Political Sociology. Secondly, it draws on scholarship on fragile and weak states in IR, especially on de facto states, and discusses their place in the international system and the rationales through which they engage diasporas abroad. Third, the chapter consults relational theories in IR, demonstrating that durable interactions among actors in international politics form structures spanning borders. These theories are useful to think about configurations of socio-spatial linkages of the four types of diaspora entrepreneurs, at the core of the typology. The chapter then lays out the socio-spatial positionality approach and its major features—relativity, power, fluidity, and perception—while delving deeper into the individual level of analysis. The four types of diaspora entrepreneurs have different socio-spatial positionalities at the intersection of various global contexts that empower them differently to pursue homeland-oriented goals. The chapter ends with a discussion about structure and agency in diaspora mobilizations.


1992 ◽  
Vol 114 (1) ◽  
pp. 92-100 ◽  
Author(s):  
S. J. Kirstukas ◽  
J. L. Lewis ◽  
A. G. Erdman

Six-revolute-joint instrumented spatial linkages (6R ISLs) have become often-used devices to measure the complete six-degree-of-freedom motion of anatomical joints. Accuracy of motion measurement depends on ISL design and calibration technique. In this paper, a design process is outlined that uses computer graphics and numerical methods as aids in developing 6R ISLs that (i) physically assemble within the desired range of motion of the joint; (ii) do not collide with either the experimental apparatus or the subject joint; (iii) avoid singular linkage configurations that can cause forces to be applied to the joint; and (iv) measure selected anatomical motions most accurately. It is found that a certain subgroup of 6R linkages are suitable for accurate measurement of specific motions, and can be the basis for new ISL designs. General guidelines are developed that can assist in the generation of unique linkage designs for different anatomical joints. The design process is demonstrated in the creation of an ISL to measure knee motion.


1965 ◽  
Vol 32 (4) ◽  
pp. 903-910 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg ◽  
R. Razi ◽  
J. J. Uicker

The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.


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