Graph theory roots of spatial operators for kinematics and dynamics

Abstract

19The passive sizing system consists of a series of low-profile pulleys attached to the front and back of the shoulder bearings on a spacesuit soft upper torso (SUT), textile cord or stainless steel cable, and a modified commercial ratchet mechanism. The cord/cable is routed through the pulleys and attached to the ratchet mechanism mounted on the front of the spacesuit within reach of the suited subject. Upon actuating the ratchet mechanism, the shoulder bearing breadth is changed, providing variable upper torso sizing.The active system consists of a series of pressurizable nastic cells embedded into the fabric layers of a spacesuit SUT. These cells are integrated to the front and back of the SUT and are connected to an air source with a variable regulator. When inflated, the nastic cells provide a change in the overall shoulder bearing breadth of the spacesuit and thus, torso sizing.The research focused on the development of a high-performance sizing and actuation system. This technology has application as a suit-sizing mechanism to Spacesuit Soft Upper Torso Sizing SystemsThis system has application in medical devices for immobilizing injured limbs or applying controlled pressure to areas of the body of a burn victim. Lyndon B. Johnson Space Center, Houston, TexasSpatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators -and the related mathematical analysis -have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems.The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models.Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems.In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematica...

Kinematic synthesis using tree topologies

“…Song and Amato [27] apply the analysis of tree-like articulated systems to folding. Jain [28] uses tree graphs for the dynamic analysis of multi-body systems; tree-systems also appear describing dynamic systems in Garcia de Jalon [29]. Tree articulated systems and their graph representation are also studied in [30] for the analysis and control of mechanical systems, where they are named forking linkages.…”

Dimensional Synthesis of Wristed Binary Hands

“…Kinematic analysis of tree topologies for applications in modular robots and robotic hands can be found in [1], [2], and [3], and dynamic analysis is found in [4] and [5]. Structural synthesis for multiple fingers with no wrist is also considered in [2], and in [6] for grasping and manipulation requirements.…”

ROMANSY 21 - Robot Design, Dynamics and Control

“…Kinematic and dynamic analysis of tree topologies is studied in de Jalon and , Jain (2010) and Tischler et al (1995), and type synthesis of tree topologies can be found in Lee and Tsai (2002) for grasping and manipulation requirements. The dimensional synthesis of the tree topologies has been explored in Simo-Serra et al (2011), Simo-Serra et al (2012 and more extensively in Simo-Serra and Perez-Gracia (2014).…”