A Unified Theory for the Finitely and Infinitesimally Separated Position Problems of Kinematic Synthesis

Chen, P.; Roth, Bernard

doi:10.1115/1.3591522

Cited by 22 publications

(4 citation statements)

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“…The problem was studied for spatial dyads and their combined linkages by Chen and Roth [5,6] to unify the formulation for finite and infinitesimal positions, and later by Tsai and Roth [7], who used the spatial triangle. In all cases, it is applied to define one rigid-body velocity per position at a set of desired positions of the end-effector.…”

Section: Introductionmentioning

confidence: 99%

Mixed Position and Twist Space Synthesis of 3R Chains

Hassanzadeh

Pérez-Gracia

2022

Robotics

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Mixed-position kinematic synthesis is used to not only reach a certain number of precision positions, but also impose certain instantaneous motion conditions at those positions. In the traditional approach, one end-effector twist is defined at each precision position in order to achieve better guidance of the end-effector along a desired trajectory. For one-degree-of-freedom linkages, that suffices to fully specify the trajectory locally. However, for systems with a higher number of degrees of freedom, such as robotic systems, it is possible to specify a complete higher-dimensional subspace of potential twists at particular positions. In this work, we focus on the 3R serial chain. We study the three-dimensional subspaces of twists that can be defined and set the mixed-position equations to synthesize the chain. The number and type of twist systems that a chain can generate depend on the topology of the chain; we find that the spatial 3R chain can generate seven different fully defined twist systems. Finally, examples of synthesis with several fully defined and partially defined twist spaces are presented. We show that it is possible to synthesize 3R chains for feasible subspaces of different types. This allows a complete definition of potential motions at particular positions, which could be used for the design of precise interaction with contact surfaces.

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Section: Introductionmentioning

confidence: 99%

Mixed Position and Twist Space Synthesis of 3R Chains

Hassanzadeh

Pérez-Gracia

2022

Robotics

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“…Kinematic synthesis of planar linkages are classically studied under three main categories: motion generation, function generation, and point-path generation and path generation with prescribed timing [1][2]. There are some studies on kinematic synthesis of spatial line-path generator linkages [3][4][5][6][7][8]. Homologous lines passing through a point or tangent to a circle in plane are issued in [5].…”

Section: Introductionmentioning

confidence: 99%

Kinematic Synthesis of Planar 4-Bar Path Generators for Finite Line Positions

Kiper

Söylemez

2019

Advances in Mechanism and Machine Science

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Although the kinematic synthesis of planar function, point-path and motion generators are vastly studied in the literature, surprisingly synthesis of line-path generators is not formulized in detail. This study presents the formulization of the planar 4-bar line-path generator synthesis problem for up to 5 homologous positions. Numerical examples for 3 and 4 line positions are presented for the illustration of the formulations.

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“…Today we are able to witness the implementation of Roth's spatial synthesis theory via virtual reality. The geometric entities called fixed and moving congruences that play a central role in the theory can be displayed spatially, along with appropriate alphanumeric labels as in Figure 1.At the same time, Roth and his student Pictiaw Chen were working to unify the theory of synthesis with finitely separated positions with what was known as curvature theory, which could be viewed as collapsing multiple design positions into a single position along with velocity and acceleration specifications in that position[9,10]. They extended synthesis with mixed motion specifications into the spatial domain.…”

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confidence: 99%

Bernard Roth: The early days of the design division at Stanford, and the beginnings of research in robotics

Waldron

2018

Mechanism and Machine Theory

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This paper comprises a review of Bernard Roth's technical contributions and contributions to his professional community. Particular attention is paid to his role in the establishment of the unique design program of the Department of Mechanical Engineering at Stanford University. Another theme is the creation of one of the very first research programs in digitally controlled robotics in the Stanford Artificial Intelligence Laboratory. No review of Roth's career would be complete without touching on the numerous fundamental contributions to research in linkages and robotics. At the same time it is not possible in a work on this type to examine every one of his publications and other contributions. We have endeavored to select the most important, but that is, of course, a personal judgment.

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A Unified Theory for the Finitely and Infinitesimally Separated Position Problems of Kinematic Synthesis

Cited by 22 publications

References 0 publications

Mixed Position and Twist Space Synthesis of 3R Chains

Mixed Position and Twist Space Synthesis of 3R Chains

Kinematic Synthesis of Planar 4-Bar Path Generators for Finite Line Positions

Bernard Roth: The early days of the design division at Stanford, and the beginnings of research in robotics

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