Limits at $3 in a New Formulation for Path-Placement in the Workcells of Planar 3-R Robots

1995 ◽  
Vol 117 (3) ◽  
pp. 485-490 ◽  
Author(s):  
J. K. Davidson ◽  
N. A. Soman
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Solution Space ◽  
Graphical Form ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Tool Paths ◽  
Planar Robot ◽  
New Formulation ◽  
Systematic Formulation

Excursion-limits at the third joint of a three-hinged planar robot are incorporated into a new systematic formulation for path-placement in which the three-dimensional solution-space is decomposed into a two-dimensional space of variables that strongly control the placement of the path and a one-dimensional space that is much less critical. The new formulation determines all acceptable positions for the first joint of the robot relative to the workpiece. All possible acceptable designs appear in a graphical form that can be readily visualized and be directly measured in a Cartesian frame of reference in the workcell. The method is extended to closed tool-paths, and the method is illustrated with practical examples.

A Two-Dimensional Formulation for Path-Placement in the Workcells of Planar 3-R Robots

1995 ◽  
Vol 117 (3) ◽  
pp. 479-484 ◽  
Author(s):  
N. A. Soman ◽  
J. K. Davidson
Keyword(s):  
Three Dimensional ◽  
Solution Space ◽  
Joint Space ◽  
Two Dimensions ◽  
Fusion Welding ◽  
Graphical Form ◽  
Tool Paths ◽  
All Solutions ◽  
Planar Robot ◽  
Systematic Formulation

A new systematic formulation is presented that determines suitable locations for a workpiece, and its associated task-motion, in the workspace of a three-hinged planar (SCARA) robotic workcell. It determines all acceptable positions for the first joint of the robot relative to the workpiece; therefore, all solutions are represented as an area in two dimensions, unlike existing methods of motion-planning that present them as a volume in a three-dimensional joint-space for the same planar robot. This simplifies the solution-space by reducing its dimension from three to two. All possible acceptable designs appear in a graphical form that can be readily visualized and directly measured in a Cartesian frame of reference in the workcell. Applications include locating workpieces with tool-paths for fusion welding and for deposition of adhesives.

Working Capability Analysis of Stewart Platforms

1996 ◽  
Vol 118 (2) ◽  
pp. 220-227 ◽  
Author(s):  
Chi-Mei Luh ◽  
F. A. Adkins ◽  
E. J. Haug ◽  
C. C. Qiu
Keyword(s):  
Numerical Methods ◽  
Motion Control ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Unilateral Constraints ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Capability Analysis ◽  
Working Capability ◽  
Stewart Platforms

Working capability analysis of planar and spatial Stewart platforms with unilateral constraints on actuator length is carried out using numerical methods based on analytical criteria for the boundary of the accessible output set. Restrictions on achievable motion at singular configurations associated with points interior to the accessible output set are also analyzed. Since movement of the working point on a spatial Stewart platform occurs in three-dimensional space, the boundary of the accessible output set is a two-dimensional surface. Numerical methods used in this analysis map one-dimensional solution sets, permitting the boundary of the accessible output set to be characterized by a family of one dimensional generators. Motion control restrictions inside the accessible output set are similarly characterized by families of interior singular curves, and barriers to motion control across surfaces defined are analyzed.

scholarly journals Efficient trajectory optimization for curved running using a 3D musculoskeletal model with implicit dynamics

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Marlies Nitschke ◽  
Eva Dorschky ◽  
Dieter Heinrich ◽  
Heiko Schlarb ◽  
Bjoern M. Eskofier ◽  
...  
Keyword(s):  
Trajectory Optimization ◽  
Environmental Changes ◽  
Optimization Problems ◽  
Dimensional Space ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Solution Space ◽  
Musculoskeletal Model ◽  
Efficient Computation ◽  
Dimensional Solution

Abstract Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes. It enables an exhaustive analysis of joint angles, joint moments, ground reaction forces, and muscle forces, among others. However, its application is still limited to simplified problems in two dimensional space or straight motions. The simulation of movements with directional changes, e.g. curved running, requires detailed three dimensional models which lead to a high-dimensional solution space. We extended a full-body three dimensional musculoskeletal model to be specialized for running with directional changes. Model dynamics were implemented implicitly and trajectory optimization problems were solved with direct collocation to enable efficient computation. Standing, straight running, and curved running were simulated starting from a random initial guess to confirm the capabilities of our model and approach: efficacy, tracking and predictive power. Altogether the simulations required 1 h 17 min and corresponded well to the reference data. The prediction of curved running using straight running as tracking data revealed the necessity of avoiding interpenetration of body segments. In summary, the proposed formulation is able to efficiently predict a new motion task while preserving dynamic consistency. Hence, labor-intensive and thus costly experimental studies could be replaced by simulations for movement analysis and virtual product design.

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

scholarly journals Synthetic Weyl Points of the Shear Horizontal Guided Waves in One-Dimensional Phononic Crystal Plates

2021 ◽  
Vol 12 (1) ◽  
pp. 167
Author(s):  
Hongbo Zhang ◽  
Shaobo Zhang ◽  
Jiang Liu ◽  
Bilong Liu
Keyword(s):  
Guided Waves ◽  
Dimensional Space ◽  
Phononic Crystal ◽  
Phase Interface ◽  
Three Dimensional ◽  
Interface States ◽  
Geometrical Parameters ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Shear Horizontal

Weyl physics in acoustic and elastic systems has drawn extensive attention. In this paper, Weyl points of shear horizontal guided waves are realized by one-dimensional phononic crystal plates, in which one physical dimension plus two geometrical parameters constitute a synthetic three-dimensional space. Based on the finite element method, we have not only observed the synthetic Weyl points but also explored the Weyl interface states and the reflection phase vortices, which have further proved the topological phase interface states. As the first realization of three-dimensional topological phases through one-dimensional phononic crystal plates in the synthetic dimension, this research demonstrates the great potential of applicable one-dimensional plate structural systems in detecting higher-dimensional topological phenomena.

Optimal Contact Force Distribution for Multi-Limbed Robots

2005 ◽  
Vol 128 (3) ◽  
pp. 566-573 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
New Strategy ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The incremental strategy of opening up the friction cones is aided by using the “force space graph” which indicates where the solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Cubic Hybrid Mechanism Based on S[T] Output Base and P/R Input Base

2012 ◽  
Vol 430-432 ◽  
pp. 1725-1728
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Parallel Mechanism ◽  
Dimensional Space ◽  
Three Dimensional ◽  
One Dimensional ◽  
Hybrid Mechanism ◽  
Hybrid Manipulator ◽  
New Type ◽  
The Stability ◽  
Serial Mechanism ◽  
Three Dimensional Space

Based on the flexibility of single couple of serial mechanism and the stability of multi couples of parallel mechanism, a new type of S[T] output base of hybrid mechanism presented, component of sphere joint run through the tiger joint, this component still the output one with the capability of rotate in three dimensional space. Add serial branch including three translation couple P or/and rotation couple R to the new type of S[T] output base, put these members on one cubic frame, twenty seven configurations obtained with 3-DOF(degree of freedom) allow of three dimensional rotation, twenty seven configurations belong to three conditions obtained with 4-DOF allow of three dimensional rotation and one dimensional translation, nine configurations belong to three conditions obtained with 5-DOF allow of three dimensional rotation and two dimensional translation, one configuration obtained with 6-DOF allow of three dimensional rotation and three dimensional translation, all those sixty four configurations have no more than six translation couple or rotation couple, and the sum of two kind of couple is equal to six. Developing new type of hybrid manipulator based on the hybrid cubic mechanism constructed with S[T] output base and P/R input base will be possible in theory and useful.

EFFECTIVE DIPOLE-RADIATION-FIELD THEORY I: ONE-DIMENSIONAL OSCILLATOR BEYOND STANDARD COUPLING

1994 ◽  
Vol 08 (17) ◽  
pp. 2307-2325 ◽  
Author(s):  
H. DEKKER
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Dipole Interaction ◽  
Quantum Mechanical ◽  
Renormalization Procedure ◽  
One Dimensional ◽  
Dipole Radiation ◽  
Consistent Treatment ◽  
Interaction Problem ◽  
Three Dimensional Space

A novel generalization is given of the standard dipole interaction between a charged particle and the electromagnetic field in the radiation gauge. The resulting nonlinear interaction problem is statistically linearized. The ensuing dynamics is solved exactly for a harmonically bound nonrelativistic electron in a finite region of three-dimensional space. The solution involves a generalized renormalization procedure and is free of runaway modes. The theory is particularly suited for a self-consistent treatment of the system's quantum mechanics. As a consequence of the generalized coupling an earlier noted ultraviolet quantum mechanical divergence is absent.

Design of Planar 3-R Robotic Workcells in Two-Space With Rotation at the Third Joint Limited to Exactly One Turn

1993 ◽  
Author(s):  
N. A. Soman ◽  
Joseph K. Davidson
Keyword(s):  
Three Dimensional ◽  
Solution Space ◽  
Joint Space ◽  
Two Dimensions ◽  
Fusion Welding ◽  
Graphical Form ◽  
Motion Trajectories ◽  
The Third ◽  
Full Turn ◽  
All Solutions

Abstract An interactive graphics-based computer scheme was developed that determines suitable locations for a workpiece, and its associated task-motion, in the dexterous workspace of a three-hinged planar robotic workcell. It determines all acceptable positions for the first joint of the robot relative to the workpiece; therefore, all solutions are represented as an area in two dimensions, unlike existing methods of motion-planning that present them as a volume in a three-dimensional joint-space for the same planar robot. This simplifies the solution-space by reducing its dimension from three to two. The method differentiates between the constraints that singular configurations, workspace boundaries, the excursion-range of one full turn at the third rotary joint, and physical obstacles impose on the design of a planar robotic workcell, thus giving a better understanding of the global properties and physical limitations of the workcell. All possible acceptable designs appear in a graphical form that can be readily visualized and be directly measured in a Cartesian frame of reference in the workcell. The method can be applied to either open or closed motion trajectories. Applications include the design of robotic workcells that are used for fusion welding and for deposition of adhesives, where, in each case, the attitude of the end-effector is as important to the task as is the path that a point on the tool follows.

Sign in / Sign up

Export Citation Format

Share Document