Redundancy in Parallel Robots: A Case Study of Kinematics of a Redundantly Actuated Parallel Chewing Robot

2019 ◽  
pp. 65-78
Author(s):  
Naser Mostashiri ◽  
Jaspreet Dhupia ◽  
Weiliang Xu
Keyword(s):  
Parallel Robots ◽  
Redundantly Actuated

Optimizing the Torque Distribution of a Redundantly Actuated Parallel Robot to Study the Temporomandibular Reaction Forces During Food Chewing

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Naser Mostashiri ◽  
Jaspreet Dhupia ◽  
Alexander Verl ◽  
John Bronlund ◽  
Weiliang Xu
Keyword(s):  
Inverse Dynamics ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Cost Functions ◽  
Measurement Tool ◽  
Redundancy Resolution ◽  
Theoretical Formulation ◽  
Temporomandibular Joints ◽  
Redundantly Actuated

Abstract Inverse dynamics solution of redundantly actuated parallel robots (RAPRs) requires redundancy resolution methods. In this paper, the Lagrange’s equations of the second kind are used to derive governing equations of a chewing RAPR. Jacobian analysis of the RAPR is presented. As redundancy resolutions, two different optimization cost functions corresponding to specific neuromuscular objectives, which are minimization of effort of the muscles of mastication and temporomandibular joints (TMJs) loads, are used to find the RAPR’s optimized actuation torque distributions. The actuation torques under the influence of experimentally determined dynamic chewing forces on molar teeth reproduced from a separate chewing experiment are calculated for realistic in vitro simulation of typical human chewing. These actuation torques are applied to the RAPR with a distributed-computed-torque proportional-derivative control scheme, allowing the RAPR’s mandible to follow a human subject’s chewing trajectory. TMJs loads are measured by force sensors, which are comparable with the computed loads from theoretical formulation. The TMJs loads for the two optimization cost functions are measured while the RAPR is chewing 3 g of peanuts on its left molars. Maximum and mean of the recorded loads on the left TMJ were higher in both cases. Moreover, the maximum and mean of the recorded loads on both TMJs were smaller for the cost function minimizing the TMJs loads. These results demonstrate validity of the model, suggesting the RAPR as a potential TMJ loads measurement tool to study the chewing characteristics of patients suffering from pain in TMJs.

Mathematical Tools for Building Setup-Maps to Optimally Locate Each Casting in a Machining Fixture: Case Study With Minimum Wall Thickness

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
N. J. Kalish ◽  
J. K. Davidson ◽  
Jami J. Shah ◽  
Jiten V. Shah
Keyword(s):  
Computer Aided Design ◽  
Inverse Kinematics ◽  
Lower Cost ◽  
Parallel Robots ◽  
Valve Body ◽  
Higher Dimensional ◽  
Space Construction ◽  
Finish Machine ◽  
Aided Design

Abstract A novel combination of mathematical tools underlies a method to lower cost of the first fixture-setup required to finish-machine surfaces on large castings or weldments where components will be attached. The computer-aided design (CAD) model, tolerance specifications, process plan, and design of the fixture, including configuration of the locators, are given. The math tools are used to build algorithms for a digital model, the Setup-Map© (S-Map©), that predictively captures all allowable locator adjustments needed to position and orient each part in its fixture before machining begins. The S-Map in this paper is generated for a case-study design, a cast valve-body with two to-be-machined (TBM) features, but the math tools are general so the same methods could be applied directly, or easily adapted, to other designs and fixture schemes. Geometric variations at the TBM features are represented with Tolerance-Maps© (T-Maps©) that are constructed with higher-dimensional linear half-spaces. The T-Maps are shifted to be aligned with, and offset from, one-sided simulated envelopes derived from scans of corresponding features on each casting. Linear programming identifies the setup-point that is chosen to most evenly distribute the required amount of machining over all the TBM features. Inverse kinematics of parallel robots is used to convert the setup-point to custom settings at the fixture locators for each casting. The half-space construction enables the identification of TBM features that have insufficient material and require repair. The algorithms were validated with 13 castings.

Kinematic Calibration for Redundantly Actuated Parallel Mechanisms

2004 ◽  
Vol 126 (2) ◽  
pp. 307-318 ◽  
Author(s):  
Jay il Jeong ◽  
Dongsoo Kang ◽  
Young Man Cho ◽  
Jongwon Kim
Keyword(s):  
Optimization Algorithm ◽  
Parallel Mechanism ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Geometrical Constraint ◽  
Kinematic Parameters ◽  
Angle Error ◽  
Calibration Algorithm ◽  
Redundantly Actuated

We present a new kinematic calibration algorithm for redundantly actuated parallel mechanisms, and illustrate the algorithm with a case study of a planar seven-element 2-degree-of-freedom (DOF) mechanism with three actuators. To calibrate a nonredundantly actuated parallel mechanism, one can find actual kinematic parameters by means of geometrical constraint of the mechanism’s kinematic structure and measurement values. However, the calibration algorithm for a nonredundant case does not apply for a redundantly actuated parallel mechanism, because the angle error of the actuating joint varies with position and the geometrical constraint fails to be consistent. Such change of joint angle error comes from constraint torque variation with each kinematic pose (meaning position and orientation). To calibrate a redundant parallel mechanism, one therefore has to consider constraint torque equilibrium and the relationship of constraint torque to torsional deflection, in addition to geometric constraint. In this paper, we develop the calibration algorithm for a redundantly actuated parallel mechanism using these three relationships, and formulate cost functions for an optimization algorithm. As a case study, we executed the calibration of a 2-DOF parallel mechanism using the developed algorithm. Coordinate values of tool plate were measured using a laser ball bar and the actual kinematic parameters were identified with a new cost function of the optimization algorithm. Experimental results showed that the accuracy of the tool plate improved by 82% after kinematic calibration in a redundant actuation case.

Force Distribution With Pose-Dependent Force Boundaries for Redundantly Actuated Cable-Driven Parallel Robots

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Han Yuan ◽  
Eric Courteille ◽  
Dominique Deblaise
Keyword(s):  
Energy Consumption ◽  
Lower Boundary ◽  
Parallel Robots ◽  
Force Distribution ◽  
Computational Accuracy ◽  
Boundary Method ◽  
Redundantly Actuated ◽  
Cable Forces ◽  
Reducing Energy

This paper addresses the force distribution of redundantly actuated cable-driven parallel robots (CDPRs). A new and efficient method is proposed for the determination of the lower-boundary of cable forces, including the pose-dependent lower-boundaries. In addition, the effect of cable sag is considered in the calculation of the force distribution to improve the computational accuracy. Simulations are made on a 6DOF CDPR driven by eight cables to demonstrate the validity of the proposed method. Results indicate that the pose-dependent lower-boundary method is more efficient than the fixed lower-boundary method in terms of minimizing the motor size and reducing energy consumption.

scholarly journals Generation of Under-Actuated Parallel Robots With Non-Holonomic Joints and Kinetostatic Analysis of a Case Study

2009 ◽  
Author(s):  
Patrick Grosch ◽  
Raffaele Di Gregorio ◽  
Federico Thomas
Keyword(s):  
Parallel Manipulators ◽  
Parallel Robots ◽  
Compact Formulation

It will be shown how to generate under-actuated manipulators by substituting non-holonomic spherical pairs (nS pairs) for (holonomic) spherical pairs (S pairs) in fully-parallel manipulators (FPMs). Through this pair substitution, an under-actuated manipulator, previously proposed by one of the authors, will be demonstrated to be generated from an inversion of the 6-3 FPM. Moreover, the kinetostatic analysis of this manipulator will be reconsidered to obtain a simple and compact formulation. This reformulated analysis can be used both in the design of the under-actuated manipulator, and in its control.

scholarly journals The Modeling of Redundantly Actuated Mechanical Systems

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Yaojun Wang ◽  
Bruno Belzile ◽  
Jorge Angeles ◽  
Qinchuan Li
Keyword(s):  
Degrees Of Freedom ◽  
Screw Theory ◽  
Mechanical Systems ◽  
Coefficient Matrix ◽  
Dynamics Modeling ◽  
Norm Minimization ◽  
Redundantly Actuated ◽  
The Right ◽  
And Control

Abstract Dynamics modeling is essential in the design and control of mechanical systems, the focus of the paper being redundantly actuated systems, which bring about special challenges. The authors resort to the natural orthogonal complement (NOC), based on an adaptation of screw theory, to derive the dynamics model. Benefiting from the elimination of the constraint wrenches, the NOC offers a simple, systematic alternative to the modeling of redundantly actuated mechanical systems. The optimum actuator-torque distribution is determined via Euclidean-norm minimization; then, by relying on the QR-decomposition, an efficient and robust method is produced to compute explicitly the right Moore–Penrose generalized inverse of the coefficient matrix. The methodology is illustrated via a case study involving a redundantly actuated parallel-kinematics machine with three degrees of freedom and four actuators.

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