The Determination of Equilibrium Configurations of Spring-Restrained Mechanisms Using (4 × 4) Matrix Methods

1967 ◽  
Vol 89 (1) ◽  
pp. 87-93 ◽  
Author(s):  
D. F. Livermore
Keyword(s):  
Kinematic Chain ◽  
External Loading ◽  
Matrix Methods ◽  
Kinematic Chains ◽  
Equilibrium Configurations ◽  
Force Systems ◽  
Velocity Information ◽  
Equilibrium Analyses ◽  
External Loads

A spring-restrained, multiple-loop, multiple-degree-of-freedom kinematic chain will normally have one or more stable equilibrium configurations when steady external loads are applied to it. The “kinematic equivalent” of a vehicle and its suspension linkages is a common example of such a system. Changes in external loading due to cornering, braking, and so on, can produce important changes in the equilibrium configuration of the suspension. This paper presents a general method for determining the equilibrium configurations of spring-restrained, kinematic chains under the action of steady external loading. The iterative (4 × 4) matrix method of displacement analysis, previously developed for single-loop chains, is extended to complex chains and is used to determine the displacement and velocity information required for equilibrium analyses. The final results are general computer programs which will determine displacement and/or equilibrium configurations for simple or complex mechanism systems wherein the applied force systems may be considered conservative.

Influence of External Loads on Thin Film Cracking

2004 ◽  
Author(s):  
Srinath S. Chakravarthy ◽  
Eric H. Jordan ◽  
Wilson K. S. Chiu
Keyword(s):  
Thin Film ◽  
External Load ◽  
Crack Arrest ◽  
External Loading ◽  
Element Analysis ◽  
Film Cracking ◽  
Two Parameters ◽  
Improved Accuracy ◽  
External Loads

Cracking in thin films under the combined influence of residual stress and an external load is examined. An improved accuracy version of the existing solution for substrate cracking absent the external load is provided. A superposition scheme that uses the solution for substrate cracking and other existing published solutions is presented for the determination of the energy release rate. The superposition scheme is validated using finite element analysis, and conditions under which the superposition scheme is valid are discussed. Crack arrest is examined and two parameters that determine the possibility of crack arrest are identified. The influence of external loading on channelling behavior in the substrate is discussed.

Modified joint connectivity approach for identification of topological characteristics of planar kinematic chains

2011 ◽  
Vol 225 (11) ◽  
pp. 2700-2717 ◽  
Author(s):  
G S Bedi ◽  
S Sanyal
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Kinematic Chains ◽  
Multiple Degrees Of Freedom ◽  
Preferred Frame ◽  
Topological Characteristics ◽  
Synthesis Stage ◽  
Different Levels ◽  
Selection Of

In a kinematic chain, the links are connected to each other through joints. The connectivity of a joint indicates the number of joints to which it is connected. The connectivity level of a joint indicates the distance by which it is separated from the adjacent joints. The concept of joint connectivity and its application to detect isomorphism among kinematic chains and their inversions has been already reported by authors. The method utilizes the connectivity of joints at different levels to detect isomorphism and inversions among planar kinematic chains. The method is applied to eight-, nine-, and ten-link planar kinematic chains. The results so obtained are in agreement with those available in the literature. In this study, the method is further improved by incorporating the type of joint to make it more effective for the detection of isomorphism and distinct inversions. A joint connectivity table completely representing the kinematic chain is proposed. The application of the method is extended for the determination of additional topological characteristics of chains such as categorization of kinematic chains and selection of preferred frame, input and output links for function and path generation. The concept of ‘Motion Transfer Ability’ is introduced and utilized to develop numerical measures for comparing and categorizing the chains at the synthesis stage of mechanism design for a specific application. The method was successfully tested on planar kinematic chains with single and multiple degrees of freedom and the results for eight- and nine-link kinematic chains are appended.

GENERIC MODEL FOR GONIOPHOTOMETER GEOMETRIES

2021 ◽  
Author(s):  
D.J. Lerch ◽  
M. Katona ◽  
K. Trampert ◽  
U. Krüger ◽  
C. Schrader ◽  
...  
Keyword(s):  
State Of The Art ◽  
Kinematic Chain ◽  
Generic Model ◽  
Chain Model ◽  
Total System ◽  
Kinematic Chains ◽  
Measurement Systems ◽  
Geometric Uncertainties ◽  
High Level

In this work, we present a method to describe the model of a goniophotometer for uncertainty analysis by state-of-the-art Universal Robotic Description Format (URDF). The parameters of the kinematic chain model are determined by measurements of the geometric properties of the goniophotometer. The uncertainties of the pose are determined using Monte Carlo (MC) simulations of the kinematic chain. The measured geometric uncertainties are input the MC simulations. The proposed framework enables high level description of kinematic chains for MC simulations of measurement systems. Furthermore, the uncertainty of the total system is demonstrated over the MC trials to prove a sufficient amount of MC trials. The results of this generic approach are evaluated against an existing model and the uncertainty determination of the same goniophotometer.

scholarly journals Stability of Manipulator Configuration Under External Loading

2012 ◽  
Author(s):  
Alexandr Klimchik ◽  
Anatol Pashkevich ◽  
Damien Chablat
Keyword(s):  
Equilibrium Configuration ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Static Equilibrium ◽  
Practical Significance ◽  
External Loading ◽  
Kinematic Chains ◽  
Cartesian Stiffness Matrix ◽  
The Stability ◽  
Cartesian Stiffness

The paper is devoted to the analysis of robotic manipulator behavior under internal and external loadings. The main contributions are in the area of stability analysis of manipulator configurations corresponding to the loaded static equilibrium. In contrast to other works, in addition to usually studied the end-platform behavior with respect to the disturbance forces, the problem of configuration stability for each kinematic chain is considered. The proposed approach extends the classical notion of the stability for the static equilibrium configuration that is completely defined the properties of the Cartesian stiffness matrix only. The advantages and practical significance of the proposed approach are illustrated by several examples that deal with serial kinematic chains and parallel manipulators. It is shown that under the loading the manipulator workspace may include some specific points that are referred to as elastostatic singularities where the chain configurations become unstable.

Structure Based Grading of Kinematic Chains

2014 ◽  
Vol 575 ◽  
pp. 501-506 ◽  
Author(s):  
Shubhashis Sanyal ◽  
G.S. Bedi
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Structural Differences ◽  
The Individual ◽  
Independent Loops

Kinematic chains differ due to the structural differences between them. The location of links, joints and loops differ in each kinematic chain to make it unique. Two similar kinematic chains will produce similar motion properties and hence are avoided. The performance of these kinematic chains also depends on the individual topology, i.e. the placement of its entities. In the present work an attempt has been made to compare a family of kinematic chains based on its structural properties. The method is based on identifying the chains structural property by using its JOINT LOOP connectivity table. Nomenclature J - Number of joints, F - Degree of freedom of the chain, N - Number of links, L - Number of basic loops (independent loops plus one peripheral loop).

Determination of the Minimum Distance Between Moving Objects Including Velocity Information

1993 ◽  
Author(s):  
Meyer Nahon
Keyword(s):  
Minimum Distance ◽  
Moving Objects ◽  
Rapid Determination ◽  
Computation Time ◽  
Optimization Techniques ◽  
Real Time Control ◽  
Time Step ◽  
Time Control ◽  
Velocity Information

Abstract The rapid determination of the minimum distance between objects is of importance in collision avoidance for a robot maneuvering among obstacles. Currently, the fastest algorithms for the solution of this problem are based on the use of optimization techniques to minimize a distance function. Furthermore, to date this problem has been approached purely through the position kinematics of the two objects. However, although the minimum distance between two objects can be found quickly on state-of-the-art hardware, the modelling of realistic scenes entails the determination of the minimum distances between large numbers of pairs of objects, and the computation time to calculate the overall minimum distance between any two objects is significant, and introduces a delay which has serious repercussions on the real-time control of the robot. This paper presents a technique to modify the original optimization problem in order to include velocity information. In effect, the minimum distance calculation is performed at a future time step by projecting the effect of present velocity. This method has proven to give good results on a 6-dof robot maneuvering among obstacles, and has allowed a complete compensation of the lags incurred due to computational delays.

Combined Graph Layout Algorithms for Automated Sketching of Kinematic Chains

2012 ◽  
Author(s):  
Martín A. Pucheta ◽  
Nicolás E. Ulrich ◽  
Alberto Cardona
Keyword(s):  
Computational Cost ◽  
Kinematic Chain ◽  
Initial Position ◽  
Graph Representation ◽  
Combinatorial Algorithms ◽  
Graph Layout ◽  
Kinematic Chains ◽  
Aesthetic Characteristics ◽  
Edge Crossings ◽  
Independent Loops

The graph layout problem arises frequently in the conceptual stage of mechanism design, specially in the enumeration process where a large number of topological solutions must be analyzed. Two main objectives of graph layout are the avoidance or minimization of edge crossings and the aesthetics. Edge crossings cannot be always avoided by force-directed algorithms since they reach a minimum of the energy in dependence with the initial position of the vertices, often randomly generated. Combinatorial algorithms based on the properties of the graph representation of the kinematic chain can be used to find an adequate initial position of the vertices with minimal edge crossings. To select an initial layout, the minimal independent loops of the graph can be drawn as circles followed by arcs, in all forms. The computational cost of this algorithm grows as factorial with the number of independent loops. This paper presents a combination of two algorithms: a combinatorial algorithm followed by a force-directed algorithm based on spring repulsion and electrical attraction, including a new concept of vertex-to-edge repulsion to improve aesthetics and minimize crossings. Atlases of graphs of complex kinematic chains are used to validate the results. The layouts obtained have good quality in terms of minimization of edge crossings and maximization of aesthetic characteristics.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

scholarly journals Determination of Neuromuscular Control of the Upper Limbs in Children - Case Study

2020 ◽  
Vol 11 (4Sup1) ◽  
pp. 46-61
Author(s):  
Carmen-Magdalena Camenidis ◽  
◽  
Irina Băițel ◽  
Amalia Oatu ◽  
Octavian Amzulescu ◽  
...  
Keyword(s):  
Kinematic Chain ◽  
Neuromuscular Control ◽  
Female Gender ◽  
Upper Limbs ◽  
Motor Action ◽  
Muscle Groups ◽  
The Moment ◽  
The Right

The objective of this case study is to observe the existence of an anticipation mechanism at the muscle groups level of the upper limbs. We tried to highlighted this anticipation process by measuring the potential of surface electric for some muscle groups representing the kinematic chain on the right side, involved in the motor action of catching a basketball and a 3kg medicine ball with two hands to the chest. We conducted a case study of a 13-year-old child, female gender. As a measurement method, we used surface electromyography signals of the EMG Trigno Delsys wireless system with 16 electrodes. We determined the moment when the muscles come into action by increasing the potential of surface electric and the moment when the action of catching the ball takes place, using the information provided by the accelerometers incorporated in the sensors of the Delsys equipment used. Therefore, we obtained information about how different muscle groups come into action which helped us to get an idea of how the child's movement is structured. Based on results of accelerations and EMG signals acquired we have formulated conclusions regarding the neuromuscular control of the tested subject. We also planned for the future to test a larger group of participants in the study research of anticipation mechanism in children who do not practice any performance sports.

scholarly journals A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Robotics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Fernando Gonçalves ◽  
Tiago Ribeiro ◽  
António Fernando Ribeiro ◽  
Gil Lopes ◽  
Paulo Flores
Keyword(s):  
Recursive Algorithm ◽  
Kinematic Chain ◽  
Robotic Systems ◽  
Mobile Manipulator ◽  
Euler Angles ◽  
Joint Angles ◽  
Main Research ◽  
Kinematic Chains ◽  
Research Fields ◽  
Forward Kinematic

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

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