The Joint Distribution Problem With Multiple Articular Contact Forces

1990 ◽  
Vol 112 (3) ◽  
pp. 364-366
Author(s):  
J. G. Andrews ◽  
C. K. Cheng
Keyword(s):  
Joint Distribution ◽  
Ad Hoc ◽  
Muscle Force ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Contact Forces ◽  
Equality Constraint ◽  
Distribution Problem ◽  
Straight Line ◽  
Force Components

The single joint distribution problem with two or more unknown bony contact forces is considered, and an optimal solution procedure free of ad hoc assumptions is described. If two bony contact forces are present, a strictly muscle force dependent equality constraint exists that allows for initial independent estimation of muscle forces, followed by unique estimation of all bony contact force components perpendicular to the straight line connecting their known points of application. However, if three or more bony contact forces are present, no strictly muscle force dependent equality constraint exists, solution separability is lost, and optimal muscle and bony contact forces are obtained simultaneously.

Partial Contact Force Controllability in Active Wheeled Vehicles

1998 ◽  
Vol 123 (2) ◽  
pp. 169-175 ◽  
Author(s):  
B. J. Choi ◽  
S. V. Sreenivasan
Keyword(s):  
Contact Force ◽  
Geometric Approach ◽  
Contact Forces ◽  
Force Distribution ◽  
Distribution Problem ◽  
Passive Components ◽  
Uneven Terrain ◽  
Partial Contact ◽  
Force Components ◽  
Wheeled Vehicles

This paper presents a geometric approach for solving the force distribution problem in active wheeled vehicles (AWVs) moving on uneven surfaces. Here an active vehicle is defined as a system that includes independent actuators for all its internal joints. In general, AWVs do not possess omni-directional mobility, and they possess fewer actuators than the number of wheel-ground contact force components. This article presents an approach for separating the contact force vectors into active and passive components such that there exists an invertible square matrix that maps the active contact forces to the actuator efforts. An appropriate force allocation algorithm can then be developed for these systems. The concepts introduced in this article are demonstrated via an example of AWVs on uneven terrain. An example of force distribution in active legged vehicles (ALVs) that possess the same number of actuators as contact forces is also provided for comparison.

scholarly journals Economic Development Based on a Mathematical Model: An Optimal Solution Method for the Fuel Supply of International Road Transport Activity

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2963
Author(s):  
Melinda Timea Fülöp ◽  
Miklós Gubán ◽  
György Kovács ◽  
Mihály Avornicului
Keyword(s):  
Decision Making ◽  
Ad Hoc ◽  
Market Competition ◽  
Optimal Solution ◽  
Cost Savings ◽  
Cost Effective ◽  
Optimization Method ◽  
Optimal Decision ◽  
Environmental Damage ◽  
Fuel Cost

Due to globalization and increased market competition, forwarding companies must focus on the optimization of their international transport activities and on cost reduction. The minimization of the amount and cost of fuel results in increased competition and profitability of the companies as well as the reduction of environmental damage. Nowadays, these aspects are particularly important. This research aims to develop a new optimization method for road freight transport costs in order to reduce the fuel costs and determine optimal fueling stations and to calculate the optimal quantity of fuel to refill. The mathematical method developed in this research has two phases. In the first phase the optimal, most cost-effective fuel station is determined based on the potential fuel stations. The specific fuel prices differ per fuel station, and the stations are located at different distances from the main transport way. The method developed in this study supports drivers’ decision-making regarding whether to refuel at a farther but cheaper fuel station or at a nearer but more expensive fuel station based on the more economical choice. Thereafter, it is necessary to determine the optimal fuel volume, i.e., the exact volume required including a safe amount to cover stochastic incidents (e.g., road closures). This aspect of the optimization method supports drivers’ optimal decision-making regarding optimal fuel stations and how much fuel to obtain in order to reduce the fuel cost. Therefore, the application of this new method instead of the recently applied ad-hoc individual decision-making of the drivers results in significant fuel cost savings. A case study confirmed the efficiency of the proposed method.

The Location Problem of Given and Indivisible Different Units

1970 ◽  
Vol 2 (3) ◽  
pp. 341-356
Author(s):  
G. Jándy
Keyword(s):  
Exact Solution ◽  
Heuristic Algorithm ◽  
Network Flow ◽  
Location Problem ◽  
Optimal Solution ◽  
Type Problem ◽  
Distribution Problem ◽  
Enumeration Algorithm ◽  
Weighted Distribution ◽  
Partial Enumeration

In cases where certain simplifications are allowed, the location optimisation of given and indivisible different economic units may be modelled as a bi-value weighted distribution problem. The paper presents a heuristic algorithm for this network-flow-type problem and also a partial enumeration algorithm for deriving the exact solution. But it is also pointed out that an initial sub-optimal solution can quickly be improved with a derivation on a direct line only, if the exact solution is not absolutely essential. A numerical example is used to illustrate the method of derivation on a direct line starting with an upper bound given by a sub-optimal solution.

Periodic Response of a Link Coupling With Clearance

1989 ◽  
Vol 111 (2) ◽  
pp. 253-259 ◽  
Author(s):  
Y. S. Choi ◽  
S. T. Noah
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Solution Procedure ◽  
Contact Forces ◽  
Steady State Response ◽  
Algebraic Equations ◽  
State Response ◽  
Contact Points ◽  
Integration Schemes ◽  
Nonlinear Algebraic Equations

The nonlinear, steady-state response of a displacement-forced link coupling with clearance with finite stiffness is determined. The solution procedure is derived from satisfying the boundary conditions at the contact points and then solving the resulting nonlinear algebraic equations by setting the duration of contact as a parameter. This direct approach to determining periodic solutions for systems with clearances with finite stiffness is substantially more efficient than numerical integration schemes. Results in terms of contact forces and durations of contact are pertinent to fatigue and wear studies. Parametric relations are presented for effects of the variation of damping, stiffness, exciting displacement, and gap length on the dynamic behavior of the link pair.

Optimal Trajectories of Open-Chain Robot Systems: A New Solution Procedure Without Lagrange Multipliers

1998 ◽  
Vol 120 (1) ◽  
pp. 134-136 ◽  
Author(s):  
Sunil K. Agrawal ◽  
Pana Claewplodtook ◽  
Brian C. Fabien
Keyword(s):  
Differential Equations ◽  
Lagrange Multipliers ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Optimal Trajectories ◽  
Point Boundary ◽  
Open Chain ◽  
Robot Systems

For an n d.o.f. robot system, optimal trajectories using Lagrange multipliers are characterized by 4n first-order nonlinear differential equations with 4n boundary conditions at the two end time. Numerical solution of such two-point boundary value problems with shooting techniques is hard since Lagrange multipliers can not be guessed. In this paper, a new procedure is proposed where the dynamic equations are embedded into the cost functional. It is shown that the optimal solution satisfies n fourth-order differential equations. Due to absence of Lagrange multipliers, the two-point boundary-value problem can be solved efficiently and accurately using classical weighted residual methods.

Contact force analysis on two-fingered robot grasping

2020 ◽  
pp. 146441932096402
Author(s):  
Jiun-Ru Chen ◽  
Wei-En Chen ◽  
CH Liu ◽  
Yin-Tien Wang ◽  
CB Lin ◽  
...  
Keyword(s):  
Kinetic Analysis ◽  
Contact Force ◽  
Numerical Procedure ◽  
Spherical Body ◽  
Solution Procedure ◽  
The Body ◽  
Contact Forces ◽  
Grasping Forces ◽  
Robot Grasping ◽  
Force Displacement

A procedure for inverse kinetic analysis on two hard fingers grasping a hard sphere is proposed in this study. Contact forces may be found for given linear and angular accelerations of a spherical body. Elastic force-displacement relations predicted by Hertz contact theory are used to remove the indeterminancy produced by rigid body modelling. Two types of inverse kinetic analysis may be dealt with. Firstly, as the fingers impose a given tightening displacement on the body, and carry it to move with known accelerations, corresponding grasping forces may be determined by a numerical procedure. In this procedure one contact force may be chosen as the principal unknown, and all other contact forces are expressed in terms of this force. The numerical procedure is hence very efficient since it deals with a problem with only one unknown. The solution procedure eliminates slipping thus only nonslip solutions, if they exist, are found. Secondly, when the body is moving with known accelerations, if the grasping direction of the two fingers is also known, then the minimum tightening displacement required for non-sliding grasping may be obtained in closed form. In short, the proposed technique deals with a grasping system that has accelerations, and in this study the authors show that indeterminancy may be used to reduce the complexity of the problem.

AN ALGORITHM TO CALCULATE THE COMPONENTS OF ALL MUSCLE FORCES DURING EACH PHASES OF THE GAIT CYCLE, FOR THE PELVIC-FEMUR COMPLEX

2005 ◽  
Vol 05 (04) ◽  
pp. 539-548 ◽  
Author(s):  
SANTANU MAJUMDER ◽  
AMIT ROYCHOWDHURY ◽  
SUBRATA PAL
Keyword(s):  
Finite Element ◽  
Hip Joint ◽  
Computational Models ◽  
Gait Cycle ◽  
Muscle Force ◽  
Fe Analysis ◽  
Muscle Forces ◽  
Force Magnitude ◽  
Flexion Extension ◽  
Force Components

With the help of finite element (FE) computational models of femur, pelvis or hip joint to perform quasi-static stress analysis during the entire gait cycle, muscle force components (X, Y, Z) acting on the hip joint and pelvis are to be known. Most of the investigators have presented only the net muscle force magnitude during gait. However, for the FE software, either muscle force components (X, Y, Z) or three angles for the muscle line of action are required as input. No published algorithm (with flowchart) is readily available to calculate the required muscle force components for FE analysis. As the femur rotates about the hip center during gait, the lines of action for 27 muscle forces are also variable. To find out the variable lines of action and muscle force components (X, Y, Z) with directions, an algorithm was developed and presented here with detailed flowchart. We considered the varying angles of adduction/abduction, flexion/extension during gait. This computer program, obtainable from the first author, is able to calculate the muscle force components (X, Y, Z) as output, if the net magnitude of muscle force, hip joint orientations during gait and muscle origin and insertion coordinates are provided as input.

scholarly journals Minimum Cell Connection in Line Segment Arrangements

2017 ◽  
Vol 27 (03) ◽  
pp. 159-176
Author(s):  
Helmut Alt ◽  
Sergio Cabello ◽  
Panos Giannopoulos ◽  
Christian Knauer
Keyword(s):  
Linear Time ◽  
Optimal Solution ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Constant Number ◽  
Line Segments ◽  
Straight Line ◽  
Minimum Number ◽  
Number Of Segments ◽  
Connection Problems

We study the complexity of the following cell connection problems in segment arrangements. Given a set of straight-line segments in the plane and two points [Formula: see text] and [Formula: see text] in different cells of the induced arrangement: [(i)] compute the minimum number of segments one needs to remove so that there is a path connecting [Formula: see text] to [Formula: see text] that does not intersect any of the remaining segments; [(ii)] compute the minimum number of segments one needs to remove so that the arrangement induced by the remaining segments has a single cell. We show that problems (i) and (ii) are NP-hard and discuss some special, tractable cases. Most notably, we provide a near-linear-time algorithm for a variant of problem (i) where the path connecting [Formula: see text] to [Formula: see text] must stay inside a given polygon [Formula: see text] with a constant number of holes, the segments are contained in [Formula: see text], and the endpoints of the segments are on the boundary of [Formula: see text]. The approach for this latter result uses homotopy of paths to group the segments into clusters with the property that either all segments in a cluster or none participate in an optimal solution.

scholarly journals Swarm-Intelligence-Centric Routing Algorithm for Wireless Sensor Networks

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5164
Author(s):  
Changsun Shin ◽  
Meonghun Lee
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Swarm Intelligence ◽  
Network Performance ◽  
Ad Hoc ◽  
Routing Algorithm ◽  
Optimal Solution ◽  
Link Quality ◽  
Wireless Sensor ◽  
Control Message

The swarm intelligence (SI)-based bio-inspired algorithm demonstrates features of heterogeneous individual agents, such as stability, scalability, and adaptability, in distributed and autonomous environments. The said algorithm will be applied to the communication network environment to overcome the limitations of wireless sensor networks (WSNs). Herein, the swarm-intelligence-centric routing algorithm (SICROA) is presented for use in WSNs that aim to leverage the advantages of the ant colony optimization (ACO) algorithm. The proposed routing protocol addresses the problems of the ad hoc on-demand distance vector (AODV) and improves routing performance via collision avoidance, link-quality prediction, and maintenance methods. The proposed method was found to improve network performance by replacing the periodic “Hello” message with an interrupt that facilitates the prediction and detection of link disconnections. Consequently, the overall network performance can be further improved by prescribing appropriate procedures for processing each control message. Therefore, it is inferred that the proposed SI-based approach provides an optimal solution to problems encountered in a complex environment, while operating in a distributed manner and adhering to simple rules of behavior.

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
Normal Vector ◽  
Optimization Criteria ◽  
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 optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this 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 for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

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