3D mathematical model for evaluation of the mass-inertial characteristics of the upper limb: Analytical results

The paper develops a mathematical model of population growth in an agricultural community, covering the 17th century ad. The model takes into account two types of resources that provided life, and the influence of management structures on population growth. The analytical results are compared with the estimated data of historians and economists on the world population. Based on the statistical approach, a model for estimating the possible dynamics of population growth is proposed.

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Development of a revolute-type kinematic model for human upper limb using a matrix approach

Robotica ◽

10.1017/s0263574721001387 ◽

2021 ◽

pp. 1-22

Author(s):

Anil Kumar Gillawat

Keyword(s):

Mathematical Model ◽

Upper Limb ◽

Wrist Joint ◽

Kinematic Model ◽

Matrix Approach ◽

Joint Torques ◽

The Matrix ◽

Distal Interphalangeal ◽

Forward Kinematic ◽

Human Upper Limb

Abstract A mathematical model is proposed for a revolute joint mechanism with an n-degree of freedom (DOF). The matrix approach is used for finding the relation between two consecutive links to determine desired link parameters such as position, velocity and acceleration using the forward kinematic approach. The matrix approach was confirmed for a proposed 10 DOF revolute type (R-type) human upper limb model with servo motors at each joint. Two DOFs are considered each at shoulder, elbow and wrist joint, followed by four DOF for the fingers. Two DOFs were considered for metacarpophalangeal (mcp) and one DOF each for proximal interphalangeal (pip) and distal interphalangeal (dip) joints. MATLAB script function was used to evaluate the mathematical model for determining kinematic parameters for all the proposed human upper limb model joints. The simplified method for kinematic analysis proposed in this paper will further simplify the dynamic modeling of any mechanism for determining joint torques and hence, easy to design control system for joint movements.

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A Probabilistic Analysis of Path Duration Using Routing Protocol in VANETs

International Journal of Vehicular Technology ◽

10.1155/2014/495036 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 12

Author(s):

Ram Shringar Rao ◽

Sanjay Kumar Soni ◽

Nanhay Singh ◽

Omprakash Kaiwartya

Keyword(s):

Mathematical Model ◽

Routing Protocol ◽

Delivery Ratio ◽

Estimation Model ◽

Routing Metrics ◽

Analytical Results ◽

Path Duration ◽

Result Analysis ◽

Duration Estimation ◽

The Mathematical Model

In recent years, various routing metrics such as throughput, end-to-end delay, packet delivery ratio, path duration, and so forth have been used to evaluate the performance of routing protocols in VANETs. Among these routing metrics, path duration is one of the most influential metrics. Highly mobile vehicles cause frequent topology change in vehicular network environment that ultimately affects the path duration. In this paper, we have derived a mathematical model to estimate path duration using border node-based most forward progress within radius (B-MFR), a position based routing protocol. The mathematical model for estimation of path duration consists of probability of finding next-hop node in forwarding region, estimation of expected number of hops, probability distribution of velocity of nodes, and link duration between each intermediate pair of nodes. The analytical results for the path duration estimation model have been obtained using MATLAB. The model for path duration estimation has been simulated in NS2. Each of the analytical results has been verified through respective simulation results. The result analysis clearly reveals that path duration increases with the increase in transmission range and node density and decreases with the increase in the number of hops in the path and velocity of the nodes.

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Body Roll and Handpath in Freestyle Swimming: An Experimental Study

Journal of Applied Biomechanics ◽

10.1123/jab.9.3.238 ◽

1993 ◽

Vol 9 (3) ◽

pp. 238-253 ◽

Cited By ~ 28

Author(s):

Qi Liu ◽

James G. Hay ◽

James G. Andrews

Keyword(s):

Mathematical Model ◽

Experimental Study ◽

Upper Limb ◽

Three Dimensional ◽

Time History ◽

The Body ◽

Long Distance ◽

Lateral Component ◽

3D Data ◽

Body Roll

The purpose of this study was to determine the influence of (a) body roll, and (b) the motion of the arm relative to the trunk, on the medial-lateral component of the path followed by the hand during the pull phase in freestyle swimming. Ten male swimmers swam three trials of freestyle at a long-distance workout pace. Three-dimensional (3D) underwater videography was used to record the body roll angle-time history and the path followed by the hand during the pull phase. A mathematical model was used to characterize the motion of a swimmer's right upper limb in accord with 3D data from the videotape images, and to determine what the path of the hand would have been as a result of body roll alone. The contribution of body roll to the actual handpath was found to be nearly equal to the contribution of medial-lateral motions of the hand relative to the trunk.

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An upper limb mathematical model of an oil palm harvester

10.1063/1.4895333 ◽

2014 ◽

Cited By ~ 3

Author(s):

N. P. Tumit ◽

A. S. Rambely ◽

Shamsul BMT ◽

Shahriman A. B. ◽

Ng Y. G. ◽

...

Keyword(s):

Mathematical Model ◽

Upper Limb ◽

Oil Palm

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Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative

Advances in Difference Equations ◽

10.1186/s13662-020-03191-x ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Saeed Ahmad ◽

Rafi Ullah ◽

Dumitru Baleanu

Keyword(s):

Mathematical Model ◽

Research Work ◽

Control Model ◽

Tuberculosis Control ◽

Fixed Point Approach ◽

Analytical Results ◽

Adomian Decomposition ◽

The Mathematical Model ◽

Tuberculosis Disease ◽

Kernel Type

AbstractThis research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further, by the use of iterative tools of Adomian decomposition and Laplace, the semi-analytical results are studied. Some graphical results are given with discussion.

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Study on Mathematical Model of Temperature Field in the Laser Welding Process

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.426-427.89 ◽

2010 ◽

Vol 426-427 ◽

pp. 89-92

Author(s):

Hong Feng Wang ◽

Dun Wen Zuo ◽

Ming Min Huang ◽

Hong Miao

Keyword(s):

Mathematical Model ◽

Temperature Field ◽

Temperature Distribution ◽

Heat Source ◽

Laser Welding ◽

Welding Process ◽

Actual Process ◽

Analytical Results ◽

The Mathematical Model ◽

Laser Welding Process

From the laser welding actual process, the welding heat source model of laser welding process was established, that is, superposition heat source. According to the knowledge of thermodynamics, the establishment of a welding process, the mathematical model of temperature distribution of laser welding process was obtained by laser welding heat source. Finally, the finite element simulation of welding temperature distribution was used. The simulated results were compared with the analytical results of mathematical model of temperature field, it was proved consistent between simulated results and analytical results, at the same time it can account for the correctness of the mathematical model of temperature field.

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