Mass Center of Planar Mechanisms Using Auxiliary Parallelograms

1999 ◽  
Vol 121 (1) ◽  
pp. 166-168 ◽  
Author(s):  
A. Gokce ◽  
S. K. Agrawal
Keyword(s):  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Mass Center ◽  
Planar Mechanisms ◽  
Physical Point ◽  
Planar Mechanism ◽  
Test Beds

Center of mass is an important property of a mechanism. In biomechanics, in many studies, one monitors the motion of this point. The center of mass has importance in development of gravity compensated exercise machines and test beds on earth that mimic the behavior of systems in space. In this paper, a method is described where auxiliary parallelograms are added to a planar mechanism to identify the location of the center of mass of the original mechanism. In this procedure, the original and the augmented mechanisms have the same number of degrees-of-freedom. During motion, the center of mass is a physical point which can be monitored or used for purposes motivated from the application.

Mass Center of Planar Mechanisms Using Auxiliary Parallelograms

1998 ◽  
Author(s):  
Ali Gökçe ◽  
Sunil K. Agrawal
Keyword(s):  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Zero Gravity ◽  
Mass Center ◽  
Planar Mechanisms ◽  
Physical Point ◽  
Physical Location ◽  
Test Beds ◽  
As If

Abstract Center of mass is an important characteristic of a mechanism during motion. In some studies of biomechanics, it is necessary to monitor the motion of this point. The physical location of the center of mass during motion may have importance in the development of gravity compensated exercise machines. Also, a mechanism with the center of mass constrained to be inertially fixed has the same motion as if it was in zero gravity. This property may be exploited to develop test beds on earth that mimic the behavior of systems in space. In this paper, a method is described to augment planar mechanisms with auxiliary parallelograms in order to identify a physical point on the augmented mechanism which is the center of mass of the original mechanism. The original and the augmented mechanisms have the same degrees-of-freedom. If the links of the augmented mechanism are massless, the original and augmented mechanisms have the same motion. During motion, the center of mass is a physical point on the mechanism which can be monitored or used for other purposes motivated from the application. In practice, however, if such an augmented mechanism is constructed, its links will have finite masses. As a result, under the same inputs, the motion of the original and augmented mechanisms will be different. In this paper, the effects of finite masses of the additional links on the original mechanism are also discussed.

Development of Planar Mechanism State Matrices for Reconfigurable Mechanisms

2010 ◽  
Author(s):  
Brian J. Slaboch ◽  
Philip A. Voglewede
Keyword(s):  
Degrees Of Freedom ◽  
Analysis Tool ◽  
State Matrix ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Reconfigurable Mechanisms ◽  
Topological Characteristics

This paper introduces mechanism state matrices as a novel way to represent the topological characteristics of planar reconfigurable mechanisms. As part of this new concept, these matrices will be used as an analysis tool to automatically determine the degrees of freedom (DOF) of planar mechanisms that only contain one DOF joints. The DOF at each state can be combined with a mechanism state matrix to form an augmented mechanism state matrix. A series of examples will be used to illustrate the proposed concept.

Detection of Vehicle Tripped and Untripped Rollovers by a Novel Index With Mass-Center-Position Estimations

2017 ◽  
Author(s):  
Fengchen Wang ◽  
Yan Chen
Keyword(s):  
Load Transfer ◽  
Center Of Mass ◽  
Roll Motion ◽  
Mass Center ◽  
Motion Models ◽  
Center Position ◽  
Before And After ◽  
Vehicle Rollover ◽  
Lift Off ◽  
Rollover Index

This paper presents a novel mass-center-position (MCP) metric for vehicle rollover propensity detection. MCP is first determined by estimating the positions of the center of mass of one sprung mass and two unsprung masses with two switchable roll motion models, before and after tire lift-off. The roll motion information without saturation can then be provided through MCP continuously. Moreover, to detect completed rollover statues for both tripped and untripped rollovers, the criteria are derived from d’Alembert principle and moment balance conditions based on MCP. In addition to tire lift-off, three new rollover statues, rollover threshold, rollover occurrence, and vehicle jumping into air can be all identified by the proposed criteria. Compared with an existing rollover index, lateral load transfer ratio, the fishhook maneuver simulation results in CarSim® for an E-class SUV show that MCP metric can successfully predict the vehicle impending rollover without saturation for untripped rollovers. Tripped rollovers caused by a triangle road bump are also successfully detected in the simulation. Thus, MCP metric can be successfully applied for rollover propensity prediction.

A Method for Type Synthesis of Mechanisms Using Phase Diagrams

1994 ◽  
Author(s):  
Sio-Hou Lei ◽  
Ying-Chien Tsai
Keyword(s):  
Phase Diagram ◽  
Degrees Of Freedom ◽  
Practical Application ◽  
Type Synthesis ◽  
Planar Mechanisms ◽  
Simple Loop ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Synthesis Of Mechanisms

Abstract A method for synthesizing the types of spatial as well as planar mechanisms is expressed in this paper by using the concept of phase diagram in metallurgy. The concept represented as a type synthesis technique is applied to (a) planar mechanisms with n degrees of freedom and simple loop, (b) spatial mechanisms with single degree of freedom and simple loop, to enumerate all the possible mechanisms with physically realizable kinematic pairs. Based on the technique described, a set of new reciprocating mechanisms is generated as a practical application.

scholarly journals The Use of Integrals in Numerical Integrations of theN-Body Problem

1971 ◽  
Vol 10 ◽  
pp. 40-51
Author(s):  
Paul E. Nacozy
Keyword(s):  
Angular Momentum ◽  
Numerical Integration ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Center Of Mass ◽  
Integration Step ◽  
Gravitational System ◽  
Systems Of Differential Equations ◽  
Numerical Integrations ◽  
Original Number

AbstractThe numerical integration of systems of differential equations that possess integrals is often approached by using the integrals to reduce the number of degrees of freedom or by using the integrals as a partial check on the resulting solution, retaining the original number of degrees of freedom.Another use of the integrals is presented here. If the integrals have not been used to reduce the system, the solution of a numerical integration may be constrained to remain on the integral surfaces by a method that applies corrections to the solution at each integration step. The corrections are determined by using linearized forms of the integrals in a least-squares procedure.The results of an application of the method to numerical integrations of a gravitational system of 25-bodies are given. It is shown that by using the method to satisfy exactly the integrals of energy, angular momentum, and center of mass, a solution is obtained that is more accurate while using less time of calculation than if the integrals are not satisfied exactly. The relative accuracy is ascertained by forward and backward integrations of both the corrected and uncorrected solutions and by comparison with more accurate integrations using reduced step-sizes.

Assembly Configurations of Planar Multi-Loop Mechanisms With Kinematic Limitations

2005 ◽  
Vol 128 (4) ◽  
pp. 747-754 ◽  
Author(s):  
David E. Foster ◽  
Raymond J. Cipra
Keyword(s):  
Degrees Of Freedom ◽  
Planar Mechanisms ◽  
Two Degrees Of Freedom ◽  
Stationary Obstacles ◽  
Joint Limits

This paper examines the problem of identifying the assembly configurations (ACs), also called circuits, of planar multi-loop mechanisms with kinematic limitations, such as joint limits, link interference, collision with stationary obstacles, and constraint regions. First, a technique is given to describe numerically the satisfaction or violation of these kinematic limitations, and then it is applied to find the ACs of mechanisms with kinematic limitations. The method is valid for planar mechanisms with one or two degrees of freedom, and is illustrated with two examples.

Development of a 6-DOF Testing Platform for Multirotor Flying Vehicles with Suspended Loads

Aerospace ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 355
Author(s):  
Saad M. S. Mukras ◽  
Hanafy M. Omar
Keyword(s):  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Performance Testing ◽  
Flight Performance ◽  
Testing Platform ◽  
Six Degrees Of Freedom ◽  
Mass Properties ◽  
Test Platform ◽  
Suspended Loads

The development of multirotor vehicles can often be a dangerous and costly undertaking due to the possibility of crashes resulting from faulty controllers. The matter of safety in such activities has primarily been addressed through the use of testbeds. However, testbeds for testing multirotor vehicles with suspended loads have previously not been reported. In this study, a simple yet novel testing platform was designed and built to aid in testing and evaluating the performances of multirotor flying vehicles, including vehicles with suspended loads. The platform allows the flying vehicle to move with all six degrees of freedom (DOF). Single or three-DOF motions can also be performed. Moreover, the platform was designed to enable the determination of the mass properties (center of mass and moments of inertia) of small multirotor vehicles (which are usually required in the development of new control systems). The applicability of the test platform for the in-flight performance testing of a multirotor vehicle was successfully demonstrated using a Holybro X500 quadcopter with a suspended load. The test platform was also successfully used to determine the mass properties of the vehicle.

Real-Time Planning and Nonlinear Control for Quadrupedal Locomotion With Articulated Tails

2021 ◽  
Vol 143 (7) ◽  
Author(s):  
Randall T. Fawcett ◽  
Abhishek Pandala ◽  
Jeeseop Kim ◽  
Kaveh Akbari Hamed
Keyword(s):  
Real Time ◽  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Hierarchical Control ◽  
Nonlinear Feedback ◽  
Nonlinear Controller ◽  
External Disturbances ◽  
Quadrupedal Locomotion ◽  
Control Scheme ◽  
High Level

Abstract The primary goal of this paper is to develop a formal foundation to design nonlinear feedback control algorithms that intrinsically couple legged robots with bio-inspired tails for robust locomotion in the presence of external disturbances. We present a hierarchical control scheme in which a high-level and real-time path planner, based on an event-based model predictive control (MPC), computes the optimal motion of the center of mass (COM) and tail trajectories. The MPC framework is developed for an innovative reduced-order linear inverted pendulum (LIP) model that is augmented with the tail dynamics. At the lower level of the control scheme, a nonlinear controller is implemented through the use of quadratic programming (QP) and virtual constraints to force the full-order dynamical model to track the prescribed optimal trajectories of the COM and tail while maintaining feasible ground reaction forces at the leg ends. The potential of the analytical results is numerically verified on a full-order simulation model of a quadrupedal robot augmented with a tail with a total of 20 degrees-of-freedom. The numerical studies demonstrate that the proposed control scheme coupled with the tail dynamics can significantly reduce the effect of external disturbances during quadrupedal locomotion.

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