Dynamic Analysis of a Multi-Rigid-Body Open-Chain System

1983 ◽  
Vol 105 (1) ◽  
pp. 28-34 ◽  
Author(s):  
G. R. Pennock ◽  
A. T. Yang
Keyword(s):  
Rigid Body ◽  
Robot Manipulators ◽  
Dynamic Equations ◽  
Newtonian Mechanics ◽  
Open Chain ◽  
Analytical Technique ◽  
Chain System ◽  
Joint Forces ◽  
Reaction Forces ◽  
Common Effort

In this paper we present an analytical technique, based on Newtonian mechanics with screw calculus and dual-number matrices, to derive the dynamic equations of a multi-rigid-body open-chain system. Next, we outline a systematic procedure to derive closed-form expressions for the joint forces and torques and the reaction forces and moments exerted on each member in the system. Finally, we illustrate the procedure with two examples of robot manipulators. It is hoped that the analytical technique presented here will provide a meaningful alternative, or serve as a complement to existing methods, in our common effort to advance the design of robot manipulators.

scholarly journals Dynamic model of multi-rigid-body systems based on particle dynamics with recursive approach

2005 ◽  
Vol 2005 (4) ◽  
pp. 365-382 ◽  
Author(s):  
Hazem Ali Attia
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Equations Of Motion ◽  
Particle Dynamics ◽  
Rigid Bodies ◽  
Constrained System ◽  
Open Chain ◽  
Chain System ◽  
Closed Chain ◽  
Serial Chains

A dynamic model for multi-rigid-body systems which consists of interconnected rigid bodies based on particle dynamics and a recursive approach is presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. A closed-chain system is transformed to open-chain by cutting suitable kinematical joints and introducing cut-joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.

Automatic Formulation of Dynamic Equations of Motion of Robot Manipulators

1988 ◽  
Vol 202 (6) ◽  
pp. 397-404 ◽  
Author(s):  
D Pan ◽  
R S Sharp
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Chain Structure ◽  
Algebraic Manipulation ◽  
Dynamic Equations ◽  
Open Chain ◽  
Scalar Form ◽  
Memory Space ◽  
Manipulation Language

Based on the use of homogeneous transformation matrices with Denavit-Hartenberg notation and the Lagrangian formulation method, a general computer program ROBDYN.RED for the symbolic derivation of dynamic equations of motion for robot manipulators has been developed and is discussed in this paper. The program is developed by using REDUCE, an algebraic manipulation language, and is versatile for open-chain structure robot manipulators with any number of degrees of freedom and with any combination of types of joint. Considerations are also given to saving computer memory space required for execution and to minimizing the runtime. Several examples are included to demonstrate the use of the program. Equations of motion in scalar form can be automatically transferred to FORTRAN format for later numerical simulations. The efficiency of the resulting equations in terms of numerical integration is also discussed and some further developments to improve the efficiency are suggested.

scholarly journals Application of the dynamic Lorentz model to modeling the motion of a rigid body

2021 ◽  
pp. 32-36
Author(s):  
Nikolay Makeyev ◽  
Keyword(s):  
Dynamical System ◽  
Qualitative Research ◽  
Rigid Body ◽  
Body Motion ◽  
Dynamic Equations ◽  
Lorentz Model ◽  
Dissipative Forces ◽  
System Parameters ◽  
Phase Trajectories ◽  
Inertia Forces

A qualitative research of the field of phase trajectories of the system of dynamic equations of an absolutely rigid body was carried out, moving around the selected pole under the influence of gyroscopic, dissipative forces and Coriolis inertia forces. The equations of body motion are reduced to a dynamical system generating a Lorentz attractor. Under parametric constraints imposed on the equations of a dynamical system, the structure of its phase trajectories is described depending on the values of the system parameters.

Investigation on Kane dynamic equations based on screw theory for open-chain manipulators

2005 ◽  
Vol 26 (5) ◽  
pp. 627-635 ◽  
Author(s):  
Liu Wu-fa ◽  
Gong Zhen-bang ◽  
Wang Qin-que
Keyword(s):  
Screw Theory ◽  
Dynamic Equations ◽  
Open Chain

New Mechanical Generators of Schoenflies Motion Implementing Bennett Linkages

2012 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Rigid Body ◽  
Special Design ◽  
Motion Group ◽  
Open Chain ◽  
Hybrid Topology ◽  
Parallel Arrangement ◽  
Axis Parallel ◽  
Mechanical Generator ◽  
Product Closure

Based on the Bennett 4R chain, we construct a rotating loop by fixing one R axis to the frame and the fixed R becomes a coaxial double R pair. The R pair opposite to the fixed double R is replaced by a spherical S pair which can be equivalent to a (RRR) open chain with non-coplanar intersecting axes. In the (RRR) sub-chain, we choose special axes and derive R|- R|(R(RRR)R chain moving with 2 DoFs. That moving R becomes a coaxial double R with the addition of another rigid body and the obtained chain with hybrid topology generates a 3-dof motion, which is mathematically modeled by a 3D submanifold of a 4D group of X motions. Because of the product closure in an X-motion group, adding an H pair with any pitch and an axis parallel to the fixed R axis leads to a mechanical generator of a 4D X-motion group. Then, parallel arrangement of two generators of the same X motion gives a new parallel generator of X motion, which can be actuated by four fixed R pairs; the two Hs must have distinct pitches. A special design with four collinear actuated axes is revealed too.

scholarly journals Effects of Gait Speed of Femoroacetabular Joint Forces

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Joshua T. Weinhandl ◽  
Bobbie S. Irmischer ◽  
Zachary A. Sievert
Keyword(s):  
Hip Joint ◽  
Gait Speed ◽  
Gait Cycle ◽  
Musculoskeletal Modeling ◽  
Joint Loading ◽  
Joint Force ◽  
Joint Forces ◽  
Reaction Forces ◽  
Vertical Ground ◽  
Vertical Ground Reaction Forces

Alterations in hip joint loading have been associated with diseases such as arthritis and osteoporosis. Understanding the relationship between gait speed and hip joint loading in healthy hips may illuminate changes in gait mechanics as walking speed deviates from preferred. The purpose of this study was to quantify hip joint loading during the gait cycle and identify differences with varying speed using musculoskeletal modeling. Ten, healthy, physically active individuals performed walking trials at their preferred speed, 10% faster, and 10% slower. Kinematic, kinetic, and electromyographic data were collected and used to estimate hip joint force via a musculoskeletal model. Vertical ground reaction forces, hip joint force planar components, and the resultant hip joint force were compared between speeds. There were significant increases in vertical ground reaction forces and hip joint forces as walking speed increased. Furthermore, the musculoskeletal modeling approach employed yielded hip joint forces that were comparable to previous simulation studies and in vivo measurements and was able to detect changes in hip loading due to small deviations in gait speed. Applying this approach to pathological and aging populations could identify specific areas within the gait cycle where force discrepancies may occur which could help focus management of care.

scholarly journals Open Chain Isokinetic Assessment and Exercise of the Knee

1994 ◽  
Vol 3 (3) ◽  
pp. 245-254 ◽  
Author(s):  
David H. Perrin
Keyword(s):  
Body Position ◽  
Peak Torque ◽  
Hamstring Muscle ◽  
Open Chain ◽  
Warm Up ◽  
Joint Forces ◽  
Test Velocity ◽  
Muscle Groups ◽  
Group Relationships ◽  
Joint Range

This paper reviews the concepts associated with isokinetic open chain assessment and exercise of the quadriceps and hamstring muscle groups. Following a review of the isokinetic concept of exercise, the paper addresses principles of assessment and exercise of the knee, including the importance of musculoskeletal and cardiovascular screening, warm-up, body position, stabilization, and joint alignment. Gravity correction, test and exercise velocity, and duration of exercise are also addressed. Interpretation of an isokinetic evaluation of the knee is also addressed within the context of force-velocity relationships, peak torque relative to body weight, and bilateral and reciprocal muscle group relationships. Joint range of motion and test velocity are also discussed with respect to patellofemoral and tibiofemoral joint forces. Finally, recommended protocols for isokinetic assessment and exercise of the quadriceps and hamstring muscle groups are presented.

Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2006 ◽  
Author(s):  
Brian M. Korte ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Open Chain ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Planar Linkages

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

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