Visual Synthesis of RRR- and RPR-Legged Planar Parallel Manipulators Using Constraint Manifold Geometry

2011 ◽  
Author(s):  
Anurag Purwar ◽  
Aditya Gupta
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Design Tool ◽  
Design Parameters ◽  
Moving Frames ◽  
Algebraic Manifold ◽  
Dimensional Synthesis ◽  
Geometric Transformations ◽  
Planar Parallel Manipulators

In this paper, we present our ongoing work on development of a visual design tool for designing planar parallel manipulators that satisfy a given rational motion. Although in this paper, we have restricted ourselves to RRR- and RPR-type legs, the approach presented here is general enough to accommodate other leg topologies. The basic idea is to represent the kinematic constraint of such parallel manipulators as an algebraic manifold and the given motion as a one-parameter curve in the image space of planar displacements. The algebraic manifold is projected in the three-dimensional space and a simple set of relationships are obtained that couple the geometry of the projected manifold to the design parameters of the parallel manipulators. Simple geometric transformations in the projected space allow a user to visually contain the image curve inside the manifold, thus satisfying the kinematic constraints. This interactive process, at the end, gives the dimensions of the links of the legs and the location of the fixed and moving frames. This is an extension of our previous work on the dimensional synthesis of planar 6R closed chains.

FORCE-UNCONSTRAINED POSES OF THE 3-PRR AND 4-PRR PLANAR PARALLEL MANIPULATORS

2005 ◽  
Vol 29 (4) ◽  
pp. 617-628 ◽  
Author(s):  
Flavio Firmani ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulator ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Task Space ◽  
Planar Parallel Manipulator ◽  
Order Polynomial ◽  
Position And Orientation ◽  
Planar Parallel Manipulators ◽  
Three Dimensional Space

Force-unconstrained (singular) poses of the 3-PRR planar parallel manipulator (PPM), where the underscore indicates the actuated joint, and the 4-PRR, a redundant PPM with an additional actuated branch, are presented. The solution of these problems is based upon concepts of reciprocal screw quantities and kinematic analysis. In general, non-redundant PPMs such as the 3-PRR are known to have two orders of infinity of force-unconstrained poses, i.e., a three-variable polynomial in terms of the task-space variables (position and orientation of the mobile platform). The inclusion of redundant branches eliminates one order of infinity of force-unconstrained configurations for every actuated branch beyond three. The geometric identification of force-unconstrained poses is carried out by assuming one variable for each order of infinity. In order to simplify the algebraic procedure of these problems, the assumed or “free” variables are considered to be joint displacements. For both manipulators, an effective elimination technique is adopted. For the 3-PRR, the roots of a 6th-order polynomial determine the force-unconstrained poses, i.e., surfaces in a three dimensional space defined by the task-space variables. For the 4-PRR, a 64th-order polynomial determines curves of force-unconstrained poses in the same dimensional space.

scholarly journals A Moving Frame Trajectory Tracking Method of a Flying-Wing UAV Using the Differential Geometry

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Flight Control ◽  
Trajectory Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Dynamic Equations ◽  
Moving Frame ◽  
Moving Frames ◽  
Tracking Method ◽  
Tracking Process

The problem of UAV trajectory tracking is a difficult issue for scholars and engineers, especially when the target curve is a complex curve in the three-dimensional space. In this paper, the coordinate frames during the tracking process are transformed to improve the tracking result. Firstly, the basic concepts of the moving frame are given. Secondly the transfer principles of various moving frames are formulated and the Bishop frame is selected as a final choice for its flexibility. Thirdly, the detailed dynamic equations of the moving frame tracking method are formulated. In simulation, a moving frame of an elliptic cylinder helix is formulated precisely. Then, the devised tracking method on the basis of the dynamic equations is tested in a complete flight control system with 6 DOF nonlinear equations of the UAV. The simulation result shows a satisfactory trajectory tracking performance so that the effectiveness and efficiency of the devised tracking method is proved.

FORCE-UNCONSTRAINED POSES FOR PARALLEL MANIPULATORS WITH REDUNDANT ACTUATED BRANCHES

2005 ◽  
Vol 29 (3) ◽  
pp. 343-356 ◽  
Author(s):  
Flavio Firmani ◽  
Ron P. Podhorodeski
Keyword(s):  
Dimensional Space ◽  
Parallel Manipulators ◽  
End Effector ◽  
Input And Output ◽  
Planar Manipulators ◽  
Order Polynomial ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Actuated Joints ◽  
Planar Parallel Manipulators

A study of the effect of including a redundant actuated branch on the existence of force-unconstrained configurations for a planar parallel layout of joints is presented1. Two methodologies for finding the force-unconstrained poses are described and discussed. The first method involves the differentiation of the nonlinear kinematic constraints of the input and output variables with respect to time. The second method makes use of the reciprocal screws associated with the actuated joints. The force-unconstrained poses of non-redundantly actuated planar parallel manipulators can be mathematically expressed by means of a polynomial in terms of the three variables that define the dimensional space of the planar manipulator, i.e., the location and orientation of the end-effector. The inclusion of redundant actuated branches leads to a system of polynomials, i.e., one additional polynomial for each redundant branch added. Elimination methods are employed to reduce the number of variables by one for every additional polynomial. This leads to a higher order polynomial with fewer variables. The roots of the resulting polynomial describe the force-unconstrained poses of the manipulator. For planar manipulators it is shown that one order of infinity of force-unconstrained configurations is eliminated for every actuated branch, beyond three, added. As an example, the four-branch revolute-prismatic-revolute mechanism (4-RPR), where the prismatic joints are actuated, is presented.

scholarly journals Design, Optimization and Analysis of Supersonic Radial Turbines

2019 ◽  
Author(s):  
Lukas Benjamin Inhestern ◽  
James Braun ◽  
Guillermo Paniagua ◽  
José Ramón Serrano Cruz
Keyword(s):  
High Performance ◽  
Ad Hoc ◽  
Three Dimensional ◽  
Critical Factor ◽  
Design Tool ◽  
Navier Stokes ◽  
Design Parameters ◽  
Design Variables ◽  
Compact Design ◽  
Radial Outflow

Abstract New compact engine architectures such as pressure gain combustion require ad-hoc turbomachinery to ensure an adequate range of operation with high performance. A critical factor for supersonic turbines is to ensure the starting of the flow passages, which limits the flow turning and airfoil thickness. Radial outflow turbines inherently increase the cross section along the flow path, which holds great potential for high turning of supersonic flow with a low stage number and guarantees a compact design. First the preliminary design space is described. Afterwards a differential evolution multi-objective optimization with 12 geometrical design parameters is deducted. With the design tool AutoBlade 10.1, 768 geometries were generated and hub, shroud, and blade camber line were designed by means of Bezier curves. Outlet radius, passage height, and axial location of the outlet were design variables as well. Structured meshes with around 3.7 million cells per passage were generated. Steady three dimensional Reynolds averaged Navier Stokes (RANS) simulations, enclosed by the k-omega SST turbulence model were solved by the commercial solver CFD++. The geometry was optimized towards low entropy and high power output. To prove the functionality of the new turbine concept and optimization, a full wheel unsteady RANS simulation of the optimized geometry exposed to a nozzled rotating detonation combustor (RDC) has been performed and the advantageous flow patterns of the optimization were also observed during transient operation.

scholarly journals Development of Dynamics for Design Procedure of Novel Grating Tiling Device with Experimental Validation

2021 ◽  
Vol 11 (24) ◽  
pp. 11716
Author(s):  
Qingshun Bai ◽  
Mohamed Shehata ◽  
Ayman Nada ◽  
Zhongxi Shao
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Real Life ◽  
Design Procedure ◽  
Industrial Applications ◽  
Differential Algebraic Equations ◽  
System Stability ◽  
Design Parameters ◽  
Measuring Instruments ◽  
Algebraic Equations

The article proposes a dynamic for design (DFD) procedure for a novel aperture grating tiling device using the multibody system (MBS) approach. The grating device is considered as a rigid-flexible MBS that is built primarily based totally at the load assumptions because of grating movement. This movement is utilized in many industrial applications, such as the compression of laser pulse, precision measuring instruments, and optical communication. A new design procedure of tiling grating device frame is introduced in order to optimize its design parameters and enhance the system stability. The dynamic loads are estimated based on the Lagrange multipliers that are obtained from the solution of the MBS model. This model is fully non-linear and moves in the three-dimensional space, and the relative movement of its bodies is restricted by the description of the constraints function in the motion manifold. The mechanism of the grating device is structurally analyzed in keeping with the dynamic conduct and therefore the generated forces. The symbolic manipulation as well as the computational work of solving the obtained differential-algebraic equations (DAEs) is carried out using MATLAB Symbolic Toolbox. Once the preliminary design has been attained, the stress behavior of the grating device is examined using the MATLAB FEATool Multiphysics toolkit, regarding system stability and design aspects. Moreover, the design was constructed in real life, and the movement has been verified experimentally, which confirms the effectiveness of the proposed procedure. In conclusion, the DFD procedure with trade-off optimization is utilized successfully to design the grating unit for maximum ranges of grating movements.

Motion Synthesis Using Kinematic Mappings

1983 ◽  
Vol 105 (3) ◽  
pp. 460-467 ◽  
Author(s):  
B. Ravani ◽  
B. Roth
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Algebraic Theory ◽  
Planar Motion ◽  
Dimensional Synthesis ◽  
Structural Error ◽  
Quality Of Motion ◽  
Kinematic Mapping ◽  
Motion Approximation

This paper studies planar motion approximation problems in the context of a kinematic mapping. Since a planar displacement is determined by three parameters, it can be mapped into a point of a three-dimensional space. A (single-degree-of-freedom) planar motion can, therefore, be represented by a space curve in the space of the mapping and the problem of motion approximation becomes a curve fitting problem in this space. A mapping introduced by Blaschke is used and a general theory for planar motion approximation is developed. The theory is then applied to dimensional synthesis of four-link mechanisms. Furthermore, since the structural error (i.e., the quality of motion approximation) is dependent on the closeness of the fit in the space of the mapping, a general algebraic theory for determining closest fits to points in this space is developed. The theory is illustrated by a numerical example.

Three-Dimensional Modeling of Opposed Biconical Cone Screw High-Pressure Seawater Hydraulic Pump

2013 ◽  
Vol 310 ◽  
pp. 287-293 ◽  
Author(s):  
Xin Hua Wang ◽  
Zhi Ben Gong ◽  
Li Wei Wang ◽  
Shun Wen Sun ◽  
Gang Zheng
Keyword(s):  
High Pressure ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Design Parameters ◽  
Hydraulic Pump ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
New Type ◽  
Design And Manufacture ◽  
Matlab Programming

The rotor and stator were major components of the opposed biconinal cone screw high pressure seawater hydraulic pump, which precision of design and manufacture was particularly high, and the combining status between the stator and rotor has a significant impact on the performance of the new type pump, so the related research on above problems are carried out. In order to satisfy the demands of design efficiency and manufacture decision, a fast and simple way was presented to model 3D cone screw and bushing. Three-dimensional space Cartesian coordinates of cone screw and bushing profile with MATLAB programming were obtained according to the cone screw and bushing surface equation and the design parameters,3D curves of cone screw and bushing with MATLAB were rendered, and the feature point space coordinates were imported to Pro/Engineer so as to build cone screw and bushing solid model. Finally, making virtual assembly and checking interference on the screw and the bushing were necessary. The proposed method can make the complex 3D modeling more accurate, feasible and efficient.

scholarly journals Implementing Speech Recognition in Virtual Reality

2002 ◽  
Author(s):  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Virtual Reality ◽  
Speech Recognition ◽  
Virtual Environment ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Design Tool ◽  
Product Development Process ◽  
Engineering Product ◽  
Digital Representations ◽  
And Control

Virtual Reality (VR) is becoming an important tool in the engineering product development process. The virtual environment provides the user with the ability to interact with three-dimensional digital representations of products using natural head and hand motions. While interacting with digital objects in VR seems natural, the use of traditional two-dimensional menu systems does not always provide a convenient interface to controlling task specifications in the three-dimensional space. New human-computer-interfaces are needed for this emerging VR design tool. This paper will present the details of implementing a speaker-independent, command and control, speech recognition menuing system for a virtual reality application. The menuing system will be described as it is incorporated into a virtual environment for the design of spatial mechanisms. Design and technical issues involved in the interface creation process are discussed and the resulting interaction system is described.

scholarly journals Design, Optimization, and Analysis of Supersonic Radial Turbines

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Lukas Benjamin Inhestern ◽  
James Braun ◽  
Guillermo Paniagua ◽  
José Ramón Serrano Cruz
Keyword(s):  
High Performance ◽  
Ad Hoc ◽  
Three Dimensional ◽  
Critical Factor ◽  
Design Tool ◽  
Navier Stokes ◽  
Design Parameters ◽  
Design Variables ◽  
Compact Design ◽  
Radial Outflow

Abstract New compact engine architectures such as pressure gain combustion require ad hoc turbomachinery to ensure an adequate range of operation with high performance. A critical factor for supersonic turbines is to ensure the starting of the flow passages, which limits the flow turning and airfoil thickness. Radial outflow turbines inherently increase the cross section along the flow path, which holds great potential for high turning of supersonic flow with a low stage number and guarantees a compact design. First, the preliminary design space is described. Afterward a differential evolution multi-objective optimization with 12 geometrical design parameters is deducted. With the design tool autoblade 10.1, 768 geometries were generated and hub, shroud, and blade camber line were designed by means of Bezier curves. Outlet radius, passage height, and axial location of the outlet were design variables as well. Structured meshes with around 3.7 × 106 cells per passage were generated. Steady three-dimensional (3D) Reynolds-averaged Navier–Stokes (RANS) simulations, enclosed by the k-omega shear stress transport turbulence model were solved by the commercial solver CFD++. The geometry was optimized toward low entropy and high-power output. To prove the functionality of the new turbine concept and optimization, a full wheel unsteady RANS simulation of the optimized geometry exposed to a nozzled rotating detonation combustor (RDC) has been performed and the advantageous flow patterns of the optimization were also observed during transient operation.

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