Synthesis of Path Generation Compliant Mechanisms Using Variable Width Spline Curves

2014 ◽  
Author(s):  
Hong Zhou ◽  
Nisar Ahmed
Keyword(s):  
Compliant Mechanisms ◽  
Path Generation ◽  
Shape Description ◽  
Control Parameters ◽  
Spline Curve ◽  
Spline Curves ◽  
Curved Paths ◽  
Generation Mechanisms ◽  
Synthesis Approach ◽  
Interpolation Nodes

Path generation is to guide a point tracing a prescribed path. Compliant mechanisms (CMs) have been synthesized for path generation mechanisms. In this paper, each connection in a synthesized CM is represented as a variable width spline curve and the entire synthesized CM is modeled as a set of variable width spline curves. The synthesis of a path generation CM is systemized as the optimization of control parameters of a set of variable width spline curves. A variable width spline curve is a center spline curve with variable perpendicular width. The center spline curve is for the shape description of its represented connection while variable width is for the size of the connection. The shape and size of a variable width spline curve is defined by its interpolation circles. The locations of interpolation circles are utilized as interpolation nodes of the center spline curve for connection shape and the diameters of interpolations circles are interpolated for connection size. The centers of all interpolation circles in a synthesized CM form a network of nodes. The network of nodes decides the topology of the synthesized CM and can be classified based on degree of genus (DOG). The presented synthesis approach is demonstrated by synthesizing CMs with different DOGs to generate curved paths.

Synthesis of Constant Torque Compliant Mechanisms

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Hari Nair Prakashah ◽  
Hong Zhou
Keyword(s):  
Compliant Mechanisms ◽  
Large Range ◽  
Compliant Mechanism ◽  
Design Domain ◽  
Control Parameters ◽  
Constant Torque ◽  
Fixed Ring ◽  
Output Torque ◽  
Spline Curves ◽  
Medical And Healthcare

Constant torque compliant mechanisms produce an output torque that does not change in a large range of input rotation. They have wide applications in aerospace, automobile, timing, gardening, medical, and healthcare devices. Unlike constant force compliant mechanisms, the synthesis of constant torque compliant mechanisms has not been extensively investigated yet. In this paper, a method is presented for synthesizing constant torque compliant mechanisms that have coaxial input rotation and output torque. The same shaft is employed for both input rotation and output torque. A synthesized constant torque compliant mechanism is modeled as a set of variable width spline curves within an annular design domain formed between a rotation shaft and a fixed ring. Interpolation circles are used to define variable width spline curves. The synthesis of constant torque compliant mechanisms is systematized as optimizing the control parameters of the interpolation circles of the variable width spline curves. The presented method is demonstrated by the synthesis of constant torque compliant mechanisms that have different number of variable width spline curves in this paper.

Synthesizing Bidirectional Constant Torque Compliant Mechanisms

2017 ◽  
Author(s):  
Bhavanam Praveen Reddy ◽  
Hong Zhou
Keyword(s):  
Unique Feature ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Control Parameters ◽  
Curved Beams ◽  
Rotation Direction ◽  
Constant Torque ◽  
Output Torque ◽  
Spline Curves

The output or resisting torque from a constant torque compliant mechanism keeps invariant in a large range of input rotation. Unlike regular constant torque compliant mechanisms that have only one input rotation direction, the input rotation of a bidirectional constant torque compliant mechanism can be either clockwise or counter-clockwise. Its resisting or output torque reverses its direction with the change of the input rotation direction. The unique feature of bidirectional constant torque compliant mechanisms makes their synthesis challenging. In this paper, a synthesis method is introduced to surmount the synthesis challenges. The constant resisting torque is generated through a set of curved beams that are mounted within an annular design domain. Because of the bidirectional requirement, the two ends of each curved beam are aligned along radial direction before deformation to avoid rotational bias. Spline curves are employed to describe curved beams and defined by their control parameters. The synthesis of a bidirectional constant torque compliant mechanism is systematized as optimizing the control parameters of its curved beams. The presented method is demonstrated by the synthesis of bidirectional constant torque compliant mechanisms that have different arrangements of curved beams in the paper.

Synthesis of Constant Torque Compliant Mechanisms

2015 ◽  
Author(s):  
Hong Zhou ◽  
Hari Nair Prakashah
Keyword(s):  
Compliant Mechanisms ◽  
Large Range ◽  
Compliant Mechanism ◽  
Design Domain ◽  
Control Parameters ◽  
Constant Torque ◽  
Fixed Ring ◽  
Output Torque ◽  
Spline Curves ◽  
Medical And Healthcare

Constant torque compliant mechanisms produce an output torque that does not change in a large range of input rotation. They have wide applications in aerospace, automobile, timing, gardening, medical and healthcare devices. Unlike constant force compliant mechanisms, the synthesis of constant torque compliant mechanisms has not been extensively investigated yet. In this paper, a method is presented for synthesizing constant torque compliant mechanisms that have coaxial input rotation and output torque. The same shaft is employed for both input rotation and output torque. A synthesized constant torque compliant mechanism is modeled as a set of variable width spline curves within an annular design domain formed between a rotation shaft and a fixed ring. Interpolation circles are used to define variable width spline curves. The synthesis of constant torque compliant mechanisms is systematized as optimizing the control parameters of the interpolation circles of the variable width spline curves. The presented method is demonstrated by the synthesis of constant torque compliant mechanisms that have different number of variable width spline curves in the paper.

Synthesis of Concave Helical Compression Springs

2015 ◽  
Author(s):  
Naresh Kumar Gandham ◽  
Hong Zhou
Keyword(s):  
Cylindrical Shape ◽  
Control Parameters ◽  
Spline Curve ◽  
Variable Diameter ◽  
Compression Spring ◽  
Spring Wire ◽  
Coil Diameter ◽  
Constant Pitch ◽  
The Common ◽  
Compression Springs

Helical compression springs are used to resist compressive forces or store energy in push mode. They are found in many applications that include automotive, aerospace and medical devices. The common configuration of helical compression springs is straight cylindrical shape that has constant coil diameter, constant pitch and constant spring rate. Unlike cylindrical helical compression springs, concave helical compression springs have a larger diameter at each end and a smaller diameter in the middle of the spring. The variable coil diameter enables them to produce desired load deflection characteristics, reduce solid height, buckling and surging, and keep them centered on a larger diameter hole. The unique features of concave helical compression springs also raise their synthesis challenges. In this paper, a method is introduced to synthesize concave helical compression springs. The variable coil diameter of a concave helical compression spring is described by a spline curve. A cylinder with variable diameter is generated by revolving the spline curve on spring axis. The concave helical compression spring is then modeled by wrapping a spring wire on the variable diameter cylinder. The synthesis of a concave helical compression spring is systemized as the optimization of the geometric control parameters of its wrapped spring wire. A synthesis example is presented in the paper to verify the effectiveness and demonstrate the procedure of the introduced method.

Design of Crashworthy Structures With Controlled Energy Absorption in the Hybrid Cellular Automaton Framework

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Punit Bandi ◽  
James P. Schmiedeler ◽  
Andrés Tovar
Keyword(s):  
Energy Absorption ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanism Synthesis ◽  
Load Paths ◽  
Fully Stressed Design ◽  
Novel Method ◽  
The Given ◽  
Synthesis Approach

This work presents a novel method for designing crashworthy structures with controlled energy absorption based on the use of compliant mechanisms. This method helps in introducing flexibility at desired locations within the structure, which in turn reduces the peak force at the expense of a reasonable increase in intrusion. For this purpose, the given design domain is divided into two subdomains: flexible (FSD) and stiff (SSD) subdomains. The design in the flexible subdomain is governed by the compliant mechanism synthesis approach for which output ports are defined at the interface between the two subdomains. These output ports aid in defining potential load paths and help the user make better use of a given design space. The design in the stiff subdomain is governed by the principle of a fully stressed design for which material is distributed to achieve uniform energy distribution within the design space. Together, FSD and SSD provide for a combination of flexibility and stiffness in the structure, which is desirable for most crash applications.

Constant Force Compliant Mechanisms Without Preloading

2021 ◽  
Author(s):  
Premkumar Pujali ◽  
Hong Zhou
Keyword(s):  
Compliant Mechanisms ◽  
Large Range ◽  
Compliant Mechanism ◽  
Experimental Results ◽  
Design Parameters ◽  
Constant Force ◽  
Spline Curves ◽  
Output Force

Abstract A constant force compliant mechanism generates an output force that keeps invariant in a large range of input displacement. Because of the constant force feature and the merits of compliant mechanisms, they are utilized in many applications. A problem in the current constant force compliant mechanisms is their preloading range that is a certain starting range of the input displacement. In the preloading displacement, the output force of a constant force compliant mechanism does not have the desired value. It goes up from zero value. The preloading displacement often occupies one quarter or more of the entire input displacement range, which weakens the performance of constant force compliant mechanisms. The preloading issue is eradicated in this research by using prebuckled beams as components for constructing constant force compliant mechanisms. It is difficult to synthesize constant force compliant mechanisms that are composed of prebuckled beams because of the intertwined force, buckling and deflection characteristics. In this research, the undeformed beams are represented by spline curves and controlled by its interpolation points. The synthesis of constant force compliant mechanisms is systemized as optimizing the design parameters of the composed prebuckled beams. Fully compliant constant force compliant mechanisms are synthesized without preloading. The synthesis solutions are validated by experimental results.

scholarly journals A Parametrization-Invariant Fourier Approach to Planar Linkage Synthesis for Path Generation

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Xiangyun Li ◽  
Peng Chen
Keyword(s):  
Design Space ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Arc Length ◽  
Efficient Synthesis ◽  
Practical Applications ◽  
Classic Problem ◽  
Fourier Theory ◽  
Planar Linkages ◽  
Synthesis Approach

This paper deals with the classic problem of the synthesis of planar linkages for path generation. Based on the Fourier theory, the task curve and the synthesized four-bar coupler curve are regarded as the same curve if their Fourier descriptors match. Using Fourier analysis, a curve must be given as a function of time, termed a parametrization. In practical applications, different parametrizations can be associated with the same task and coupler curve, respectively; however, these parametrizations are Fourier analyzed to different Fourier descriptors, thus resulting in the mismatch of the task and coupler curve. In this paper, we present a parametrization-invariant method to eliminate the influence of parametrization on the values of Fourier descriptors by unifying given parametrizations to the arc length parametrization; meanwhile, a new design space decoupling scheme is introduced to separate the shape, size, orientation, and location matching of the task and four-bar curve, which leads naturally to an efficient synthesis approach.

T-B Spline Curves with a Shape Parameter

2012 ◽  
Vol 241-244 ◽  
pp. 2144-2148
Author(s):  
Li Juan Chen ◽  
Ming Zhu Li
Keyword(s):  
Shape Parameter ◽  
Simple Structure ◽  
Control Points ◽  
Curve Segment ◽  
Closed Curves ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves

A T-B spline curves with a shape parameter λ is presented in this paper, which has simple structure and can be used to design curves. Analogous to the four B-spline curves, each curve segment is generated by five consecutive control points. For equidistant knots, the curves are C^2 continuous, but when the shape parameter λ equals to 0 , the curves are C^3 continuous. Moreover, this spline curve can be used to construct open and closed curves and can express ellipses conveniently.

Approximate Merging B-Spline Curves via Least Square Approximation

2014 ◽  
Vol 556-562 ◽  
pp. 3496-3500 ◽  
Author(s):  
Si Hui Shu ◽  
Zi Zhi Lin
Keyword(s):  
Approximation Error ◽  
Least Square ◽  
Error Tolerance ◽  
Knot Insertion ◽  
Least Squares Approximation ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves ◽  
Insertion Algorithm ◽  
Approximate Merging

An algorithm of B-spline curve approximate merging of two adjacent B-spline curves is presented in this paper. In this algorithm, the approximation error between two curves is computed using norm which is known as best least square approximation. We develop a method based on weighed and constrained least squares approximation, which adds a weight function in object function to reduce error of merging. The knot insertion algorithm is also developed to meet the error tolerance.

Sign in / Sign up

Export Citation Format

Share Document