Singularity Free Revolute–Prismatic–Revolute and Spherical–Prismatic–Spherical Chains for Actuating Planar and Spherical Single Degree of Freedom Mechanisms

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
David A. Perkins ◽  
Andrew P. Murray
Keyword(s):  
Reference Frame ◽  
Unique Fixed Point ◽  
Degree Of Freedom ◽  
Moving Frame ◽  
Dimensional Synthesis ◽  
Planar Case ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Fixed Frame ◽  
Spherical Mechanism

Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually increases or decreases in distance from a point in the fixed frame over the entire motion. These points can be used to define a revolute–prismatic–revolute (RPR) chain for a planar mechanism or a spherical–prismatic–spherical (SPS) chain for a spherical mechanism capable of actuating the device over its entire range of motion. Moreover, the singularities relative to the joints in the original mechanism are not a concern and the dimensional synthesis can focus on creating the set of circuit-defect free solutions. From this analysis, a unique fixed point is determined in the planar case relative to two positions and their velocities with the following characteristic. All points in the moving reference frame that are moving away from it in the first position are approaching it in the second position, and vice versa. This point is as critical to the identification of singularity-free driving chains as the centrodes or the poles.

Singularity-Free RPR and SPS Chains for Actuating Single Degree of Freedom Planar and Spherical Mechanisms

2010 ◽  
Author(s):  
David A. Perkins ◽  
Andrew P. Murray
Keyword(s):  
Reference Frame ◽  
Unique Fixed Point ◽  
Degree Of Freedom ◽  
Moving Frame ◽  
Dimensional Synthesis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Fixed Frame ◽  
Spherical Mechanisms ◽  
Spherical Mechanism

This paper presents a method of selecting joints relative to a fixed and moving (coupler) frame that can be used to actuate a single degree of freedom planar mechanism using a revolute-prismatic-revolute (RPR) chain or a spherical mechanism via a spherical-prismatic-spherical (SPS) chain. Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually increases or decreases in distance from a point in the fixed frame over the entire motion. The mechanism can then be moved by placing an actuated prismatic joint between the two points. Moreover, the singularities relative to the joints in the original mechanism are not a concern and the dimensional synthesis can focus on creating the set of circuit-defect free solutions. From this analysis, a unique fixed point is determined relative to two positions and their velocities with the following characteristic. All points in the moving reference frame that are moving away from it in the first position are approaching it in the second position, and vice versa.

Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 232-241 ◽  
Author(s):  
Xichun Nie ◽  
Venkat Krovi
Keyword(s):  
Low Cost ◽  
Synthesis Method ◽  
Path Following ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Serial Chain ◽  
End Effectors ◽  
Serial Chains

Single degree-of-freedom coupled serial chain (SDCSC) mechanisms are a class of mechanisms that can be realized by coupling successive joint rotations of a serial chain linkage, by way of gears or cable-pulley drives. Such mechanisms combine the benefits of single degree-of-freedom design and control with the anthropomorphic workspace of serial chains. Our interest is in creating articulated manipulation-assistive aids based on the SDCSC configuration to work passively in cooperation with the human operator or to serve as a low-cost automation solution. However, as single-degree-of-freedom systems, such SDCSC-configuration manipulators need to be designed specific to a given task. In this paper, we investigate the development of a synthesis scheme, leveraging tools from Fourier analysis and optimization, to permit the end-effectors of such manipulators to closely approximate desired closed planar paths. In particular, we note that the forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. The proposed Fourier-based synthesis method exploits this special structure to achieve the combined number and dimensional synthesis of SDCSC-configuration manipulators for closed-loop planar path-following tasks. Representative examples illustrate the application of this method for tracing candidate square and rectangular paths. Emphasis is also placed on conversion of computational results into physically realizable mechanism designs.

Analytical method for the singularity analysis and exhaustive enumeration of the singularity conditions in single-degree-of-freedom spherical mechanisms

2012 ◽  
Vol 227 (8) ◽  
pp. 1830-1840 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytical Method ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Systems Of Equations ◽  
Single Degree Of Freedom ◽  
Planar Mechanism ◽  
Single Degree ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism

In spherical-mechanism kinematics, instantaneous pole axes play the same role as, in planar-mechanism kinematics, instant centres. Their locations only depend on the mechanism configuration when spherical single-degree-of-freedom mechanisms are considered. Such a property makes them a tool to visualize and/or to analyse the instantaneous kinematics of those mechanisms. This article addresses the singularity analysis of single-degree-of-freedom spherical mechanisms by exploiting the properties of instantaneous pole axes. An exhaustive enumeration of the geometric conditions which occur for all the singularity types is given, and a general analytical method based on this enumeration is proposed for implementing the singularity analysis. The proposed analytical method can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Kinematic and Kinetostatic Synthesis of Planar Coupled Serial Chain Mechanisms

2002 ◽  
Vol 124 (2) ◽  
pp. 301-312 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Solution Approach ◽  
Single Degree ◽  
Design Specifications ◽  
Serial Chain ◽  
Gear Trains ◽  
External Loads

Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms form a novel class of modular and compact mechanisms with a single degree-of-freedom, suitable for a number of manipulation tasks. Such SDCSC mechanisms take advantage of the hardware constraints between the articulations of a serial-chain linkage, created using gear-trains or belt/pulley drives, to guide the end-effector motions and forces. In this paper, we examine the dimensional synthesis of such SDCSC mechanisms to perform desired planar manipulation tasks, taking into account task specifications on both end-effector motions and forces. Our solution approach combines precision point synthesis with optimization to realize optimal mechanisms, which satisfy the design specifications exactly at the selected precision points and approximate them in the least-squares sense elsewhere along a specified trajectory. The designed mechanisms can guide a rigid body through several positions while supporting arbitrarily specified external loads. Furthermore, torsional springs are added at the joints to reduce the overall actuation requirements and to enhance the task performance. Examples from the kinematic and the kinetostatic synthesis of planar SDCSC mechanisms are presented to highlight the benefits.

scholarly journals GEOMETRICAL METHODS TO LOCATE SECONDARY INSTANTANEOUS POLES OF SINGLE-DOF INDETERMINATE SPHERICAL MECHANISMS

2011 ◽  
Vol 41 (2) ◽  
pp. 80-88 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Great Circle ◽  
Direct Application ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Spherical Mechanisms ◽  
Geometric Methods ◽  
Point Of Intersection ◽  
Spherical Mechanism ◽  
Work Done

A single-degree-of-freedom (DOF) indeterminate spherical mechanism is defined as a mechanism for which it is not possible to find all the instantaneous poles by direct application of the Aronhold-Kennedy theorem. This paper shows that a secondary instantaneous pole of a two DOFs spherical mechanism lies on a unique great circle instantaneously. Using this property, two geometric methods are presented to locate secondary instantaneous poles of indeterminate single DOF spherical mechanisms. Common approach of the methods is to convert a single DOF indeterminate spherical mechanism into a two DOFs mechanism and then to find two great circles that the unknown instantaneous pole lies on the point of intersection of them. The presented methods are directly deduced from a work done for indeterminate single DOF planar mechanisms.DOI: http://dx.doi.org/10.3329/jme.v41i2.7471

Serial Chains of Spherical Four-Bar Mechanisms to Achieve Design Helices

2014 ◽  
Author(s):  
Kevin S. Giaier ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Design Methodology ◽  
Degree Of Freedom ◽  
Spherical Equivalent ◽  
Kinematic Synthesis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Spherical Mechanisms ◽  
Spherical Mechanism ◽  
Serial Chains

This paper presents a method for designing serial chains of spherical four-bar mechanisms that can achieve up to five design helices. The chains are comprised of identical copies of the same four-bar mechanism by connecting the coupler of the prior spherical mechanism to the base link of the subsequent spherical mechanism. Although having a degree of freedom per mechanism, the design methodology is based upon identically actuating each mechanism. With these conditions, the kinematic synthesis task of matching periodically spaced points on up to five arbitrary helices may be achieved. Due to the constraints realized via the spherical equivalent of planar Burmester Theory, spherical mechanisms produce at most five prescribed orientations resulting in this maximum. The methodology introduces a companion helix to each design helix along which the intersection locations of each spherical mechanisms axes must lie. As the mechanisms are connected by rigid links, the distance between the intersection locations along the companion helices is a constant. An extension to the coupler matches the points along the design helices. An approach to mechanically reducing the chain of mechanisms to a single degree of freedom is also presented. Finally, an example shows the methodology applied to three design helices.

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