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.

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.

Dimensional Synthesis of Planar Eight-Bar Linkages Based on a Parallel Robot With a Prismatic Base Joint

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Fangtian Ying
Keyword(s):  
Rigid Body ◽  
Design Process ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Prismatic Joint ◽  
Serial Chain ◽  
Different Types

This paper details the dimensional synthesis for the rigid body guidance of planar eight-bar linkages that could be driven by a prismatic joint at its base. We show how two RR cranks can be added to a planar parallel robot formed by a PRR and 3R serial chain to guide its end-effector through a set of five task poses. This procedure is useful for designers who require the choice of ground pivot locations. The results are eight different types of one-degree of freedom planar eight-bar linkages. We demonstrate the design process with the design of a multifunctional wheelchair that could transform its structure between a self-propelled wheelchair and a walking guide.

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.

scholarly journals A Design System for Six-Bar Linkages Integrated With a Solid Modeler

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Kaustubh H. Sonawale ◽  
J. Michael McCarthy
Keyword(s):  
Degree Of Freedom ◽  
Design System ◽  
Solid Model ◽  
Design Algorithm ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Serial Chain ◽  
Tolerance Zones ◽  
Spherical Linkages ◽  
Solid Modeler

This paper presents a design system for planar and spherical six-bar linkages, which is integrated with a solid modeler. The user specifies a backbone 3R chain in five task configurations in the sketch mode of the solid modeler and executes the design system. Two RR constraints are computed, which constrain the 3R chain to a single degree-of-freedom six-bar linkage. There are six ways that these constraints can be added to the 3R serial chain to yield as many as 63 different linkages in case of planar six-bar linkages and 165 in case of spherical six-bar linkages. The performance of each candidate is analyzed, and those that meet the required task are presented to the designer for selection. The design algorithm is run iteratively with random variations applied to the task configurations within user-specified tolerance zones, to increase the number of candidate designs. The output is a solid model of the six-bar linkage. Examples are presented, which demonstrate the effectiveness of this strategy for both planar and spherical linkages.

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.

Detection of Degenerate Structure in Single Degree-of-Freedom Planetary Gear Trains

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
Graph Theory ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Structural Synthesis ◽  
Drastic Reduction ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Planetary Gear Trains ◽  
Gear Trains

Graph theory is a powerful tool in structural synthesis and analysis of planetary gear trains (PGTs). In this paper, a new algorithm has been developed for detecting degenerate structure in planetary gear trains. The proposed algorithm is based on the concept of fundamental circuits' rotation graphs. Detection of degeneracy is entirely based on finding one key element. The key element or link that makes planetary gear train into two groups is found in this work. The main advantage of the proposed method lies in the drastic reduction in the required combinatorial analysis compared to other methods available.

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