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.

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.

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.

Kinetostatic Synthesis of Coupled Serial Chains

1998 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Virtual Work ◽  
Degree Of Freedom ◽  
Optimal Synthesis ◽  
Synthesis Problem ◽  
Equilibrium Equations ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Angular Velocities ◽  
Kinematic Loop ◽  
Serial Chains

Abstract Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms are a novel class of modular and compact mechanisms with single degree-of-freedom actuation and control. In this paper, the kinetostatic synthesis of SDCSC mechanisms is addressed. Using the principle of virtual work, the static force equilibrium equations are developed for two-link SDCSCs. These are combined with the previously developed kinematic loop-closure equations to solve the kinetostatic precision point synthesis problem. Since the ratios of the angular velocities at the joints are constants by virtue of cable-pulley coupling in SDCSCs, it possible to render the kinetostatic equations linear in terms of the mechanism parameters. As a result, the solution of the precision point synthesis problem of SDCSCs becomes simpler compared to that of the four-bar mechanism. In order to meet additional criteria such as minimizing the maximum torque required over the entire range of motion of the mechanism, an optimization problem is formulated. The free choices in the precision point synthesis are used as variables in the optimal synthesis problem. The paper also addresses how torsional springs at the joints can be utilized to reduce the required input torque in supporting a specified load at the end-effector. Numerical examples are presented to illustrate the precision point and the optimal synthesis of two-link SDCSC mechanism with and without torsional springs at the joints.

Dimensional Synthesis of CRR Serial Chains

2003 ◽  
Author(s):  
Alba Perez ◽  
J. M. McCarthy
Keyword(s):  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Dual Quaternion ◽  
Kinematic Synthesis ◽  
Revolute Joints ◽  
Serial Chain ◽  
In Series ◽  
Synthesis Methodology ◽  
Serial Chains

This paper presents the kinematic synthesis of a CRR serial chain. This is a four-degree-of-freedom chain constructed from a cylindric joint and two revolute joints in series. The design equations for this chain are obtained from the dual quaternion kinematics equations evaluated at a specified set of task positions. In this case, we find that the chain is completely defined by seven task positions. Furthermore, our solution of these equations has yielded 52 candidate designs, so far; there may be more. This synthesis methodology shows promise for the design of constrained serial chains.

Synthesis and Application of a Single Degree-of-Freedom Six-Bar Linkage with Mixed Exact and Approximate Pose Constraints

2020 ◽  
pp. 1-39
Author(s):  
Xiong Zhao ◽  
Chennan Yu ◽  
Jianneng Chen ◽  
Xincheng Sun ◽  
Jun Ye ◽  
...  
Keyword(s):  
Synthesis Method ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Test Results ◽  
Single Degree Of Freedom ◽  
Solution Domain ◽  
Rehabilitation Training ◽  
Single Degree ◽  
New Synthesis ◽  
The Ideal

Abstract Existing research on synthesis methods for single degree-of-freedom (DOF) six-bar linkages mainly include four or five exact poses. However, an ideal trajectory cannot be synthesized using only five exact poses, thus, it is necessary to introduce additional poses to constrain the trajectory. If more exact poses are introduced, then the linkage may have no solution. Therefore, the constraints of the approximate pose are considered to make the trajectory conform to the desired trajectory. This paper successfully introduces mixed poses into a six-bar linkage, based on Z (Z<5) exact poses and K approximate poses of a given error range, and a new synthesis method for single DOF six-bar linkages is proposed. The solution domain of the linkages synthesized by this method is wide and can be adjusted by controlling the error of the approximate poses, which reduces the difficulty of selecting the solution, ensures theoretical feasibility, and enables the trajectory of the final linkage to more closely match the ideal trajectory. Finally, for the coordinated training of multiple joints in human limbs, a rehabilitation device is designed based on the above six-bar linkage, and a prototype is developed and tested. The test results reveal the accuracy of the proposed method and the effectiveness of rehabilitation training.

Synthesis of Spatial Two-Link Coupled Serial Chains

1998 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Path Following ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Serial Chain ◽  
Serial Chains ◽  
Selection Of

Abstract We address the synthesis of serial chain spatial mechanisms with revolute joints in which the rotations about the joints are coupled via cables and pulleys. Such coupled serial chain mechanisms offer a middle ground between the more versatile and compact serial chains and the simpler closed chains by combining some of the advantages of both types of systems. In particular, we focus on the synthesis of single degree-of-freedom, coupled serial chains with two revolute joints. We derive precision point synthesis equations for two precision points by combining the loop closure equations with the necessary geometric constraints in terms of the unknown mechanism parameters. This system of equations can now be solved linearly for the link vectors after a suitable selection of free choices. We optimize over the free choices to generate an end effector trajectory that closely approximates a desired end effector trajectory for motion generation and path following applications.

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.

Design of a Single Degree-of-Freedom, Adaptable Electromechanical Gait Trainer for People With Neurological Injury

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Sung Yul Shin ◽  
Ashish D. Deshpande ◽  
James Sulzer
Keyword(s):  
Low Cost ◽  
Degree Of Freedom ◽  
Neurological Injury ◽  
Link Length ◽  
Gait Patterns ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Wide Range ◽  
Robotic Gait ◽  
Gait Trainer

The cost of therapy is one of the most significant barriers to recovery after neurological injury. Robotic gait trainers move the legs through repetitive, natural motions imitating gait. Recent meta-analyses conclude that such training improves walking function in neurologically impaired individuals. While robotic gait trainers promise to reduce the physical burden on therapists and allow greater patient throughput, they are prohibitively costly. Our novel approach is to design a new single degree-of-freedom (DoF) robotic trainer that maintains the key advantages of the expensive trainers but with a simplified design to reduce cost. Our primary design challenge is translating the motion of a single actuator to an array of natural gait trajectories. We address this with an eight-link Jansen mechanism that matches a generalized gait trajectory. We then optimize the mechanism to match different trajectories through link length adjustment based on nine different gait patterns obtained from gait database of 113 healthy individuals. To physically validate the range in gait patterns produced by the simulation, we tested kinematic accuracy on a motorized wooden proof-of-concept of the gait trainer. The simulation and experimental results suggested that an adjustment of two links can reasonably fit a wide range of gait patterns under typical within-subject variance. We conclude that this design could provide the basis for a low-cost, patient-based electromechanical gait trainer for neurorecovery.

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