A Fourier Descriptor Approach to Integrated Type and Dimensional Synthesis of Coupled Serial Mechanism for Motion Generation

2019 ◽  
Author(s):  
Hao Lv ◽  
Yuanfei Han ◽  
Xiangyun Li ◽  
Liuxian Zhu
Keyword(s):  
Fourier Descriptor ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Motion Generation ◽  
End Effector ◽  
Novel Approach ◽  
Descriptor Approach ◽  
Harmonic Components ◽  
The Given ◽  
Serial Mechanism

Abstract Coupled serial mechanism is a class of mechanisms that couple the relative rotation of successive links utilizing gears or cable-pulley systems. They can be used to generate complex end-effector trajectories or motions with a single actuator. With the employment of Fourier descriptors, a novel approach to integrate type synthesis and dimensional synthesis of such mechanisms is proposed in this paper. Through the Fourier analysis of two arbitrary trajectories from the given motion, the simplest trajectory that contains the least number of harmonic components is identified. Then, characteristic information of those harmonics such as their numbers, amplitudes and initial phases are used to determine the topology and dimensions of the corresponding coupled serial mechanism, thus effectively solving the motion synthesis problem of this type of mechanisms. Finally, three examples are given to demonstrate the validity of the proposed method.

A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Q. J. Ge ◽  
Feng Gao
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Geometric Framework ◽  
Kinematic Chains ◽  
Kinematic Mapping ◽  
Spherical Linkages ◽  
Spatial Displacements ◽  
The Given

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

Task Driven Unified Synthesis of Planar Four-Bar and Six-Bar Linkages With Revolute and Prismatic Joints for Five Position Synthesis

2013 ◽  
Author(s):  
Ping Zhao ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Simple Algorithm ◽  
Standing Position ◽  
Type I ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Prismatic Joints ◽  
Seating Position ◽  
Position Synthesis ◽  
The Given ◽  
Synthesis Approach

This paper deals with the problem of integrated joint-type and dimensional synthesis of planar four-bar and six-bar linkages with revolute (R) and prismatic (P) joints for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. The current paper extends this algorithm to the integrated joint-type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages with a combination of R and P joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (Type I), one dyad (Type II), or no dyad (Type III). We demonstrate this task driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

A Fourier Descriptor-Based Approach to Design Space Decomposition for Planar Motion Approximation

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Xiangyun Li ◽  
Jun Wu ◽  
Q. J. Ge
Keyword(s):  
Design Space ◽  
Shape Descriptor ◽  
Harmonic Series ◽  
Design Parameters ◽  
Fourier Descriptor ◽  
Rotational Component ◽  
Motion Generation ◽  
Motion Approximation ◽  
Four Bar Linkage ◽  
The Given

In an earlier work, we have combined a curve fitting scheme with a type of shape descriptor, Fourier descriptor (FD), to develop a unified method to the synthesis of planar four-bar linkages for generation of both open and closed paths. In this paper, we aim to extend the approach to the synthesis of planar four-bar linkages for motion generation in an FD-based motion fitting scheme. Using FDs, a given motion is represented by two finite harmonic series, one for translational component of the motion and the other for rotational component. It is shown that there is a simple linear relationship between harmonic content of the rotational component and that of the translational component for a planar four-bar coupler motion. Furthermore, it is shown that the rotational component of the given motion identifies a subset of design parameters of a four-bar linkage including link ratios, while the translational component determines the rest of the design parameters such as locations of the fixed pivots. This leads naturally to a decomposed design space for four-bar mechanism synthesis for approximate motion generation.

Type Synthesis of a Family of Novel Four, Five, and Six Degrees-of-Freedom Sea Lion Ball Mechanisms With Three Limbs

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Rongfu Lin ◽  
Weizhong Guo ◽  
Feng Gao
Keyword(s):  
Mathematical Models ◽  
Degrees Of Freedom ◽  
Type Synthesis ◽  
Sea Lion ◽  
End Effector ◽  
Motion Patterns ◽  
Six Degrees Of Freedom ◽  
Rotational Motions ◽  
The Given ◽  
Actuated Joints

A family of novel mechanisms with three limbs called sea lion ball mechanisms (SLBMs) is investigated that looks like a sea lion playing with a ball. The SLBM-type mechanism is composed of an upper part and a lower part connected together by three limbs in parallel, and the translational and rotational motions are fully/partially decoupled. The end-effector position is determined by inputs of the lower part, while the posture is mainly determined by inputs of the upper part. First, two compositional principles are abstracted and the corresponding mathematical models are built for the SLBM-type mechanisms that the commutative feature of the SLBMs is found. Then, two type synthesis procedures containing five steps are proposed correspondingly. Following the procedure, a family of novel four, five, and six degrees-of-freedom (DOF) SLBM-type mechanisms is synthesized systematically. The motion patterns of the limbs are enumerated according to the given desired ones of the mechanisms and the limbs are synthesized correspondingly. Finally, several novel SLBM-type mechanisms are achieved by assembling the obtained limbs and selecting the actuated joints.

A Task-Driven Unified Synthesis of Planar Four-Bar and Six-Bar Linkages With R- and P-Joints for Five-Position Realization

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Ping Zhao ◽  
Xiangyun Li ◽  
A. Purwar ◽  
Q. J. Ge
Keyword(s):  
Simple Algorithm ◽  
Standing Position ◽  
Type I ◽  
Dimensional Synthesis ◽  
New Classification ◽  
End Effector ◽  
Prismatic Joints ◽  
Seating Position ◽  
The Given ◽  
Synthesis Approach

This paper deals with the problem of integrated joint type and dimensional synthesis of planar four-bar and six-bar linkages, which could contain both revolute (R) and prismatic (P) joints, for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. This paper extends this algorithm to the integrated joint type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages that contain both R- and P-joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (type I), one dyad (type II), or no dyad (type III). In the end, we demonstrate this task-driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

Parameterization of Three-Dimensional Rigid Body Guidance Incorporating Planar Gear Connections in a Spatial Closed-Loop Mechanism With Parallel Consecutive Axes

2008 ◽  
Author(s):  
Javier Rolda´n Mckinley ◽  
Carl Crane ◽  
David B. Dooner
Keyword(s):  
Computer Animation ◽  
Closed Loop ◽  
Three Dimensional ◽  
Motion Generation ◽  
Repetitive Motion ◽  
End Effector ◽  
Spatial Mechanism ◽  
Joint Axis ◽  
Position And Orientation ◽  
Six Degree Of Freedom

This paper introduces a reconfigurable closed-loop spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of non-circular gears into a six degree-of–freedom closed-loop spatial chain. The gear pairs are designed based on given mechanism parameters and a user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, ..., and the eleventh is parallel to the twelfth. This paper presents the synthesis of the gear pairs that satisfy a specified three-dimensional position and orientation need. Numerical approximations were used in the synthesis the non-circular gear pairs by introducing an auxiliary monotonic parameter associated to each end-effector position to parameterize the motion needs. The findings are supported by a computer animation. No previous known literature incorporates planar non-circular gears to fulfill spatial motion generation needs.

Synthesis of Parallel Manipulator with Single DOF

2013 ◽  
Vol 330 ◽  
pp. 639-643 ◽  
Author(s):  
Chung Huang Yu ◽  
Wen Yeuan Chung
Keyword(s):  
Parallel Manipulator ◽  
Design Concept ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Numerical Example ◽  
Geometrical Constraints ◽  
Moving Platform ◽  
Manipulator Design

This paper proposed a new manipulator design concept which leads to a single DOF system. The system composed of a moving platform and several supporting legs. It can execute the tasks of 3D body guidance or path generation and thus replace expensive manipulators with high DOF in some conditions. There are mainly two steps in designing this manipulator. The first step is type synthesis to determine the number and types of legs. Dimensional synthesis is then executed based on the movement requirements and geometrical constraints. In this study the reduction of the DOF is also analyzed for various legs added between the moving platform and the ground. A numerical example of executing 3D body guidance is given to verify the proposed new concept.

scholarly journals Dynamic approach to minimize overhead and response time in scheduling periodic real-time tasks

2021 ◽  
Vol 8 (4) ◽  
pp. 75-81
Author(s):  
Ahmed A. Alsheikhy ◽  
Keyword(s):  
Response Time ◽  
Real Time ◽  
Periodic Tasks ◽  
Dynamic Priority ◽  
New Novel ◽  
Context Switching ◽  
Novel Approach ◽  
Efficiency And Effectiveness ◽  
Time Systems ◽  
The Given

In real-time systems, a task or a set of tasks needs to be executed and completed successfully within a predefined time. Those systems require a scheduling technique or a set of scheduling methods to distribute the given task or the set of tasks among different processors or on a processor. In this paper, a new novel scheduling approach to minimize the overhead from context switching between several periodic tasks is presented. This method speeds up a required response time while ensuring that all tasks meet their deadline times and there is no deadline miss occurred. It is a dynamic-priority technique that works either on a uniprocessor or several processors. In particular, it is proposed to be applied on multiprocessor environments since many applications run on several processors. Various examples are presented within this paper to demonstrate its optimality and efficiency. In addition, several comparison experiments with an earlier version of this approach were performed to demonstrate its efficiency and effectiveness too. Those experiments showed that this novel approach sped up the execution time from 15% to nearly around 46%. In addition, it proved that it reduced the number of a context switch between tasks from 12% to around 50% as shown from simulation tests. Furthermore, this approach delivered all tasks/jobs successfully and ensured there was no deadline miss happened.

scholarly journals Synthesis of Spatial RPRP Closed Linkages for a Given Screw System

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Alba Perez-Gracia
Keyword(s):  
Design Method ◽  
Parallel Robots ◽  
Synthesis Problem ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Serial Chain

The dimensional synthesis of spatial chains for a prescribed set of positions can be applied to the design of parallel robots by joining the solutions of each serial chain at the end-effector. This design method does not provide with the knowledge about the trajectory between task positions and, in some cases, may yield a system with negative mobility. These problems can be avoided for some overconstrained but movable linkages if the finite-screw system associated with the motion of the linkage is known. The finite-screw system defining the motion of the robot is generated by a set of screws, which can be related to the set of finite task positions traditionally used in the synthesis theory. The interest of this paper lies in presenting a method to define the whole workspace of the linkage as the input task for the exact dimensional synthesis problem. This method is applied to the spatial RPRP closed linkage, for which one solution exists.

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