Developments in quantitative dimensional synthesis (1970-present): four-bar motion generation

2017 ◽  
Vol 26 (1) ◽  
pp. 133-148 ◽  
Author(s):  
Wen-Tzong Lee ◽  
Kevin Russell
Keyword(s):  
Dimensional Synthesis ◽  
Motion Generation

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Locations

2013 ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyads rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed locations to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain; also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. An example that demonstrates the synthesis technique is included.

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.

Use of Resultant in the Dimensional Synthesis of Linkage Components: Motion Generation With Prescribed Timing

1992 ◽  
Author(s):  
Chuen-Sen Lin ◽  
Bao-Ping Jia
Keyword(s):  
Angular Displacement ◽  
Solution Process ◽  
Original System ◽  
Polynomial Equations ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Closed Form Solutions ◽  
Resultant Theory

Abstract Resultant theory is applied to derive closed-form solutions for the dimensional synthesis of linkage components for a finite number of precision positions for motion generation with prescribed timing. The solutions are in forms of polynomial equations of the exponential of a single unknown angular displacement. The degree of the derived polynomial depends on the number of links in the linkage component and the number of precision positions to be synthesized for, or the number of compatibility equations. The resultant theory is discussed in detail, and the procedure for the derivation of resultant polynomials is demonstrated. This paper shows that, for the case of two compatibility equations, the solution is a six-degree polynomial. For the case of three compatibility equations, the solution is a fifty-fourth degree polynomial. The Bernshtein formula is applied to check the exact number of solutions of the original system of polynomial equations and to verify the validity of the derived resultant polynomials. An algorithm is also proposed for screening out extra solutions which may be generated through the solution process.

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.

On RCCC Linkage Motion Generation With Defect Elimination for an Indefinite Number of Precision Positions

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Wen-Tzong Lee ◽  
Jose Cosme ◽  
Kevin Russell
Keyword(s):  
Optimization Model ◽  
Software Package ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Analysis Software ◽  
Order Branch ◽  
Indefinite Number ◽  
Cylindrical Joint ◽  
Circuit Defects ◽  
Defect Elimination

A general optimization model for the dimensional synthesis of defect-free revolute-cylindrical-cylindrical-cylindrical joint (or RCCC) motion generators is formulated and demonstrated in this work. With this optimization model, the RCCC dimensions required to approximate an indefinite number of precision positions are calculated. The model includes constraints to eliminate order branch and circuit defects—defects that are common in dyad-based dimensional synthesis. Therefore, the novelty of this work is the development of a general optimization model for RCCC motion generation for an indefinite number of precision positions that simultaneously considers order, branch, and circuit defect elimination. This work conveys both the benefits and drawbacks realized when implementing the optimization model on a personal computer using the commercial mathematical analysis software package matlab.

A Unified Formulation for Dimensional Synthesis of Stephenson Linkages

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Shaoping Bai ◽  
Delun Wang ◽  
Huimin Dong
Keyword(s):  
Dimensional Synthesis ◽  
Motion Generation ◽  
The Subject

The unified formulation of dimensional synthesis of Stephenson linkages for motion generation is the subject of this paper. Burmester theory is applied to the six-bar linkage, which leads to a unified formulation applicable for all three types of Stephenson linkages. This is made possible by virtue of parameterized position vectors, which simplify the formulation of synthesis equations. A design example is included to demonstrate the application of the method developed.

Motion Generation of Planar Six- and Eight-Bar Slider Mechanisms as Constrained Robotic Systems

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Gim Song Soh ◽  
Fangtian Ying
Keyword(s):  
Design Process ◽  
Design Methodology ◽  
Robotic Systems ◽  
Outpatient Rehabilitation ◽  
Systematic Design ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Complex Motion ◽  
Different Types ◽  
Crank Mechanism

In this paper, we formulated a systematic design methodology for the design of planar six- and eight-bar slider mechanisms for motion generation applications that require more complex motion than the slider–crank mechanism. We show how two RR dyads can be synthesized and attached to planar PRR and PRR–3R chain for the dimensional synthesis of planar six- and eight-bar slider mechanisms, respectively. The results are 15 different types of one degree-of-freedom planar six- and eight-bar linkages with a prismatic joint at its base. 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 meant for outpatient rehabilitation purpose.

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

2012 ◽  
Author(s):  
Xiangyun Li ◽  
Ping Zhao ◽  
Q. J. Ge
Keyword(s):  
Design Space ◽  
Translational Motion ◽  
Classical Problem ◽  
Harmonic Series ◽  
Design Parameters ◽  
Rotational Component ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Motion Approximation ◽  
Four Bar Linkage

This paper deals with the classical problem of dimensional synthesis of planar four-bar linkages for motion generation. Using Fourier Descriptors, 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 motion and that of the translational motion for a planar four-bar linkage. Furthermore, it is shown that the rotational component can be used to identify the initial angle and the link ratios of a four-bar linkage. The rest of the design parameters of a four-bar linkage such as location of the fixed and moving pivots can be obtained from the translational component of the given motion. This leads naturally to a decomposed design space for four-bar motion synthesis for approximate motion generation.

scholarly journals Motion Generation of Passive Slider Multiloop Wearable Hand Devices

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Guan Rong Tan ◽  
Nina Patarinsky Robson ◽  
Gim Song Soh
Keyword(s):  
Human Skin ◽  
Motion Capture ◽  
Synthesis Method ◽  
Middle Finger ◽  
Wearable Devices ◽  
Least Square ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Optical Motion ◽  
Optical Motion Capture

This paper describes a dimensional synthesis method used in the design of a passive finger exoskeleton that takes into account the user limb anthropometric dimensions and contact requirements for grasping objects. The paper is the first step in our current efforts on the design of wearable devices that use a common slider at the hand to passively drive each exofinger. The finger exoskeleton is comprised of a 3R serial limb and is constrained to multiloop eight-bar slider mechanism using two RR constraints. To design the exolimb, the pose of the limb was captured using an optical motion capture and its dimensions were determined using a constrained least square optimization, which takes into account human skin movement. To illustrate the generality of our approach, an example of the design of an index and middle finger exolimb is described.

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