Graphical Synthesis of Fourbar Mechanisms by Three-Position, Instant-Center Specification

2012 ◽  
Author(s):  
Thomas J. Thompson
Keyword(s):  
Computational Method ◽  
Front Suspension ◽  
Point Pair ◽  
Prosthetic Knee ◽  
Center Point ◽  
Practical Synthesis ◽  
Instantaneous Center ◽  
Triangle Theory ◽  
Position Problem ◽  
Position Synthesis

In four-bar mechanism synthesis, solutions to both the three-position and four-position synthesis problems are well-known. However, certain practical synthesis problems also require consideration of the instantaneous center of velocity for one of the precision positions. Examples are the double-wishbone front suspension of an automobile (camber in jounce and rebound, along with roll center), and four-bar prosthetic knee (standing stability, flexion length, and sitting cosmetic advantage). Because specifying the location of the instant center constrains the solution by one free choice per dyad, it reduces the number of free choices available in a three-position problem from two to one. Thus, center point and circle point solutions to the three-position, instant center specified synthesis (TPICS) problem are located along point-pair solution curves similar to the Burmester curves in four-position synthesis. The purpose of this paper is to present a direct, graphical method for finding pivot locations in three-position, instant-center synthesis of four-bar mechanisms. The method uses pole triangle theory to determine pivot locations along center point and circle point curves. A summary of a previously-presented computational method is included. As an example, both the graphical and the computational method are used to generate TPICS center-point curves for an automotive front suspension.

Geometric Characteristics of the Center-Point Curve Based on the Kinematics of the Compatibility Linkage

1992 ◽  
Author(s):  
J. A. Schaaf ◽  
J. A. Lammers
Keyword(s):  
Complex Number ◽  
Change Point ◽  
Double Point ◽  
Classification Scheme ◽  
Center Point ◽  
Degenerate Form ◽  
Point Curve ◽  
Position Synthesis ◽  
Point Form

Abstract In this paper we develop a method of characterizing the center-point curves for planar four-position synthesis. We predict the five characteristic shapes of the center-point curve using the kinematic classification of the compatibility linkage obtained from a complex number formulation for planar four-position synthesis. This classification scheme is more extensive than the conventional Grashof and non-Grashof classifications in that the separate classes of change point compatibility linkages are also included. A non-Grashof compatibility linkage generates a unicursal form of the center-point curve; a Grashof compatibility linkage generates a bicursal form; a single change point compatibility linkage generates a double point form; and a double or triple change point compatibility linkage generates a circular-degenerate or a hyperbolic-degenerate form.

Identifying Sets of Four and Five Positions That Generate Distinctive Center-Point Curves

2009 ◽  
Author(s):  
David H. Myszka ◽  
Andrew P. Murray
Keyword(s):  
Closed Form ◽  
The Other ◽  
Specific Design ◽  
Opposite Pole ◽  
Center Point ◽  
Point Curve ◽  
Position Synthesis ◽  
Two Sides ◽  
Cubic Function

The fixed pivots of a planar 4R linkage that can achieve four design positions are constrained to a center-point curve. The curve is a circular cubic function and plots can take one of five different forms. The center-point curve can be generated with a compatibility linkage obtained from an opposite pole quadrilateral of the four design positions. This paper presents a method to identify design positions that generate distinctive shapes of the center-point curves. The form of the center-point curve is dependent on whether the shape of the opposite pole quadrilateral is an open or closed form of a rhombus, kite, parallelogram, or when the sum of two sides equals the other two. Interesting cases of three and five position synthesis are also explored. Four and five position cases are generated that have center points at infinity allowing a PR dyad with line of slide in any direction to achieve the design positions. Further, a center-point curve for five specific design positions is revealed.

The Opposite Pole Quadrilateral as a Compatibility Linkage for Parameterizing the Center Point Curve

1993 ◽  
Vol 115 (2) ◽  
pp. 332-336 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Complex Number ◽  
Kinematic Analysis ◽  
Special Form ◽  
Body Form ◽  
Kinematic Theory ◽  
Opposite Pole ◽  
Center Point ◽  
Point Curve ◽  
Position Problem ◽  
Four Bar Linkage

In planar four-position kinematics, the centers of circles containing four positions of a point in a moving rigid body form the center point curve. This curve can be parameterized by analyzing a “compatibility linkage” obtained from a complex number formulation of the four-position problem. In this paper, we present another derivation of the center point curve using a special form of dual quaternions and the fact that it is identical to the pole curve. The defining properties of the pole curve lead to a parameterization by kinematic analysis of the opposite pole quadrilateral as a four-bar linkage. Thus the opposite pole quadrilateral becomes the compatibility linkage. This derivation generalizes to provide parameterizations for the center point cone of spherical kinematics and the central axis congruence of spatial kinematic theory.

Design of Adjustable Spherical Four-Bar Linkages As Continuous Passive Motion Devices for Anatomic Joints Rehabilitation

1996 ◽  
Author(s):  
Boyang Hong ◽  
Arthur Erdman ◽  
Kealy Ham
Keyword(s):  
Clinical Data ◽  
Common Ground ◽  
Synthesis Method ◽  
Single Type ◽  
Continuous Passive Motion ◽  
Design Parameters ◽  
Passive Motion ◽  
Center Point ◽  
Joint Application ◽  
Position Synthesis

Abstract Continuous passive motion (CPM) is an important treatment in postoperative rehabilitation of human joints. It can improve the range of motion (ROM), reduce joint stiffness and accelerate the recovery process. The concept of CPM can be applied in many joint rehabilitation applications, including ankle joints, knee joints and elbow joints. However, even within a single type of joint, the ROM can be significantly different from person to person. Adjustable spherical linkage is appropriate for these applications. The following procedure is introduced: synthesize the first set of positions and selects the center point and circle point. Then, with the same center point and circle point, by altering some design parameters, i.e., the length of the input link and output link, a new set of positions can be synthesized. This idea is more practical in three-plus-two position synthesis, but can also be applied to four-plus-three position synthesis, with a significant increase in complexity. The above synthesis method can be applied to any generic adjustable spherical linkage application. In this paper, this method is tailored to an anatomical joint application for CPM machine design. Clinical motion data is directly used to define the orientation of the joint. The details of this method are illustrated by an example, the ankle joint. The first set of synthesis positions is obtained from the clinical data and a list of designed candidates is presented. After that, we introduced a second set of synthesis positions from the clinical data. The adjustable spherical linkage is synthesized with the common ground pivot. By using this method, an adjustable CPM machine can be designed to cover the minimum ROM and maximum ROM. This machine can be used to more than one patient, as well as throughout a single patient’s full recovery.

Generalized Cardan Motion

1969 ◽  
Vol 91 (1) ◽  
pp. 135-141 ◽  
Author(s):  
D. Tesar ◽  
H. Anderson
Keyword(s):  
Design Procedures ◽  
Center Point ◽  
Point Curve ◽  
Moving Plane ◽  
Position Problem ◽  
Graphical Design

Cardan motion has been treated in the literature principally in terms of infinitesimally separated positions. Here Cardan motion is synthesized for all combinations of up to five infinitesimally and finitely separated positions of the moving plane. For each of the five distinct combinations which exist for four positions, the circle point curve is shown to degenerate into a circle and a line and the center point curve into a line at infinity and a hyperbola. Elementary analytical and graphical design procedures are provided and supported by examples. The five position problem is shown to be constrained only by the well-known Scott-Russell mechanism or a double-slider mechanism.

Design of a novel bionic prosthetic knee joint

2016 ◽  
Vol 36 (4) ◽  
pp. 398-404 ◽  
Author(s):  
Xiufeng Zhang ◽  
Huiqun Fu ◽  
Xitai Wang ◽  
Guanglin Li ◽  
Rong Yang ◽  
...  
Keyword(s):  
Knee Joint ◽  
Design Method ◽  
Experimental Tests ◽  
Content Type ◽  
Prosthetic Knee ◽  
Theoretical Support ◽  
Instantaneous Center ◽  
And Performance ◽  
Swing Speed ◽  
Four Bar Linkage

Purpose This paper aims to find a new method that could be applied to the high and mid-grade prosthesis knee joint. Design/methodology/approach Based on analysis, calculation, modeling, simulation and experimental study of the motion law of knee joint, this paper not only determines the structure and parameters of the knee joint and calculates the instantaneous center but also analyzes the stance stability and completes the optimization. With the help of experimental tests (fatigue test and gait curve test), the quality and performance of the designed knee joint is verified. Findings The experimental results show that the gait curve of the designed knee joint is much closer to health people. The designed prosthesis knee joint, with adjustable swing speed and gait curve which are close to health limb, has a better performance when compared to the ordinary knee joint with four-bar linkage structure. Originality/value This paper developed a prosthesis knee joint based on a novel design method that could be applied to the “high and mid” grade prosthesis knee joint and verified its function on an amputee performed the lower amputation, which could provide theoretical support for researches and designs related to prosthesis knee joint in future.

A Unified Analysis and Implementation of Four Multiply Separated Position Synthesis of Four-Bar Linkages

1992 ◽  
Author(s):  
P. Srikrishna ◽  
Kenneth J. Waldron
Keyword(s):  
Rigid Body ◽  
Design Procedure ◽  
Unified Approach ◽  
Center Point ◽  
Point Curve ◽  
Position Synthesis

Abstract The objective of this paper is to derive analytically the circle-point and center-point curve equations for the synthesis of four-bar linkages for rigid body guidance through four multiply separated design positions. A unified approach is evolved to deal with the different combinations of four finitely and infinitesimally separated design position, namely the PP-P-P, PP-PP and PPP-P cases. The design procedure incorporates the rectification procedures developed by Waldron (1977) to eliminate the branch and order problems and is implemented in the interactive synthesis package RECSYN.

The Synthesis of Planar Linkages to Satisfy an Approximate Motion Specification

1993 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Design Space ◽  
Accurate Position ◽  
Solution Region ◽  
Pass Through ◽  
Position Problem ◽  
The Individual ◽  
Planar Linkages ◽  
Position Synthesis ◽  
Individual Design ◽  
Complete Process

Abstract This paper introduces the method of quasi-precision position synthesis for planar linkages. A quasi-precision position is defined by an approximate region that the mechanism must pass through. The quasi-precision position problem specification generates an increased design region by not requiring the accurate position specification that is characteristic of optimization and precision position methods. The design space is generated by intersecting the individual design regions of different four position sets. Each four position set consists of three exact positions plus one quasi-precision position. The method allows for the use of any number of quasi-precision positions. The result of using quasi-precision positions is an increase in the available design space without violating the basic problem constraints. The increased solution region gives the designer a greater variety of choices while reducing the number of required design iterations. The complete process of quasi-precision position synthesis is presented through the use of an example.

scholarly journals Design of a Semi-Active Prosthetic Knee for Transfemoral Amputees: Gait Symmetry Research by Simulation

2021 ◽  
Vol 11 (12) ◽  
pp. 5328
Author(s):  
Zhewen Zhang ◽  
Hongliu Yu ◽  
Wujing Cao ◽  
Xiaoming Wang ◽  
Qiaoling Meng ◽  
...  
Keyword(s):  
Hydraulic Cylinder ◽  
Swing Phase ◽  
Ball Screw ◽  
Gait Symmetry ◽  
Prosthetic Knee ◽  
Symmetry Index ◽  
Good Potential ◽  
Instantaneous Center ◽  
Index Value ◽  
Four Bar Linkage

The key technology of the prosthetic knee is to simulate the torque and angle of the biological knee. In this work, we proposed a novel prosthetic knee operated in semi-active mode. The structure with ball-screw driven by the motor and the passive hydraulic damping cylinder was presented. A four-bar linkage was adapted to track the instantaneous center motion of human knee. The mathematical models of hydraulic cylinder damping and active torque were established to simulate the knee torque and angle. The results show that the knee torque symmetry index is smaller than 10% in the whole gait. The knee angle symmetry index value is 34.7% in stance phase and 11.5% in swing phase. The angle in swing phase is closer to the intact knee. The semi-active prosthetic knee could provide similar torque and angle of the biological knee in the simulation. It has shown good potential in improving the gait symmetry of the transfemoral amputee.

Kinematic Synthesis of Binary Actuated Mechanisms for Rigid Body Guidance

2000 ◽  
Author(s):  
Michael S. Hanchak ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Design Space ◽  
Kinematic Synthesis ◽  
Prismatic Joint ◽  
Revolute Joints ◽  
Binary State ◽  
Parallel Arrangement ◽  
Position Problem ◽  
Position Synthesis ◽  
Kinematic Solution

Abstract This paper presents a method for designing mechanisms composed of Revolute-Binary state prismatic-Revolute (RBR) chains for rigid body guidance. Where a prismatic joint allows for any distance between two revolute joints, a binary state prismatic joint reaches two distances precisely. A single RBR chain can be designed to reach six positions. A parallel arrangement of three RBR chains can be assembled at the six positions but, in general, is not a viable kinematic solution. By requiring the arrangement of three RBR chains to share specific fixed and moving pivots, called an N-type arrangement, four positions are reachable. Further, the design space is quickly searchable for singularity-free solutions. Examples illustrate a solution to a four position synthesis problem and a ten position problem using a serial assembly of these mechanisms.

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