# ISOTROPIC COORDINATES , CIRCULARITY , AND BEZOUT NUMBERS : PLANAR KINEMATICS FROM A NEW PERSPECTIVE

@inproceedings{Wampler1996ISOTROPICC, title={ISOTROPIC COORDINATES , CIRCULARITY , AND BEZOUT NUMBERS : PLANAR KINEMATICS FROM A NEW PERSPECTIVE}, author={Charles W. Wampler}, year={1996} }

It is commonly recognized that a convenient formulation for problems in planar kinematics is obtained by considering links to be vectors in the complex plane. However, scant attention has been paid to the natural interpretation of complex vectors as isotropic coordinates. These coordinates, often considered a special trick for analyzing four-bar motion, are in fact uniquely suited to two new techniques for analyzing polynomial systems: the BKK bound and the product-decomposition bound. From…

## 31 Citations

### Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

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- 2001

This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute and slider joints. The method combines the complex plane formulation of…

### Parallel Manipulators in Terms of Dual Cayley-Klein Parameters

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- 2018

Cayley-Klein parameters are an alternative to Euler parameters for describing the spherical motion group. Based on Study’s and Kotelnikov’s “Principle of Transference” one can use dual Cayley-Klein…

### Finding Straight Line Generators through the Approximate Synthesis of Symmetric Four-bar Coupler Curves

- Mathematics
- 2022

In this paper, equations for the approximate synthesis of symmetric fourbar coupler curves are formulated. Our approach specifies a number of desired trace points, and finds a number of four-bar…

### An algorithm to compute the finite roots of large systems of polynomial equations arising in kinematic synthesis

- MathematicsMechanism and Machine Theory
- 2019

### Synthesis of Stephenson III Timed Curve Generators Using a Probabilistic Continuation Method

- Computer ScienceVolume 5B: 43rd Mechanisms and Robotics Conference
- 2019

The Cyclic Coefficient Parameter Continuation (CCPC) method is applied to obtain for the first time the complete solution of a Stephenson III six-bar that traces a path and coordinates the angle of its input link along that path.

### Synthesis of Six-Bar Timed Curve Generators of Stephenson-Type Using Random Monodromy Loops

- Computer Science
- 2020

The computation of nearly complete solution sets for these six-bar design equations has been facilitated by recent root finding techniques belonging to the field of numerical algebraic geometry, and the solution sets are reported to all relevant six-bars of the Stephenson topology.

### Formulation and Solution for the Direct and Inverse Kinematics Problems for Mechanisms and Mechatronics Systems

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- 1998

The formulation of a kinematic analysis problem often leads to a set of nonlinear equations. There are a variety of both numerical and algebraic techniques available to solve such systems of…

### Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets

- Mathematics, Computer ScienceJ. Complex.
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An embedding of the original polynomial system is presented, which leads to a sequence of homotopies, with solution paths leading to generic points of all components as the isolated solutions of an auxiliary system.

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