Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages

This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree-of-freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for performing smooth equidistant travel of the tool is provided by applying arc-length reparameterization. This general approach can be applied to one-DoF mechanisms with four to seven joints characterized by a rational motion, without any additional geometrical analysis. An experiment was performed to demonstrate the usage in a laboratory setup.

Rational Linkages: From Poses to 3D-printed Prototypes

In this paper, a set of tools is introduced that simplifies the synthesis and rapid-prototyping of single-loop rational kinematic chains. It allows the user to perform rational motion interpolation of up to four given poses and yields the design parameters of a linkage that can execute this motion. The package also provides a visualization of the output and performs a self-collision analysis with the possibility to adapt the design parameters. The results can be imported into CAD-systems for fast 3D printing.

An Automated Conversion Between Selected Robot Kinematic Representations

This paper presents a methodology that forms an automated tool for robot kinematic representation conversion, called the RobKin Interpreter. It is a set of analytical algorithms that can analyze an input robot representation, express the joints globally in matrix form, and map to other representations such as standard Denavit-Hartenberg parameters, Roll-Pitch-Yaw angles with translational displacement, and Product of Exponentials with a possibility to generate a URDF (Universal Robot Description Format) file from any of them. It works for revolute and prismatic joints and can interpret even arbitrary kinematic structures that do not have orthogonally placed joints.