The Improved DLR Wrist: Design and Analysis of 2-Degrees-of-Freedom Rotational Mechanism Using Spatial Antiparallelogram Linkages

This article presents a kinematic analysis and modification of a wrist mechanism of the DLR robot arm, which is based on antiparallelogram linkages. This mechanism is modified to improve the range of motion (ROM), to reduce the parasitic motion, and to approximately perform the decoupled output motion. For these purposes, the elliptical rolling motion of an overconstrained antiparallelogram is first investigated in consideration of its structural modification. Also, a specific joint that has a relatively small movement is developed as a flexible hinge by further minimizing its angular displacement for design simplification. The axode analysis of the instantaneous screw axis for wrist movements is conducted to compare the rotational performance between the original and modified mechanisms. Moreover, their workspace qualities are evaluated through analyses of the workspace and the kinematic isotropy index. Finally, the improved DLR wrist of the final modification is prototyped, and its wide circumduction is demonstrated.

Estimating the Instantaneous Screw Axis and the Screw Axis Invariant Descriptor of Motion by Means of Inertial Sensors: An Experimental Study with a Mechanical Hinge Joint and Comparison to the Optoelectronic System

The motion of a rigid body can be represented by the instantaneous screw axis (ISA, also known as the helical axis). Recently, an invariant representation of motion based on the ISA, namely, the screw axis invariant descriptor (SAID), was proposed in the literature. The SAID consists of six scalar features that are independent from the coordinate system chosen to represent the motion. This method proved its usefulness in robotics; however, a high sensitivity to noise was observed. This paper aims to explore the performance of inertial sensors for the estimation of the ISA and the SAID for a simple experimental setup based on a hinge joint. The free swing motion of the mechanical hinge was concurrently recorded by a marker-based optoelectronic system (OS) and two magnetic inertial measurement units (MIMUs). The ISA estimated by the MIMU was more precise, while the OS was more accurate. The mean angular error was ≈2.2° for the OS and was ≈4.4° for the MIMU, while the mean standard deviation was ≈2.3° for the OS and was ≈0.2° for the MIMU. The SAID features based on angular velocity were better estimated by the MIMU, while the features based on translational velocity were better estimated by the OS. Therefore, a combination of both measurements systems is recommended to accurately estimate the complete SAID.

Dynamic Analysis of the 3-RRPS Metamorphic Parallel Mechanism Based on Instantaneous Screw Axis

The 3-rRPS metamorphic parallel mechanism can change its configurations thanks to the reconfigurable (rR) joint. The analysis in this paper will focus on one specific configuration where the moving-platform is able to perform 2-dof coupled rotational motions and 1-dof translational motion, which is well-known as 1T2R motion. In this configuration, the mechanism has two types of operation modes, i.e. x0 = 0 and x3 = 0, which have been extensively studied by many researchers. However, the dynamic behaviours of the mechanism in those two operation modes have not been studied. Accordingly, this paper presents the dynamic analysis of the 3-rRPS metamorphic parallel mechanism in both operation modes based on the Instantaneous Screw Axis (ISA). The types of operation mode are initially characterized by means of Euler-Quaternion parameters. The time derivative of transformation matrix is performed in each operation mode and the ISA can be determined. By using the ISA, velocities and accelerations of all points on the moving-platform can be evaluated, which become the foundation of the dynamic analysis in this paper. This approach can be applied to parallel mechanisms having multiple operation modes of different mobility.

On the kinematic interpretation of timelike ruled surfaces

Timelike ruled surfaces are studied in dual Lorentzian space [Formula: see text] by considering E. Study Mapping and Blaschke frame. A reference timelike ruled surface is considered and associated surfaces are defined. First, it is shown that the surface generated by the instantaneous screw axis (ISA) is a Mannheim offset of reference surface. Later, the kinematic interpretations between these surfaces are introduced by means of Blaschke invariants.

Instantaneous Screws of Weight-Bearing Knee: What Can the Screws Tell Us About the Knee Motion

There are several ways to represent a given object's motion in a 3D space having 6DOF i.e., three translations and three rotations. Some of the methods that are used are mathematical and do not provide any geometrical insight into the nature of the motion. Screw theory is a mathematical, while at the same time, geometrical method in which the 6DOF motion of an object can be represented. We describe the 6DOF motion of a weight-bearing knee by its screw parameters, that are extracted from 3D Optical Reflective motion capture data. The screw parameters which describe the transformation of the shank with respect to the thigh in each two successive frames, is represented as the instantaneous screw axis of the motion given in its Plücker line coordinate, along with its corresponding pitch and intensity values. Moreover, the Striction curve associated with the motion provides geometrical insight into the nature of the motion and its repeatability. We describe the theoretical background and demonstrate what the screw can tell us about the motion of healthy subjects' knee.

Axodes Analysis of the Multi DOF Parallel Mechanisms and Parasitic Motion

The general motion of a spatial mechanism is a screw motion about an instantaneous screw axis (ISA). The locus of a series of ISAs will form a ruled surface, which can be called as an axode. For a spatial mechanism with only one degree of freedom (DOF), the ISAs or the axodes of the moving platform are unique. However, the axodes of the parallel mechanisms (PMs) with multi DOF are related to the specific motion which has various possibilities. In this paper, the ISAs of the multi DOF PMs are studied using the jacobian matrix which is changing with the configurations of the moving platform. The axodes of the multi DOF PMs with different inputs or outputs are obtained using this method. Based on the analyzed results, it is very clear that the general motions of the PMs are screw motions or rotations about a series of ISAs. In the end, the parasitic motion of the PMs is studied. For a PM, the parasitic motion will exist if the rotational freedoms are not rotations about a fixed point or axis.