On the kinematic interpretation of timelike ruled surfaces

2015 ◽  
Vol 12 (10) ◽  
pp. 1550127 ◽  
Author(s):  
Mehmet Önder ◽  
Zehra Ekinci
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
Reference Surface ◽  
Screw Axis ◽  
Lorentzian Space ◽  
Timelike Ruled Surface ◽  
Instantaneous Screw Axis ◽  
Associated Surfaces ◽  
Instantaneous Screw ◽  
Mannheim Offset

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.

Generating Swept Volumes With Instantaneous Screw Axes

1994 ◽  
Author(s):  
Zeng-Jia Hu ◽  
Zhi-Kui Ling
Keyword(s):  
Moving Object ◽  
Ruled Surfaces ◽  
Screw Axis ◽  
Spherical Surfaces ◽  
Swept Volumes ◽  
Instantaneous Screw Axis ◽  
Swept Volume ◽  
Instantaneous Screw ◽  
Plane Polygon ◽  
Boundary Surfaces

Abstract The instantaneous screw axis is used in the generation of the swept volume of a moving object. The envelope theory is used to determine the boundary surfaces of the swept volume. Specifically, the envelope surfaces generated by a plane polygon, cylindrical and spherical surfaces are presented. Furthermore, the ruled surfaces generated by edges of the moving object are discussed.

On the invariants of Mannheim offsets of timelike ruled surfaces with spacelike rulings

2015 ◽  
Vol 08 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Mehmet Önder ◽  
H. Hüseyin Uğurlu
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
Lorentzian Space ◽  
Integral Invariants ◽  
Timelike Ruled Surface ◽  
Spherical Images

In this paper, we give the characterizations for Mannheim offsets of timelike ruled surfaces with spacelike rulings in dual Lorentzian space [Formula: see text]. We obtain the relations between terms of their integral invariants and also we give new characterization for the Mannheim offsets of developable timelike ruled surface. Moreover, we find relations between the area of projections of spherical images for Mannheim offsets of timelike ruled surfaces and their integral invariants.

scholarly journals On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Cumali Ekici ◽  
Yasin Ünlütürk ◽  
Mustafa Dede ◽  
B. S. Ryuh
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
End Effector ◽  
Timelike Ruled Surface ◽  
Curvature Theory ◽  
Differential Properties

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effector's motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling.

scholarly journals 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

Sensors ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 49 ◽  
Author(s):  
Andrea Ancillao ◽  
Maxim Vochten ◽  
Erwin Aertbeliën ◽  
Wilm Decré ◽  
Joris De Schutter
Keyword(s):  
Inertial Sensors ◽  
High Sensitivity ◽  
Helical Axis ◽  
Screw Axis ◽  
Invariant Representation ◽  
Optoelectronic System ◽  
Hinge Joint ◽  
Instantaneous Screw Axis ◽  
The Mean ◽  
Instantaneous Screw

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.

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

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Alon Wolf
Keyword(s):  
Screw Theory ◽  
Weight Bearing ◽  
Theoretical Background ◽  
Geometrical Method ◽  
Screw Axis ◽  
Knee Motion ◽  
3D Space ◽  
Instantaneous Screw Axis ◽  
Instantaneous Screw ◽  
Insight Into

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

2013 ◽  
Author(s):  
Ziming Chen ◽  
Huafeng Ding ◽  
Wenao Cao ◽  
Zhen Huang
Keyword(s):  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Screw Axis ◽  
Spatial Mechanism ◽  
Parasitic Motion ◽  
Screw Motions ◽  
Instantaneous Screw Axis ◽  
Moving Platform ◽  
Instantaneous Screw ◽  
General 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.

A Generalized Kinematic for Calculating and Evaluating Surface Geometry of Gears and Cutting Tools

1992 ◽  
Author(s):  
J. Grill ◽  
K. H. Hirschmann ◽  
G. Lechner
Keyword(s):  
General Equation ◽  
Cutting Tools ◽  
Grinding Process ◽  
Spatial Motion ◽  
Line Geometry ◽  
Surface Geometry ◽  
Screw Axis ◽  
On Line ◽  
Instantaneous Screw Axis ◽  
Instantaneous Screw

Abstract A new method for simulating the cutting and grinding process of gears has been developed. The procedure, implemented on a workstation, allows to describe the most general case of spatial motion based on line coordinates. The meshing of two gears is replaced by the motion of two axodes, rolling and sliding on each other about and along the instantaneous screw axis. A general equation of meshing has been developed, also based on line geometry. Velocity, acceleration and jerk can be determined, which are used for calculating the generated surfaces and their derivatives.

Velocity Analysis of Truss-Type Manipulators

1996 ◽  
Author(s):  
Stephen L. Canfield ◽  
R. Randall Soper ◽  
Scott L. Hendricks ◽  
Charles F. Reinholtz
Keyword(s):  
Ad Hoc ◽  
A Priori ◽  
Velocity Analysis ◽  
General Description ◽  
Screw Axis ◽  
Output Plane ◽  
The Past ◽  
Instantaneous Screw Axis ◽  
Instantaneous Screw ◽  
Variable Geometry Truss

Abstract A generalized method for the velocity analysis of truss-type manipulators is presented. This analysis relies on a priori knowledge of the position analysis for the manipulator. The approach uses a connectivity chart to define the equations required to determine the velocities of the nodal points of the truss. The problem of determining the nodal velocities is formulated as a linear algebraic relationship for ease of analytical and numerical manipulation. Once each nodal velocity is known, a general description of the overall manipulator velocity is formed by determining the instantaneous screw axis for the output plane. An analytical method for characterizing this output velocity in terms of the instantaneous screw axis is presented. Analysis of each of the four basic variable geometry truss modules (tetrahedron, octahedron, decahedron, and dodecahedron) is presented. Although ad hoc velocity analyses of many of these manipulators have been presented in the past, the technique presented in this paper is unified for any truss-type manipulator.

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