Rigid Body Hyper-jerk Analysis Using Screw Theory

2014 ◽  
pp. 411-422
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. Garcia-Murillo
Keyword(s):  
Rigid Body ◽  
Screw Theory

Sir Robert Stawell Ball and methodologies of modern screw theory

2002 ◽  
Vol 216 (1) ◽  
pp. 1-11 ◽  
Author(s):  
H Lipkin ◽  
J Duffy
Keyword(s):  
Computational Geometry ◽  
Rigid Body ◽  
Lie Algebra ◽  
Screw Theory ◽  
Mechanical Design ◽  
Ball Screw ◽  
Dual Numbers ◽  
Body Dynamics ◽  
Rigid Body Mechanics ◽  
Multi Body

The theory of screws was largely developed by Sir Robert Stawell Ball over 100 years ago to investigate general problems in rigid body mechanics. Nowadays, screw theory is applied in many different but related forms including dual numbers, Plilcker coordinates and Lie algebra. An overview of these methodologies is presented along with a perspective on Ball. Screw theory has re-emerged after a hiatus to become an important tool in robot mechanics, mechanical design, computational geometry and multi-body dynamics.

Application of Screw Theory to Rigid Body Dynamics

1992 ◽  
Vol 114 (2) ◽  
pp. 262-269 ◽  
Author(s):  
G. R. Pennock ◽  
B. A. Oncu
Keyword(s):  
Rigid Body ◽  
Euler Equation ◽  
Computer Aided Design ◽  
Graphical Representation ◽  
Screw Theory ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Dynamic State ◽  
Disk Rolling ◽  
Insight Into

This paper applies screw theory to the dynamic analysis of a rigid body in general spatial motion. Particular emphasis is placed upon the geometric interpretation of the velocity screw, the momentum screw, and the force screw which provide valuable physical insight into the dynamic behavior of the rigid body. The geometric relation between the velocity screw and the momentum screw is discussed in some detail. The paper shows that the dual angle between the two screws provides insight into the kinetics of the rigid body. The dynamic state of motion of the body is then described by a dual vector equation, referred to as the dual Euler equation. The paper shows that the geometric equivalent of the dual Euler equation is a spatial triangle which can be used as a graphical method of solution, or as a check, of the analytical formulation. The concepts introduced in this paper are illustrated by the well-known example of a thin, homogeneous, circular disk rolling without slipping on a flat horizontal surface. With the widespread use of computer graphics and computer-aided design, the geometric approach presented here will prove useful in the graphical representation of the dynamics of a rigid body.

Screw Theory and Helicoidal Fields

1998 ◽  
Author(s):  
Jaime Gallardo A. ◽  
José María Rico M.
Keyword(s):  
Vector Field ◽  
Rigid Body ◽  
Screw Theory ◽  
Geometric Representation ◽  
Formal Approach

Abstract Chevallier [1991] regarded a screw as the geometric representation of a “helicoidal” field: i.e. a vector field with helicoidal properties. In this contribution, this identification is employed to develop a formal approach to systematically define “reduced acceleration state” and “reduced jerk state”. Furthermore, it is shown that the comparison of the velocity state, “reduced acceleration state” and “reduced jerk state” is sufficient to determine if a pair of infinitesimal motions of a rigid body are, or not, equal.

Kinematics and Friction in Grasping by Robotic Hands

1987 ◽  
Vol 109 (3) ◽  
pp. 398-404 ◽  
Author(s):  
E. N. Ohwovoriole
Keyword(s):  
Rigid Body ◽  
Kinematic Analysis ◽  
Screw Theory ◽  
Robotic Hands ◽  
Kinematic Theory ◽  
Novel Method ◽  
Total Freedom ◽  
The Stability

Using the extended screw theory, grasping is analyzed in terms of the complete and partial constraint of a rigid body. The underlying kinematic theory is first reviewed and illustrated. The extended screw theory is then used to determine the disturbing and nondisturbing external wrenches, and resulting disturbances for a grasped object. This is a new application of the concept of total freedom based on the idea of component motions and the wrenches that can cause them. Determining the disturbing and nondisturbing wrenches is tantamount to determining the stability of the grasp in regard to total freedom. Finally, a novel method of incorporating friction in the kinematic analysis of grasping using screw theory is also developed using the concepts of apparent normals and apparent motions.

A Dual-Vector Method to Derive the Equivalent Screw of Two Successive Finite Screw Displacements for Line Segments

2020 ◽  
Vol 12 (4) ◽  
Author(s):  
Zetao Yu ◽  
Kwun-Lon Ting
Keyword(s):  
Rigid Body ◽  
Line Segment ◽  
Screw Theory ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Vector Method ◽  
Dual Vector ◽  
Similar Relation ◽  
Vector Algebra ◽  
Illustrative Purpose

Abstract For finite rigid body motion, every two successive screw displacements can be represented by one equivalent screw displacement. However, such phenomenon should not be considered naturally to be valid for incompletely specified displacements (ISDs). There is neither a precise statement for such phenomenon nor an understanding of its range of validity within ISD, such as line segment displacements. As one of the main contributions in this paper, based on dual vector algebra and screw theory, an algorithm is provided to prove the existence of the subset within the scope of the line segment motion, which expresses the similar relation as shown in finite rigid body motion. A numerical example is presented for illustrative purpose.

Synthesis of a Rear Wheel Suspension Mechanism With Pure Rectilinear Motion

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Jing-Shan Zhao ◽  
Fulei Chu ◽  
Zhi-Jing Feng ◽  
Sheng Zhao
Keyword(s):  
Rigid Body ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Rear Wheel ◽  
Rectilinear Motion ◽  
Rear Suspension ◽  
Kinematic Chains ◽  
Redundant Constraint ◽  
Straight Line ◽  
Suspension Structure

This paper focuses on the synthesis of an independent suspension that can guide the wheel to track a straight line when moving up (jounce) and down (rebound). With displacement subgroups, it first synthesizes a rigid body guidance mechanism and verifies the result through screw theory. To simplify and optimize the loads of each kinematic chain of the knuckle, it investigates the static equations and ultimately synthesizes a symmetric redundant-constraint suspension structure, which could not only eliminate the shambling shocks induced by the jumping of wheels but also decrease the abrasion of tires. Theoretically, only one pair of noncoplanar kinematic chains is necessary to realize straight line guidance. However, a second pair of noncoplanar kinematic chains is particularly utilized to improve the load status of the links. Because of the redundant constraints induced by the suspension structures, the whole weight can be significantly reduced compared with the initial one. ADAMS simulations with a set of real parameters indicate that the rear suspension mechanism proposed in this paper can guide the wheel to follow a rectilinear locus during jounce and rebound. Therefore, this kind of independent suspension can improve the ride and handling properties of advanced vehicles.

A Line Geometric Approach to Determining Displacements Based on Line Specifications

2008 ◽  
Author(s):  
Wuchang Kuo ◽  
Chintien Huang
Keyword(s):  
Rigid Body ◽  
Measurement Errors ◽  
Systematic Approach ◽  
Screw Theory ◽  
Geometric Approach ◽  
Line Geometry ◽  
Line Complex ◽  
Numerical Example ◽  
On Line ◽  
Best Fit

This paper presents a systematic approach to determining the displacements of a rigid body from line specifications. The underlying concept of the proposed approach pertains to screw theory and line geometry. We utilize the correspondence between a pair of homologous lines and a regulus and that between a screw and a linear line complex. In this paper, a displacement screw is obtained by fitting a linear line complex to two or more line reguli. When two exact pairs of homologous line are specified, we obtain a unique linear line complex, which determines the displacement screw correspondingly. When more than two pairs of homologous lines with measurement errors are specified, it becomes a redundantly specified problem, and a linear line complex that has the best fit to more than two reguli is determined. A numerical example with the specification of four pairs of homologous lines is provided.

Synthesis of Decoupled Spatial Translational Compliant Parallel Mechanisms via Freedom and Actuation Method (FAM)

2014 ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao ◽  
Richard Kavanagh
Keyword(s):  
Rigid Body ◽  
Mechanism Design ◽  
Screw Theory ◽  
Synthesis Process ◽  
Parallel Mechanisms ◽  
Mathematical Expressions ◽  
Function Modules ◽  
Function Module ◽  
Design Experience ◽  
Actuation Method

This paper introduces a screw theory based approach termed the freedom and actuation method (FAM) to the synthesis of decoupled spatial translational compliant parallel mechanisms (XYZ CPMs) with consideration of actuator isolation (input decoupling). This approach is unique in that (a) actuator arrangement is taken into account; and (b) it is based on a set of rules and mathematical expressions, rather than rigid-body mechanism design experience mainly used at present. According to the rules, XYZ CPMs are firstly decomposed into simple function modules, and the degrees of freedom (DOF) of each function module are identified based on the mathematical expressions. Each function module is then synthesized based only on the DOF without consideration of the actuator arrangement, so existing flexure mechanism design approaches such as the constraint-based design, the screw-theory-based method, and the freedom and constraint topology can be employed for the synthesis of the function module. The synthesis process is finally summarized and demonstrated step by step via a monolithic XYZ CPM design example. It can be envisaged that a variety of configurations of each function module can be derived under a specific DOF. Therefore, one can obtain a great number of XYZ CPM designs with consideration of actuator isolation through changing the structure of each function module, even though there is no any rigid-body mechanism design experience. The proposed FAM will enable designers to (a) decompose XYZ CPMs into the function modules; (b) yield multiple solutions to meet the DOF requirement of each compliant function module; and (c) obtain a variety of XYZ CPMs with consideration of actuator isolation.

Profile Determination of Planar and Spatial Cams with Cylindrical Roller-Followers

1996 ◽  
Vol 210 (6) ◽  
pp. 565-574 ◽  
Author(s):  
D M Tsay ◽  
B J Lin
Keyword(s):  
Rigid Body ◽  
Screw Theory ◽  
Curve Surface ◽  
Pitch Curve ◽  
Rigid Body Transformation ◽  
Analytical Expressions ◽  
Cylindrical Roller ◽  
Offset Surface

A simple and useful procedure that can be used to determine profile surfaces of planar and spatial cams with cylindrical roller-followers is presented. Based on the rigid-body transformation between the cam and the roller-follower, the pitch (curve) surface which is the path of the point of the roller centre can be easily generated. Then the analytical profile surface of the cam can be represented by the offset surface of the pitch surface with a distance equal to the radius of the roller. To illustrate the ease and effectiveness of the approach, analytical expressions of profile surfaces of a disc cam, two cylindrical cams and two globoidal cams are typically given. Furthermore, in order to show the validity of this method, the results are then compared to those derived by an earlier procedure based on the screw theory.

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