Constructing 3D motions from curvature and torsion profiles

Cripps, Robert J.; Mullineux, Glen

doi:10.1016/j.cad.2012.01.004

Cited by 7 publications

(6 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The jerk vector would then gain a binormal component. Incorporating a binormal vector may also provide a means of describing the characteristic nature of motions where a tool's orientation may be allowed to change with respect to the workpiece [41,42]. This could then motivate the study of the motions of a machine's rotational axes.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Characterising the effects of shape on tool path motion

Chanda

Cripps

2018

International Journal of Machine Tools and Manufacture

View full text Add to dashboard Cite

This paper presents a methodology for a priori shape characterisation of tool path motion. Many current methods to describing tool path motion require explicit knowledge of the motion control algorithms implemented on a specific machine. Either a method proposes novel algorithms or requires knowledge of the algorithms currently implemented in a given machine's controller (e.g. minimum jerk, harmonic jerk and minimum jounce). This paper provides a method, that may be applied on any machine, to characterise motion in terms of a tool path's intrinsic shape properties. The characterisation identifies the achievable set of kinematics for a tool path of a given shape without the need for physical machining and a knowledge of the motion control algorithms. The characterisation may be employed in a pre-processing manner to inform the selection of NC file tool path motions. This can therefore help to reduce the material and energy resources being consumed during iterative machining trials and so improve the efficiency and productivity of the manufacturing process.

show abstract

Section: Accepted Manuscriptmentioning

confidence: 99%

Characterising the effects of shape on tool path motion

Chanda

Cripps

2018

International Journal of Machine Tools and Manufacture

View full text Add to dashboard Cite

show abstract

“…There are a number of ways to define or construct geometric (or Clifford) algebras (Perwass 2009, Dorst et al 2007, González Calvet 2007. The approach adopted here is that described in detail in (Cripps andMullineux 2012, Mullineux andSimpson 2011) which creates an algebra called G 4 . Some alternative approaches are given in the appendix.…”

Section: Overview Of Geometric Algebra Gmentioning

confidence: 99%

“…Suppose also that p ∈ G 4 is a vector and so represents a point in (projective) 3-space. The product SpS has odd grade and is equal to its own reverse, and so it is also a vector (Cripps and Mullineux 2012). Hence the mapping…”

Section: Transformsmentioning

confidence: 99%

“…An approach which is a natural extension of quaternions is the use of geometric algebra (Perwass 2009, Dorst et al 2007, González Calvet 2007 and the proposed method presented in this paper uses a geometric algebra to represent tool path motions. This allows any rigid-body transform to be represented exactly (Cripps andMullineux 2012, Mullineux andSimpson 2011), meaning that it can deal with the translational and rotational elements of a tool pose and can do so in a single theoretical framework. This is one of the aspects of the geometric algebra formulation that makes it very attractive for a number of applications.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Using geometric algebra to represent and interpolate tool poses

Cripps

Mullineux

2015

International Journal of Computer Integrated Manufacturing

View full text Add to dashboard Cite

In conventional computer aided manufacturing techniques, a tool path is sent to the machine tool controller as a sequence of precision points. This means that errors are introduced when the controller interpolates between the points to recover the intended path. For 4-and 5-axis machining, a sequence of precision poses (positions and orientations) is needed. The use of geometric algebra in representing poses is discussed. The form of algebra used can represent rigidbody transforms exactly and can interpolate, in a natural way, between two or more poses using spherical linear interpolation (slerp). Sequences of poses from free-form surfaces are investigated. Tool motions are generated and compared with tool paths derived from purely positional information. It is found that the motion paths more naturally follow the original surface so that the interpolation errors are smaller.

show abstract

“…Planning smooth motions of rigid bodies in 3D has also been studied [41,2,4,9]. This requires planning in the space of 3D positions and orientations, also commonly referred to the SE(3) group.…”

Section: Related Workmentioning

confidence: 99%

Planning Curvature and Torsion Constrained Ribbons in 3D With Application to Intracavitary Brachytherapy

Patil

Pan

Abbeel

et al. 2015

IEEE Trans. Automat. Sci. Eng.

View full text Add to dashboard Cite

Abstract. A "ribbon" is a surface traced out by sweeping a constant width line segment along a spatial curve. We consider the problem of planning multiple disjoint and collision-free ribbons of finite thickness along curvature and torsion constrained curves in 3D space. This problem is motivated by the need to route multiple smooth channels through a 3D printed structure for a healthcare application and is relevant to other applications such as defining cooling channels inside turbine blades, routing wires and cables, and planning trajectories for formations of aerial vehicles. We show that this problem is equivalent to planning motions for a rigid body, the cross-section of the ribbon, along a spatial curve such that the rigid body is oriented along the unit normal to the curve defined according to the Frenet-Serret frame. We present a two stage approach. In the first stage, we use sampling-based rapidly exploring random trees (RRTs) to generate feasible curvature and torsion constrained ribbons. In the second stage, we locally optimize the curvature and torsion along each ribbon using sequential quadratic programming (SQP). We evaluate this approach for a clinically motivated application: planning multiple channels inside 3D printed implants to temporarily insert high-dose radioactive sources to reach and cover tumors for intracavitary brachytherapy treatment. Constraints on the curvature and torsion avoid discontinuities (kinks) in the ribbons which would prevent insertion. In our experiments, our approach achieves an improvement of 46% in coverage of tumor volumes as compared to an earlier approach that generates each channel in isolation.

show abstract

Constructing 3D motions from curvature and torsion profiles

Cited by 7 publications

References 47 publications

Characterising the effects of shape on tool path motion

Characterising the effects of shape on tool path motion

Using geometric algebra to represent and interpolate tool poses

Planning Curvature and Torsion Constrained Ribbons in 3D With Application to Intracavitary Brachytherapy

Contact Info

Product

Resources

About