Five-axis pencil-cut planning and virtual prototyping with 5DOF haptic interface

Five-axis pencil-cut planning and virtual prototyping

with 5-DOF haptic interface

Weihang Zhu, Yuan-Shin Lee*

Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, USA

Received 22 August 2003; received in revised form 22 January 2004; accepted 30 January 2004

Abstract

In this paper, techniques of 5-axis pencil-cut machining planning with a 5-DOF (degree of freedom) output haptic interface are presented.

Detailed techniques of haptic rendering and tool interference avoidance are discussed for haptic-aided 5-axis pencil-cut tool path generation.

Five-axis tool path planning has attracted great attention in CAD/CAM and NC machining. For efficient machining of complex surfaces,

pencil-cut uses relatively smaller tools to remove the remaining material at corners or highly curved regions that are inaccessible with larger

tools. As a critical problem for 5-axis pencil-cut tool path planning, the tasks of tool orientation determination and tool collision avoidance

are achieved with a developed 5-DOF haptic interface. A Two-phase rendering approach is proposed for haptic rendering and force-torque

feedback calculation with haptic interface. A Dexel-based volume modeling method is developed for global tool interference avoidance with

surrounding components in a 5-axis machining environment. Hardware and software implementation of the haptic pencil-cut system

with practical examples are also presented in this paper. The presented technique can be used for CAD/CAM, 5-axis machining planning and

virtual prototyping.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: 5-axis machining; Pencil-cut planning; Haptic rendering; CAD/CAM; NC machining; Virtual prototyping

1. Introduction

Five-axis tool path planning has attracted great attention

in Computer-aided Manufacturing (CAM) and NC

machining. Many issues of 5-axis machining need to be

addressed; among them the tool path generation and tool

orientation control are two main issues. Great progress has

been made in 5-axis tool path planning after years of

research [1–3]. While continuing work is being pursued to

improve 5-axis tool path planning, haptic interface has

gradually aroused the interest of the Computer-aided Design/

Computer-aided Manufacturing (CAD/CAM) research area.

Haptics is concerned with information and object manipu-

lation through touch. Besides transducing position and

motion commands from the user, the haptic devices can

present controlled forces to the user, allowing him or her to

feel virtual objects and to control or deform the objects [4].

Haptic interface has found its applications in design,

medicine, entertainment, education, industry, graphic arts,

etc [5]. In this paper, we are especially interested in the haptic

application in CAD/CAM and NC machining.

In the CAD area, researchers from University of Utah

have published their work on direct manipulating of

NURBS surface with their special haptic manipulator [6].

Basically, it is a system wherein one can trace along a

NURBS surface and feel it. A dynamic sculpting system for

free-form subdivision solids was developed at SUNY Stony

Brook [7]. A virtual carving system with a commercial

haptic interface was developed at University of Missouri-

Rolla [8]. These presented systems, although different in

their implementations and some underlying theories, can

both be traced back to volume sculpting [9].

In the CAM area, some initial attempts and inspiring

work have been developed at MIT. Researchers have

produced some interesting results in 5-axis tool path

generation. In their work, a quick collision detection

method was proposed between a tool and a machining

environment represented by point clouds [10]. In their tool

path generation application, they machined a part with a

constant Z-height machining method [11]. In our earlier

work presented in Ref. [12,13], techniques of haptic virtual

sculpting of complex surfaces have been developed.

0010-4485/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.cad.2004.01.013

Computer-Aided Design 36 (2004) 1295–1307

www.elsevier.com/locate/cad

* Corresponding author. Tel.: þ1-919-515-7195; fax: þ1-919-515-5281.

E-mail address: [email protected] (Y.-S. Lee).

This paper presents the techniques of employing

haptic interface for 5-axis pencil-cut tool path planning. A

lab-built 5-DOF (degree of freedom) haptic device, haptic

hardware controller and haptic rendering software are

developed. The remainder of this paper is organized as

follows. Section 2 introduces the problem of pencil-cut

machining operation. Section 3 describes the methodology

of the haptic-aided 5-axis pencil-cut tool path generation in

details. Section 4 discusses the software and hardware issues

in implementing the haptic interface system. Practical

examples and experiment results are presented in

Section 5, followed by concluding remarks and future work.

2. Problems of pencil-cut machining

of sculptured surfaces

In sculptured surface machining, the several stages of

machining include roughing, semi-finishing, finishing and

clean-up [1]. Roughing removes the bulk material outside

the design surface. After semi-finishing and finishing,

the shape of the machined surface is very close to the

designed part surface. Clean-up machining removes the

remaining material left at the sharp corners or edges.

Pencil-cut is used for clean-up machining (Fig. 1(a)).

Pencil-cut in 3-axis machining has been researched for

years, and this function is provided in some commercial

software for parametric surfaces. In our earlier work

presented in Ref. [14], algorithms for 3-axis pencil-cut of

polyhedral models have been developed for sculptured

surface machining. To the best of our knowledge, research

work on 5-axis pencil-cut has not been reported.

Five-axis pencil-cut has the obvious advantage over

3-axis pencil-cut, due to the former’s better accessibility

with the additional rotation axes. For 3-axis pencil-cut,

the tool orientation is fixed as the Z-axis, as shown in

Fig. 1(a). Five-axis pencil-cut is especially useful for

cleaning remaining materials in complex surfaces. As can

be seen from Fig. 1(b), the curved corner region can be

accessed by 5-axis machining but is not accessible by 3-axis

machining. In our earlier work presented in Ref. [14],

a method has been developed to identify the clean-up

regions on complex part surfaces. For 5-axis pencil-cut,

the difficulty for tool path planning lies mostly in

determining the tool orientation.

In 5-axis machining, a cutting tool can be oriented by

rotating around one axis with an inclination angle lL and

another axis with a tilt angle vL; as shown in Fig. 2.

To facilitate searching for a feasible tool orientation, usually

a local coordinate system is set up as follows: XL-axis is the

instantaneous feed direction (cutting direction); ZL-axis is

the surface normal direction at the current cutter contact

(CC) point; YL-axis is determined by the right-hand rule

(Fig. 2(a)) [3]. Then the tool orientations are searched based

on this local coordinate system. To find a good tool

orientation control in 5-axis machining, a configuration-

space (C-space) is formed with the inclination angle lL and

the tilt angle vL; as shown in Fig. 2(b) [1]. As discussed in

Ref. [2], a machining C-space MCS of a given CC point CCi

on a designed part surface, PS, machined with a cutter C can

be defined as follows (also see Fig. 2(b))

MCSðC; PS; {CCi}Þi¼0;…;n ¼lL

vL

" #ð1Þ

Past research on the tool orientation mainly adjusts the

inclination angle lL; due to the theoretically infinite

combinations of inclination angle lL and tilt angle vL:

Most of the research considers only the local optimal tool

orientation, which is based on analysis of the part surface

property and cutting conditions near the CC point.

When seeking the globally optimized tool orientation in

5-axis machining, we have to deal with expensive

computation and searching concerning the interference

between the whole tool assembly and the stock. The reason

is that we have to find the feasible (not necessarily the

optimal) tool orientation by trial and error. Several attempts

were made in circumventing this exhaustive search [15,16].

However, there are also some limitations in the results, due

to the different assumptions made about the designed part

surface or the cutting tool [2].

In this paper, we developed a haptic system to help

determine and select the tool orientations for 5-axis

pencil-cut machining in a complex machining environment

[13]. Details of developing the haptic system are discussed

in the following sections.

3. Proposed haptic system for 5-axis pencil-cutmachining

3.1. Identification of pencil-cut region and tool

path generation

The first step for pencil-cut machining is to identify

where the pencil-cut operation should be executed. In this

paper, a designed surface is represented in stereo

lithography (STL) format, which is composed of a

collection of triangles and basically is a kind of polyhedral

model (see Fig. 3(a)). The use of STL format for

representing a CAD model has been widely accepted inFig. 1. Pencil-cut of complex surfaces. (a) Three-axis pencil-cut. (b) Five-

axis pencil-cut.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–13071296

industry for some time [17]. As shown in Fig. 3, a

Rolling-ball method developed in our earlier work presented

in [14,18] was revised to extract the pencil-cut regions of

sculptured surfaces. The Rolling-ball method works in the

way described as follows.

Fig. 3(a) shows an example polyhedral model. A CC-net,

which is a net of CC points, is cast on the polyhedral model, as

shown in Fig. 3(b). A ball with an appropriate radius, which is

usually set as the radius of a finishing cutter, rolls along this

CC-net to identify the pencil-cut boundary points [18].

Two smaller balls, whose radii are usually set as half of

the radius of the previous big reference ball, are rolling along

a route parallel to the pencil-cut boundary, as shown in

Fig. 3(c). In this way, the pencil-cut regions can be identified

and the parallel pencil-cut tool paths can be traced for each

pencil-cut region, as detailed in Ref. [14].

For 5-axis pencil-cut, the tool orientations are to be

determined by considering both the local surface property

and the surrounding machining environments.

These problems of global tool collision and local gouging

Fig. 2. Coordinate systems in 5-axis machining and the C-Space definition.

Fig. 3. Rolling-ball method for identifying pencil-cut regions of sculptured surfaces. (a) An example polyhedral model. (b) Finding pencil-cut regions [14].

(c) Tracing pencil-cut tool paths with two smaller balls.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–1307 1297

in 5-axis machining, as shown in Fig. 4, still need to be

solved for the determination of 5-axis tool orientation

control. More detailed discussion of solving these problems

will follow in Section 4.

3.2. Developing haptic interface for 5-axis pencil-cut tool

path planning

After the pencil-cut regions are identified, the feasible

5-axis cutter trajectory and tool orientation are determined by

using haptic interface. Fig. 5 shows our lab setup of the haptic

system. The haptic device we are using is a lab-built 5-DOF

pen-based electro-mechanical device made by Suzuki, Inc.,

Japan. It can detect 6-DOF of haptic probe movement and

provides 5-DOF force feedback, with both force and torque

feedback. Fig. 5 shows the lab setup with the haptic device

located in the middle. In Fig. 5, the left hand side is the

constructed controller. Its right hand side is the dual 2.4 GHz

CPU workstation with the implemented software and haptic

rendering programs presented in this paper.

Fig. 6 shows the working principle of our developed

haptic system. The movement of the haptic device probe is

recorded by the encoders. The encoders’ signals are collected

by a counter board, which is installed in a dual-CPU

workstation. As shown in Fig. 6, the program computes the

haptic response of force feedback and sends the control

signals out via the D/A board. The control signals are

amplified to drive the motors on the haptic device.

The motors’ movements let the user feel the force feedback.

The control driver for the haptic system was developed

for this hardware. The tasks of this driver include interfacing

with the D/A board and counter board and distributing the

desired forces to the haptic device’s actuators’ (DC motors)

torques. As shown earlier in Fig. 5, the haptic device has a

left-manipulator and a right one. Both of them working

together feedback the force and torque to the user. Fig. 7

shows the corresponding force and torque configuration in

the virtual tool assembly with the physical haptic device

probe. For virtual reality calculation, assume the left

manipulator needs to generate force ~fL and the right

manipulator needs to generate force ~fR; the haptic rendering

needs to calculate the necessary torques ~tL and ~tR for

the haptic device’s motors by using the Jacobian Matrices

(JTL and JT

R), as shown in Fig. 7. The relationship between

the haptic force responses (~fL and ~fR) and the correspondent

haptic torques ( ~tL and ~tR) is shown as follows [13]

~tL ¼ JTL~fL ð2Þ

~tR ¼ JTR~fR ð3Þ

where JTL and JT

R are the Jacobian Matrices. The derivation

of the Jacobian Matrix is dependent on the link structure of

Fig. 4. Global collision and local gouging in 5-axis NC machining.

Fig. 5. Lab set-up of haptic controller and 5-DOF haptic device, with a

dual-CPU workstation.

Fig. 6. Controlling principle of the developed haptic rendering system.

Fig. 7. Mechanism transformation between the tool assembly and the

physical haptic system link structure.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–13071298

a specific haptic device, which is a kind of special robot

arms [13,19]. Eqs. (2) and (3) will be used later in this paper

for force–torque calculation. Details of force ~f and torque ~t

feedback calculation for the haptic interface will be

discussed in Section 4, as part of haptic rendering.

In the virtual tool assembly, the pivot point is defined as

the rotation center of a NC machine spindle head, as shown

in Fig. 7. There are different types of 5-axis CNC milling

machines, based on the spindle and rotary table structure.

The one we are modeling in this paper is a spindle-tilt 5-axis

machine, which has a rotatable spindle around either A-axis

and C-axis. The intersection of A-axis and C-axis is defined

as the pivot point for the spindle-tilt 5-axis machine.

Corresponding to the virtual pivot point of the CNC

machine in the Virtual Environment, there is a correspond-

ing physical pivot point in the haptic device to facilitate the

simulation and calculation. The 5-DOF haptic device has a

left manipulator and a right one. Both manipulators joined

together at the stylus (or the haptic probe) (see Fig. 7 for

details). Based on its link structure, the pivot point is the

middle point between the two ends of the left and right

manipulators (Fig. 7). The pivot point is used for calculating

the torque feedback required in the virtual world.

3.3. Determining the feasible 5-axis tool orientation

using haptic interface

Generally in 5-axis NC machining, the interference

between the workpiece and the tool assembly can be divided

into two types (see Fig. 4):

† Global collision between the workpiece, fixtures and the

non-cutting portion of the tool assembly, e.g. tool holder

and tool shank;

† Local gouging between the designed part surface and

cutting portion of the tool.

The user needs to eliminate both of them when choosing

a feasible 5-axis tool orientation. During the haptic

interaction process, the user can easily orient the tool

assembly to avoid global collision, as one can feel the force~f and torque ~t feedback from the haptic system in the case of

tool collision. On the other hand, local gouging is relatively

difficult to completely eliminate. During the haptic

interaction process, the virtual tool touches the surfaces,

which means there must be at least a slight

interference between the tool and the designed surface.

Hence global collision is removed during the haptic

interaction. Post-processing for the tool path is invoked to

eliminate local gouging. Details on how interferences are

detected and corrected will be discussed in Section 4.

Fig. 8 shows an example surface designed for

demonstrating pencil-cut tool path planning. Two parallel

pencil-cut tool paths were identified along the edges using the

Rolling-ball method mentioned earlier. During the haptic

interaction process, the nearest CC point to the current virtual

tool tip is found and highlighted with its normal vector, as

shown in Fig. 8. To speed up the computation and to reduce

the interaction load of the haptic system, it is proposed that

only the tool orientations of those critical CC points need to

be specified and the other CC points’ tool orientation are to be

defined by interpolation. This is analogous to animation

creation, where key animation frames are defined and interim

animation frames are automatically created by interpolation.

During the interaction process, if a certain CC point is picked

up as a key point, the user moves the virtual tool to that CC

point, orients the virtual tool along an appropriate orien-

tation, based on what she/he sees and the force and torque

she/he feels at the haptic probe, and presses a hot key to

record the current tool orientation for this CC point.

A complex machining environment can be composed of a

workpiece, jigs and fixtures, etc. The interference between

the tool and all these components should be considered and

thus affects the tool orientation selected. Fig. 9(a) shows

the critical tool orientations specified by a user via haptic

probe. The selection of the critical tool orientations can be

done based on the graphical and haptic feedback offorce ~f and

torque ~t:These critical tool orientations are usually located at

where surface features changes. Fig. 9(b) shows the

interpolated tool orientations between the critical tool

orientations. If the user is unsatisfied with the current results,

she/he can choose to re-specify the critical tool orientation or

adjust the interpolated tool orientations directly, until all the

orientations are satisfying. Assume two adjacent critical tool

orientations are ~O1 and ~O2 and there are n CC points between

them, the ith tool orientation on of the ith interim CC point is

interpolated as (Fig. 10)

~Oi ¼i·ð ~O2 2 ~O1Þ

n þ 1þ ~O1 ð4Þ

~Oi;unit ¼ Normalizeð ~OiÞ ð5Þ

Fig. 8. Pencil-cut tool path (two blue parallel trajectories) identified on an

example surface, with the nearest CC point identified with its normal vector

(For interpretation of the references to colour in this figure legend, the

reader is referred to the web version of this article).

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–1307 1299

This will be explained more clearly with the examples

presented later in Section 5. The calculation of interference

detection and force feedback is presented in Section 4.

3.4. Post-processing and eliminating local gouging

in tool path generation

After the tool orientations are selected, the tool path

information is post-processed to eliminate local gouging.

Notice that the local gouging is not completely eliminated

during the haptic rendering process, since there must be

some collision between the haptic probe and design surface

in order to give the user the force feedback. Hence, the local

gouging is eliminated during the post-processing. In the

post-processing, the tool orientation for each CC point is

kept intact and the tool assembly is checked for local

gouging. The basic idea is to lift the tool up if there is

collision between the tool and the triangles on the STL

model (Fig. 11(a)). The tool is lifted up to a position along

the current tool orientation to eliminate any local gouging.

Fig. 11(a) shows this process. After the automated post-

processing, the tool path can be generated by computing

cutter location (CL) points CLi��!

from the CC points CCi��!

with

the following formula for filled-end mill (Fig. 11(b))

CLi��!

¼ CCi��!

þ rtc~ni þeðð~ni £ ~OiÞ £ ~OiÞ

lðð~ni £ ~OiÞ £ ~OiÞlþ rtc

~Oi ð6Þ

where

rtc is the minor radius of a fillet-end mill,

e is the major radius of a fillet-end mill,

~ni is the normal vector associated with the current CC

point,~Oi is the tool orientation for the current CC point.

The CL data are further processed to generate NC code to

drive the NC machine. In this paper, the generated NC code

is simulated on commercial NC simulation and verification

software. Simulation results for a practical part surface are

presented in Section 5.

4. Haptic rendering programming for 5-axis pencil-cut

Haptic rendering programming first checks the

interference/collision (including both global collision and

local gouging) between a moving tool assembly and the

static product surface in a complex machining environ-

ment. If any interference is detected, the program

continues to calculate the extent of interference and to

calculate the required force and torque in the virtual

world. The desired force and torque are converted to

haptic manipulator force fL and fR; as indicated earlier in

Eqs. (2) and (3), so that they can be used to drive the

haptic device and to provide feed back to the user.

The collision detection speed is critical for haptic

applications. The update rate is estimated to be at least

1000 Hz in order to maintain a sustained feeling of force

feedback [4]. In every 1 ms, the computer needs to detect the

coordinates of the haptic probe, transform the coordinate

values from the physical device coordinate system to

the graphics environment, detect the collisions between the

virtual objects and calculate the force feedback. Object/

object collision detection methods are required in the current

application. In order to achieve a high update rate for

complex environments, computing techniques like the spatial

decomposition tree [20,21] and the object oriented bounding-

box (OBB) tree [22] are adopted in this paper.

In the current application, both the designed part surface

and its fixtures are assumed to constitute the surrounding

machining environment. The designed part surfaces are

assumed to be freeform surfaces with complex geometry. The

fixtures, on the contrary, are most likely prismatic and more

regular in shape. In this paper, a Two-phase rendering

Fig. 9. Tool orientations generated for the pencil-cut tool paths. (a) Critical

tool orientations (cyan vectors in light color) specified on the example

surface (b) Interpolated tool orientations (blue vectors in dark color) on the

example surface. (For interpretation of the references to colour in this figure

legend, the reader is referred to the web version of this article).

Fig. 10. Tool orientation interpolations from two critical tool orientations.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–13071300

approach to tool collision detection and local gouging

elimination is proposed for haptic pencil-cut of sculptured

surfaces. A Dexel-based volume modeling method is used for

global tool interference avoidance with surrounding com-

ponents, such as fixtures or tables, of a machining environ-

ment. Both approaches are detailed in the following sections.

4.1. Two-phase rendering approach to collision detection

and force response

In this paper, a Two-phase rendering approach is

proposed for the haptic pencil-cut interface and the

rendering programming, as shown in Fig. 12. In the Two-

phase approach, for the convenience of the first phase, the

triangular polygons in STL models are organized into OBB

trees, as shown in the ‘First phase’ of Fig. 13.

In the first phase (see Figs. 12 and 13), the possible

collision triangles (PCT) are extracted by checking the

interference between the OBB-trees of STL surface models

and the simple OBB-tree of the tool assembly. In our

approach, the tool definition is a combination of implicit

surfaces. To improve the computing efficiency, we try to

simplify the definition of the tool while trying to

accommodate a more complex part surface. A triangulated

STL model is adopted in this paper because the computation

and geometric processing of the STL model are relatively

faster. The next step is to find out how we can quickly detect

the collision and calculate the force feedback. The STL

surface model’s OBB-tree is static during the interaction

process. During the movement of the haptic probe, the tool

assembly’s OBB-tree is updated (Fig. 13). There is little

overhead in updating the tool assembly’s OBB-tree.

In the second phase (Figs. 12 and 13), to improve the

efficiency of collision detection, the triangles in the STL

model are discretized into sampling point clouds at the

beginning of the haptic application, as shown in the

‘Second phase’ in Fig. 13. Each point is associated with a

normal direction, which is set as the normal direction of the

triangle it belongs to. Adaptive point cloud density is used

for different features of the tool assembly. In the second

phase, the points corresponding to the PCT are checked

against the tool’s implicit surface for the collision test, as

shown in Fig. 12. If a point is inside the tool assembly,

we find the tool surface point nearest the collision point and

then calculate the distance between the collision point

and the corresponding tool surface point. The force

magnitude is proportional to this distance. Assuming this

distance is Dxi and k is a pre-defined coefficient, the

responding force magnitude fi;mag is calculated as follows

fi;mag ¼ kDxi ð7Þ

The unit force direction ~fi;dir has already been associated

with the collision point, as mentioned earlier in the process

of generating point cloud. A component force ~fiðfi;mag;~fi;dirÞ

is determined by its magnitude fi;mag and direction ~fi;dir: If we

assume that the virtual pivot point’s location is Ppvt;

the collision point’s location is Pi; and the force magnitude

of fi;mag is calculated by Eq. (7), the torque ti induced by this

Fig. 11. Computing CL points from CC Points. (a) Retracting cutter to avoid local gouging; (b) computing CL point from CC point.

Fig. 12. Two-phase approach for haptic rendering.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–1307 1301

collision point is calculated as follows (Fig. 14)

~ti ¼ fi;mag·ð~fi;dir £ ðPiPpvt����!

ÞÞ ð8Þ

Eqs. (7) and (8) will be used for accumulation of total force ~f

and torque ~t fed back to the user. This will be presented in

Section 4.3. The advantages of the proposed Two-phase

approach include

(i) The Two-phase algorithm and the OBB-tree used for

the haptic application environment can significantly

speed up the computation efficiency, especially when

the sculptured surfaces become complex.

(ii) The densities of the point clouds can be adaptive for

different geometries of end mills.

(iii) The cutting tool’s shape can be complex and a

generalized APT type end-mill [23] is used as the

general representation for different types of ball-end

mills, flat-end mills, taper-end mills and fillet-end

mills.

(iv) The force and torque feedback calculation (discussed

in Section 4.3) can be tightly integrated with the

hardware driver level.

4.2. Dexel-based global tool collision and force-torque

analysis

Dexel volume model is a popular format that is widely

used in NC simulation [24]. In our earlier research presented

in [25], Dexel volume models are used for haptic virtual

sculpting of complex surfaces. A Dexel model represents a

CAD model with many columns packed together (Fig. 15).

Each column, as the basic element, is called a Dexel.

Basically it has a 2D grid, and each grid point consists of a

linked list of Dexel volume elements. Usually a high density

of Dexel grid is needed to represent a freeform surface.

For most of the fixtures in the machining environment,

however, the shapes are usually prismatic and regular and

thus the density does not have to be high. Comparatively the

haptic rendering method introduced in Section 4.1 is

computationally intensive because the point cloud density

could be high. On the other hand, for prismatic objects, Dexel

volume models can be a less expensive solution for haptic

rendering [26]. Hence STL models of fixtures can be

converted to Dexel volume models in a virtual machining

environment. A virtual tool can be used to check against

fixtures, which are represented with Dexel volume models,

for collision detection and force-torque feedback calculation.

Fig. 16(a) shows a virtual tool interferes with a fixture

represented with a Dexel model. The interfered Dexels can

be identified. The force magnitude fDj;mag is proportional to

the length of intersection DzDj between the tool and the

Dexels, as shown in Fig. 16(b), shown as follows

fDj;mag¼kD·ðDZDj·DxareaÞ¼ðkD·DxareaÞ·Dxi¼k0D·Dxi ð9Þ

where

DzDj is the intersection Dexel length,

Dxarea is the cross section of the Dexel elements,

Fig. 13. Two-phase haptic rendering with collision detection and force

response.

Fig. 14. Calculation of torque feedback at a collision point Pi:

Fig. 15. Dexel volume model used for haptic rendering and collision

detection.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–13071302

kD is the pre-defined cross-section dependent force

coefficient,

k0D is the cross-section independent force coefficient.

Now the force direction ~fDj;dir needs to be defined.

As shown in Fig. 16(b), the whole cutter assembly is

considered to be composed of two portions: holder and cutter.

The geometric center of the holder and cutter portions can be

defined, respectively, as Pholder_center and Pcutter_center:The tool

assembly may be intersected with the Dexel model of the

holder or cutter portion. Assuming that the geometric enter of

the intersected dexel element is PD;mid; the force direction~fDj;dir is defined as follows (Fig. 16(b))

~fDj;dir ¼PD;midPholder_center�������������!

; for holder portion

PD;midPcutter_center������������!

; for cutter portion

8<: ð10Þ

A component force ~fDjðfDj;mag;~fDj;dirÞ is determined by its

magnitude fDj;mag and direction ~fDj;dir: Assuming that the

virtual pivot point’s location is Ppvt; the center location of the

intersected Dexel is PDj; and the force magnitude of fDj;mag is

calculated with Eq. (9), the torque tDj induced by this

collision point is calculated as follows (Fig. 16(b))

~tDj ¼ fDj;mag·ð~fDj;dir £ ðPDjPpvt�����!

ÞÞ ð11Þ

The collision force ~fDjðfDj;mag;~fDj;dirÞ and the correspondent

torque ~tDj found by using Eqs. (9)–(11) are used in the haptic

rendering to provide force–torque feedback to the users.

Details are discussed in Section 4.3.

4.3. Force and torque feedback distribution to the haptic

device hardware

For the force–torque feedback on the haptic device during

pencil-cut of the complex surfaces, two types of force–tor-

ques need to be considered. These two types of force–torque

feedbacks need to be distinguished in the haptic rendering:

1. Tracing force. As the tool moves on the surface and traces

along the tool path, the force feedback is the tracing force

and the force–torque (~fi and ~ti) feedback is calculated by

using Eqs. (7) and (8).

2. Collision force. If the tool holderof the tool system collides

withpart surface(ie.~fi and ~ti usingEqs. (7)and(8)),or if the

tool collides with the fixtures in the machining environ-

ment (i.e. ~fDj and ~tDj using Eqs. (9)–(11)), the force

feedback is classified as the collision force. The force–

torque feedback can be calculated by using Eqs. (7)–(11).

In general, the collision force is relatively strong

compared to the tracing force. Assuming that there are a

total of m collision points and q Dexel intersections in the

current instance, from Eqs. (7)–(11), the force ~f and torque ~t

feedback via the haptic probe can be calculated as follows:

~f¼Xmi¼1

~fiþXq

j¼1

~fDj¼kXmi¼1

ðDxi·~fi;dirÞþk0DXq

j¼1

ðDzDj·~fDj;dirÞ ð12Þ

~t¼Xmi¼1

~tiþXq

j¼1

~tj¼kXmi¼1

ðDxi·ð~fi;dir£ðPiPpvt����!

ÞÞÞ

þk0DXq

j¼1

ðDzDj·ð~fDj;dir£ðPDjPpvt�����!

ÞÞÞ ð13Þ

Force ~f is distributed to two manipulators as follows

(Fig. 17)

~fLf ¼ f =2 ð14Þ

~fRf ¼ f =2 ð15Þ

In both Figs. 7 and 17, if we assume that the vector from the

left haptic manipulator end PL to right manipulator end PR is

~rLR; the torque is distributed to two manipulators as follows

~fLt¼~t

l~rLRl·~t£~rLR

l ~t£~rLRl¼2~fRt ð16Þ

Then the desired forces on the left and right manipulators are

calculated as follows

~fL¼~fLf þ~fLt ð17Þ

~fR¼~fRf þ~fRt ð18Þ

The desired forces ~fL and ~fR are then substituted into Eqs. (2)

and (3) to get the corresponding DC motor torques ~tL and ~tR:

The rotation of the DC motors applies force on the user’s

hand through the haptic device structure.

Fig. 16. Calculation of force–torque feedbacks using Dexel volume models.

(a) A virtual tool collision with a Dexel volume model. (b) Calculation of

torque feedback with collision points PDi in the Dexel volume model.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–1307 1303

5. Implementation and examples

The proposed techniques and the haptic hardware have

been developed and implemented in our lab at North

Carolina State University (Fig. 5). Based on the developed

haptic controller system, the haptic rendering programs and

the software driver have been implemented for this haptic

system. The haptic controller and haptic rendering program

were implemented on a dual 2.4 GHz CPU workstation,

with Visual Cþþ and OpenGLw. The interaction scheme is

designed for the haptic application. Since we constructed

the haptic device controller and developed the rendering

programs from the hardware level, we have the greatest

flexibility in designing our specific haptic applications.

Fig. 18(a) shows the overview of a user’s operation of the

haptic 5-axis pencil-cut system. Fig. 18(b) shows an example

part of a computer mouse model in STL format. As shown in

Fig. 18(c), two parallel pencil-cut tool paths are identified

along the sharp edges by using the Rolling ball method

developed in our earlier work in Ref. [14,18]. Fig. 19(a)

shows some sample 5-axis tool orientations for machining of

the pencil-cut critical regions of the example part. Fig. 19(b)

shows the generated 5-axis pencil-cut tool paths for

machining the pencil-cut regions on the example part

surface. The tool holders are temporarily hidden in

Fig. 19(b) to show the tool orientations more clearly. Without

considering the surrounding machining environment, 5-axis

tool paths could easily collide with the adjacent object

unintentionally. It can be seen from Fig. 19(c) that

the generated 5-axis tool paths are actually colliding with

the fixtures nearby during 5-axis tool motions. As demon-

strated in Fig. 19(c), these tools actually penetrate the

fixtures. By taking the whole machining environments into

account, the haptic system actually responds and enables the

user to feel the collision force feedback. By using the haptic

interface, the user is able to correct the tool orientations.

Fig. 17. Force and torque distribution to two haptic manipulators.

Fig. 18. Pencil-cut tool path (dark blue trajectories) identified on an example computer mouse model. (a) An overview of haptics operation process of the 5-axis

pencil-cut path planning. (b) An STL model of example computer mouse. (c) Pencil-cut tool path on the example STL model (For interpretation of the

references to colour in this figure legend, the reader is referred to the web version of this article).

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–13071304

When one feels the force and torque feedback and sees

the movement of the tool, she/he can orient the tool to avoid

or correct the global collision with ease.

Fig. 20(a) shows the corrected 5-axis pencil-cut tool

orientations generated with the developed haptic system.

Fig. 20(b) shows the re-computation of the corrected

tool orientations for 5-axis pencil-cut after the global

collisions have been eliminated by using the haptic system.

Local gouging is further eliminated by the automated post-

processing of the tool paths, as described earlier in Section

3. In Fig. 20(b), the vectors in cyan (in the web version, light

colour in greyscale printout) represent those critical tool

orientations specified by the user during the haptic inter-

action. In Fig. 20(b), the vectors in blue (in the web version,

dark color in greyscale printout) represent those interpolated

tool orientations. Fig. 20(c) shows the generated tool paths

and the corrected tool orientations are also rendered in a

view where sample tools are displayed with both the

example part surface and the surrounding fixture. Fig. 20(c)

shows how the tool orientations are changing along the 5-

axis pencil-cut tool paths without colliding with the

surrounding work holders.

The final outputs of the haptic system are the 5-axis NC

tool paths. The generated NC code is simulated by using the

Predator w NC simulation software in our lab. Fig. 21(a)

shows the example part surface after finishing. Fig. 21(b)

Fig. 19. 5-Axis tool orientations that cause collisions with surrounding

unmachinable objects. (a) Tool orientations selected for pencil-cut

machining of the example CAD model. (b) Tool orientations selected for

pencil-cut tool on the example mouse model. (c) Tool collision with

adjacent fixtures by the selected tool orientations in (b) the tool penetrates

into the fixtures virtually.

Fig. 20. Using haptic interface to correct 5-axis tool orientation in a complex

machining environment. (a) Using haptic interface to correct tool orientation

for 5-axis machining in a complex machining environment. (b) Re-

computing pencil-cut tool orientations after correction of tool collisions.

(c) Corrected tool orientation selection in a complex machining environment.

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–1307 1305

shows the example part surface after pencil-cut operation has

been performed with the generated NC code. The remaining

material near the shared sharp edges has been cleared by the

pencil-cut tool path, as shown in Fig. 21(b).

A practical shoe sole model was used as another

illustrative example for 5-axis pencil-cut tool path generated

by the developed machining planning system. Fig. 22

shows the process of determining tool orientation using

the developed haptic pencil-cut system. The NC codes

generated from the haptic 5-axis pencil-cut system were

simulated by commercial NC simulation software in our lab.

Fig. 22(a) shows the example part surface after finishing

and before pencil-cut. Fig. 22(b) shows the example part

surface during 5-axis pencil-cut operation. The rest of the

material near the shared sharp edges is being removed by

the pencil-cut tool path, as shown in Fig. 22(c). The NC

machining simulation results shows the effectiveness of the

proposed 5-axis pencil-cut. From these examples, it can be

seen that the resultant 5-axis pencil-cut tool path generated

by the haptic-computer interface is quite satisfying.

6. Conclusions

In this paper, techniques of haptic rendering and

pencil-cut planning have been developed in a complex

machining working environment. A Two-phase rendering

approach has been proposed for haptic 5-axis pencil-cut

of complex sculptured surfaces. Dexel-based modelling is

used for global tool interference avoidance with other

components of a machining environment. The presented

techniques enable the haptic device be utilized to help

determine feasible 5-axis tool orientations in a complex

machining environment. Although the haptic-computer

system described here deals mainly with 5-axis pencil-cut

machining operations, it can actually also be used for

other complex surface machining strategies [25,26].

The experiments presented in this paper show that the

involvement of a haptic system in 5-axis tool path

planning is promising. The presented technique can be

used for CAD/CAM, 5-axis machining planning and

virtual prototyping.

Fig. 21. 5-axis pencil-cut machining of the example computer mouse

model. (a) Mouse model after finishing without pencil-cut. (b) Mouse

model during pencil-cut.

Fig. 22. Using haptic interface for planning 5-axis pencil-cut of a shoe sole

model. (a) Shoe sole model after finishing without pencil-cut (rop surface).

(b) Shoe sole model during the 5-axis pencil-cut (top surface). (c) Shoe sole

model after the 5-axis pencil-cut (top surface).

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–13071306

Acknowledgements

This work was partially supported by the National Science

Foundation (NSF) CAREER Award (DMI-9702374), NSF

Grant (DMI-0300297) and the Army Research Office (Grant

#DAAG55-98-D-0003) to Dr Y. S. Lee at North Carolina

State University. Their support is greatly appreciated. The

authors would also like to thank Dr Y. Adachi at Suzuki, Inc.

(Japan), Dr S. Sarma at MIT, and Dr Y. Ren at NCSU for their

helpful discussion and suggestions.

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Weihang Zhu is a PhD student in the Depart-

ment of Industrial Engineering, North Carolina

State University, USA. He received his BS and

MS, both in Energy Engineering, from Zhejiang

University, China, in 1997 and 2000, respect-

ively. His research interests include Computer

haptics, CAD/CAM, multi-axis NC surface

machining, polyhedral machining, applied

computational geometry, discrete-event com-

puter simulation, and logistics.

Yuan-Shin Lee is Professor of Industrial

Engineering at North Carolina State University,

USA. He received his PhD (1993) and MS

(1990) degrees from Purdue University, USA,

both in industrial engineering, and his BS

degree from National Taiwan University,

Taiwan, in mechanical engineering. His

research interests include 3- and 5-axis sculp-

tured surface manufacturing, CAD/CAM, com-

putational geometry for design and

manufacturing, rapid prototyping, and high

speed machining. He is a registered Pro-

fessional Engineer (PE) in mechanical engineering. He is also a certified

manufacturing engineer in system integration and control. Dr Lee received

the National Science Foundation (NSF) CAREER Award. He also received

the 1997 Outstanding Young Manufacturing Engineer Award from the

Society of Manufacturing Engineers (SME), the 1998 Norman Dudley Award

from the Taylor and Francis Journals, London, U.K., the 1999 Anderson

Outstanding Faculty Award and the 2000 Alumni Faculty Outstanding

Teaching Award from North Carolina State University, and the 2001 ALCOA

Foundation Engineering Research Achievement Award. He serves as an

Associate Editor for the Journal of Manufacturing Systems (JMS).

W. Zhu, Y.-S. Lee / Computer-Aided Design 36 (2004) 1295–1307 1307