Plane Thermoelastic Waves in Infinite Half-Space Caused
FACTA UNIVERSITATIS
Series: Mechanical Engineering Vol. 15, N
o
3, 2017, pp. 367 - 381
https://doi.org/10.22190/FUME171002020F
Original scientific paper
A NEW WINCH CONSTRUCTION FOR THE SMOOTH CABLE
WINDING/UNWINDING
UDC 531
Mirjana Filipović
1
, Ljubinko Kevac
2
1
Mihajlo Pupin Institute, University of Belgrade, Serbia
2
School of Electrical Engineering, University of Belgrade, Serbia
Abstract. New constructive solutions of the winches for single-row radial multi-layered
cable smooth winding/unwinding are described. Two new structural solutions of
winches are defined. The nonlinear phenomenon of a cable smooth winding/unwinding
process on the winch by using one of the two proposed constructive solutions is defined
and analyzed. To facilitate understanding of this concept, the cable winding/unwinding
process on only one winch is analyzed. The obtained variables which characterize the
kinematics of the cable smooth winding/unwinding process are nonlinear and smooth.
This result is important because the systems for the smooth cable winding/unwinding
process on the winch could be parts of any cable driven mechanism. These systems can
be used in various fields of human activity. For the verification of the presented
theoretical contributions, a novel software package named SMOWIND – OW has been
developed using MATLAB.
Key Words: Analysis, Kinematics, Cable Winding/unwinding, Winch Construction,
Simulation
1. INTRODUCTION
The problem of the cable winding/unwinding on the winch is present in various
systems used in different technical areas. These systems can have completely different
applications and also different constructions but their characteristic is that they consist of
one or more sub-systems for cable winding/unwinding. All these systems require stable
control for implementation of defined task. Only several systems will be mentioned:
measuring mechanism, machines in textile industry, cable logging systems in civil
engineering and forestry, cranes, systems in shipping industry, CPR (Cable-suspended Parallel
Robot) and other complex cable driven systems.
Received October 02, 2017 / Accepted November 22, 2017
Corresponding author: Mirjana Filipović
Mihajlo Pupin Institute, University of Belgrade, Volgina 15, 11000, Belgrade, Serbia
E-mail: mirjana.filipovic@pupin.rs
368 M. FILIPOVIĆ, LJ. KEVAC
For many decades, many researchers have dealt with analyzing the cable winding/
unwinding process on the winch. In this paper, only some of these investigations, namely,
those that have inspired this research, will be presented. Authors of [1] have reviewed
application of the cable logging systems. They have defined a user’s manual which helps
them to solve several problems such as protection of workers, soil and forests. Samset [2]
has given a historic review of the systems which use winches for cable winding/
unwinding. The author gives information that these systems are used for more than five
millennia which emphasizes their importance. Abdel-Rahman et al. [3] have analyzed
dynamics and control of the cranes having cable winding/unwinding sub-systems as the
main part. This is a review paper which shows historic development of cranes.
In [4-6], authors present theoretical and experimental contribution to analysis and
synthesis of kinematics and dynamics of the winding/unwinding process of thread from a
balloon. Fluctuating tensions in a perfectly flexible string unwinding from a stationary
package is considered by Padfield [4]. Also, dependence of unwinding tensions on air
resistance, unwinding speed, angle of winding on the package etc. is examined. Based on
results of Padfield [4], Fraser et al. [5] have considered over-end unwinding of the yarn
from a stationary helically wound cylindrical package. An improved theory for the
variation of the yarn tension during high speed over-end unwinding from cylindrical yarn
packages based upon the theory of the bent and twisted elastic rods is presented by Clark
et al. [6].
Imanishi et al. [7] have presented a dynamic simulation of a wire rope involving both
contacts with the winch drum and hydraulic systems using the finite element method. The
rapid winch operation often causes a disorderly winding of the wire rope, which is an
important quality problem. Dynamic simulation is, therefore, required for design of the
hydraulic winch system on construction machinery. The wire rope is modeled using truss
elements considering a large displacement motion.
Szczotka et al. [8] have presented the mathematical model of a pipelay spread. In the
model, elasto-plastic deflections of the pipe, its large deformations and contact problems
are considered. The modification of the rigid finite element method (REFM) is used to
discretize the pipe.
Wire-guided control technologies are widely used to increase the targeting accuracy
of advanced military weapons through the use of unwinding dispensers to guarantee that
unwinding occurs without any problems, such as tangling or cutting. Lee et al. [9] have
investigated transient behaviors of the cables unwinding from inner-winding cylindrical
spool dispensers. The cable is withdrawn from the spool dispenser at a constant velocity
through a fixed point located along the axis of the spool dispenser.
Filipovic et al. [10] have dealt with design, analysis and synthesis of the cable
suspended parallel robotic system (CPR system). They have used a well-known winding/
unwinding sub-system presented by von Zietzwitz et al. [11].
A wide application of the process of cable winding/unwinding on the winch is
important; that is why it deserves a detailed analysis and it is the subject of this paper. In
this paper, two new forms of winches for ensuring single-row radial multi-layered cable
smooth winding/unwinding have been constructed:
a) The first constructive solution is composed of two semicylindrical bodies of
different radii: a two-cylinder winch.
b) The second constructive solution has a spiral shape: a spiral winch.
These two constructive solutions are the main contribution of this paper.
The Basic Theoretical Principles of the Kinematics of Smooth Cable Winding/Unwinding on a Winch 369
For analysis and synthesis of the results from this paper a new software package
SMOWIND – OW has been synthesized using MATLAB.
Kevac et al. [12] have presented a general form of mathematical model of the cable
winding/unwinding system. Also, it can be noticed that the problem which will be
analyzed in this paper is only one special case.
After Introduction, in Section 2 the basic theoretical principles of the kinematics of a
smooth single-row radial multi-layered cable winding/unwinding process on the winch
are presented. In Section 3 the program package SMOWIND – OW is defined. This
program package is used to make simulation experiments and these simulations are
shown in Section 4. Finally, the last part of the paper presents the conclusions, remarks,
and plans for future research.
2. THE BASIC THEORETICAL PRINCIPLES
Kinematics of the single-row radial multi-layered smooth cable winding/unwinding
process on the winch, hereinafter abbreviated as: the cable smooth winding/unwinding
process on the winch, is a very complex and nonlinear process.
2.1. Problem definition
The solution presented in this paper comes as a result of analyzing the standard winch
for single - row radial multilayered cable winding (unwinding) from Fig. 1. The analysis
of the behavior of a circular winch intended for a single-row radial multi-layer cable
winding/unwinding system indicates that this system is far from ideal and contains a
series of constructive problems.
This simple construction of the winch has caused abrupt changes of important variables of
this system: radius of cable winding/unwinding: Ri, cable length: lwi, and inclination of the
cable with respect to yi axis: i. A detailed description of this problem is given by Kevac et
al. [13].
In this sub-section, the problem of cable winding/unwinding is only presented on standard
winch for single - row radial multilayered cable winding (unwinding), but it should be
emphasized that this problem is present in other forms of cable winding/unwinding systems,
for example: a cable winding/unwinding system for a multi-row radial and axial cable
winding/unwinding process, see Kevac et al. [12].
Because of the described effects, it is required to find a solution in the form of a new
construction of the winch. Constructively, only a winding/unwinding system which does not
generate abrupt changes of the variables involved presents a good system for this purpose.
The main point of this research is a geometric and mathematic definition of the cable
winding/unwinding process on a novel shape of the winch intended for smooth rope
(cable) winding/winding, unlike in the work by Kevac et al. [12], where the general form
of mathematical model of the cable winding/unwinding system is defined.
2.2. Problem solution
In this paper, a kinematics model of the smooth cable winding/unwinding process on the
winch will be developed. The new constructive solution of the winch is presented in Fig. 2 in
which one can see a new shape of the winch which is adapted to the user’s need that the
370 M. FILIPOVIĆ, LJ. KEVAC
winding/unwinding process should occur in a smooth and nonlinear fashion.
Fig. 1 Standard winch for the cable winding/unwinding system
Fig. 2 Winch for the smooth cable winding/unwinding process:
a) two-cylinder winch, b) spiral winch
To achieve a smooth cable winding/unwinding process, two new constructive solutions
of the winch are designed:
1) The first constructive solution consists of two semi cylindrical bodies of different
radii, as shown in Fig. 2a. In view of the characteristics of this winch, it has been
named a two-cylinder winch. The two-cylinder winch will be presented in this paper
in detail, and
2) The second constructive solution has a spiral shape, as shown in Fig. 2b. It has been
named a spiral winch.
Similar effects of the smooth cable winding/unwinding process are achieved for both the
spiral and the two-cylinder winch.
The Basic Theoretical Principles of the Kinematics of Smooth Cable Winding/Unwinding on a Winch 371
In this paper, the two – cylinder winch will be used for performing the corresponding
theoretical analysis. In the continuation of this Section, the geometry of the cable smooth
winding/unwinding process on one winch will be shown and analyzed in detail. The cable is
mounted so that it emerges from the winch at a place where there is a joint of two semi
cylindrical bodies.
The starting position of the cable during the winding/unwinding process on the winch is
shown in Fig. 3. The starting position is systematically (by calibration) defined to be at the
direction of the negative part of xi axis. Selection of the starting position affects further
kinematics of the cable winding/unwinding process on the winch.
Fig. 3 The starting position of the winding/unwinding system
A more detailed look at the starting position of the system for cable winding/unwinding
is shown in Fig. 4a. In order to facilitate understanding of the kinematics of the cable smooth
winding/unwinding process on the winch, the geometry of this complex process will be
shown.
Defining the geometry of the cable smooth winding/unwinding process is needed for
specifying the kinematic and dynamic models of this process. Also, for a good understanding
it is sufficient only to analyze the winding process of the cable on the winch; thus the
analysis of the process of unwinding will be omitted since the phenomena are the same but
only occur in the reverse order with respect to winding.
Figure 3 shows the starting position of the system for the smooth winding/unwinding of
the cable on the winch. This system consists of a newly shaped motorized winch, hereinafter
referred to as winch, which is positioned along one axis of the xi - yi coordinate system. This
winch (winds up)/unwinds a cable of diameter d=0.0008 m. From the other side this cable
goes over a smaller pulley (which is not motorized) which has radius r=0.009 m. This pulley
is positioned at the center of xi1 - yi1 coordinate system. The axis of rotation of the pulley is
372 M. FILIPOVIĆ, LJ. KEVAC
positioned at the base of this coordinate system, point C. This point in relation to the xi - yi
coordinate system has coordinates (-a, b). Distance a=0.045 m presents a horizontal distance
between rotation axes of the winch and the pulley, while distance b=0.524 m presents a
vertical distance between these two axes.
The new shape of the winch is composed of two semicylindrical bodies. The smaller
semicylinder has a basis of radius Ri0=0.0136 m with the center at point Oi(0, 0). Radius of
the bigger semicylinder 0iR
~
is geometrically defined by the shape function of this winch in
relation to the radius of the smaller semicylinder Ri0. The bigger semicylinder has a radius of
basis m014.02/dRR
~
0i0i with the center at point )0,2/d(O
~
i .
The system for smooth winding/unwinding of the cable on the winch is constructed so
that when shown in the plane perpendicular to the winding/unwinding axis, it looks as shown
in Fig. 3. To simplify the terminology, the two semicylinders will further on be referred to as
two semicircles.
The center of the smaller semicircle is at the origin, Oi, of the coordinate system xi - yi .
The rotation axis of the motorized winch is labeled as oi. Unlike point Oi, the center of the
bigger semicircle, point iO
~
, keeps on changing its position constantly during the cable
winding/unwinding process on the winch. Point iO
~
is constantly rotating around point Oi at
distance d/2.
Fig. 4 a) The starting position of the winding/unwinding system – close-up;
b) Position of the winding/unwinding system for 0<i
A better view of the winch is shown in Fig. 4a. Here one can clearly see the place
where the cable emerges from the winch. Point E belongs to the outer contour of the
winch and it is positioned at the intersection of the smaller semicircle and the flat part of
the winch. At the starting position, this point belongs to the negative part of xi axis. This
point has a stationary position in comparison with the winch during the whole of the
cable winding/unwinding process on the winch. It is assumed that the deflection angle
between line OiE and negative part of xi axis defines the winding/unwinding process of
the cable. This deflection is denoted as angle i whose value at the starting position is:
0i (1)
The Basic Theoretical Principles of the Kinematics of Smooth Cable Winding/Unwinding on a Winch 373
Unlike point E, point T constantly changes its position on the winch. This point presents
the place where the cable touches the winch or the cable wound so far. At the starting
position, points E and T overlap, as can be seen in Figs. 3 and 4a. The winch and the pulley
are positioned so that angle i has a positive value at any moment. Angle I presents one of
the variables of the system which characterize the cable winding/unwinding process. At the
starting position, angle i has the largest value of 0.04116 rad, which is defined by the
constructive solution of the mechanical part. This angle is defined in the following fashion:
the first leg of the angle is the line running through origin Oi in parallel with the tangent
drawn at point T to the circle having radius r + d, centered at point C; the second leg is
positive part of the yi axis.
It is presumed that the cable is wound at constant angular speed, i.e. consti
. This
presumption presents an idealized theoretical condition, which has been introduced for an
easier and clearer explanation of the smooth cable winding process on the winch.
It is assumed that the cable force acts through the central axis of the cable, i.e. along
direction of the line sm (see Figs. 3 and 4a). Usually, it is presumed that the winding/
unwinding radius is calculated at the position where the force acts upon the winch. With this
presumption and from Figs. 3 and 4a it can be seen that this radius presents distance OiAR at
the starting position. The value of this radius can be calculated as follows:
)cos(AOR iiii (2)
At the starting position, point A is positioned at the intersection between line OiA and
the line which contains point T and is rotated about point T by angle i.
The angle between lines OiA and OiT is labeled as i. This angle has the biggest value at
the starting position. The position of point AR is at the intersection between lines sm and or.
Point B is positioned at the intersection between line sm and the line which contains point C
and which is parallel to line or. Distance AB labeled as lwi presents a dynamic variable
during the cable smooth winding/unwinding process on the winch. This variable has its
dynamics of change and thus affects the dynamic response of the system (see Fig. 3).
Figure 4b shows the position of the system when values of angle i meet the following
requirement:
ii0 (3)
For this position of the system, the winding/unwinding radius is calculated as:
)cos(AOR iiiii (4)
As in the previous case (Figs. 3 and 4a), point AR is positioned at the intersection of lines
sm and or, while point A is at the intersection of line sm and the line which contains point T
and is parallel to line or. In relation to the initial value of angle i, its value is smaller now,
while distance lwi is growing in relation to its initial value. The angle between lines OiA and
OiT decreases during the period of winding which is specified by Eq. (3). The system’s
position which is analyzed next is shown in Fig. 5a. This is the position when the following
condition is satisfied:
ii (5)
At this moment, points AR and A are at the same position and they are lying on line OiT.
From this moment on, point A is always on line OiT during the winding process. At this
374 M. FILIPOVIĆ, LJ. KEVAC
moment, angle i achieves value 0 and further on it does not affect the cable winding
process. In Fig. 5a, it can be seen that line OiT is lying on x axis (also line OiE is lying on
this axis) – axis x presents the axis that is deflected by angle i compared to the positive part
of xi axis. Coordinate system x - y is always defined by angle i. At this moment, the cable
is tangential to the winch at point T. Also, it is the last moment when points E and T overlap.
From that moment on, point E maintains its fixed position on the body of the winch, while
point T follows winding dynamics of the cable.
At this moment, the winding/unwinding radius has the following value:
2/dRAOAOR 0iRiii (6)
Also, at this moment, distance lwi has the biggest value during the cable winding process
on the winch.
The cable keeps on winding and angle i takes values from the following range:
iii (7)
Fig. 5 Position of the system for a) i = i and b) i =
The range defined by Eq. (7) has been named a con range (constant). Throughout this
range, radius Ri, length lwi, and angle i (important variables of the cable smooth winding/
unwinding process) have constant values which they have acquired at the moment when the
condition defined by Eq. (5) is satisfied. An example of the position from this range is shown
in Fig. 5b. In this example line OiE overlaps with the positive part of xi axis, i.e. i = . From
Fig. 5b it can be seen that positions of points E and T are different.
An important moment is when the following condition is satisfied:
ii (8)
because at that moment the system leaves the con range and a new law of change of all
relevant variables: winding/unwinding radius Ri length lwi, and angle i starts. It can be
seen that at this moment line OiE lies on x axis (see Fig. 6a), but, in comparison with the
positions from Fig. 5a, this line is rotated about point Oi by angle . After that moment,
the cable is starting to wind smoothly on the part of the winch with a bigger radius, i.e. a
bigger semicircle.
The Basic Theoretical Principles of the Kinematics of Smooth Cable Winding/Unwinding on a Winch 375
From that moment on, angle i takes the values defined by the following equation:
iii 2 (9)
The range when all the relevant variables are changing their values is named a smvar
(smooth variable) and one position of the system within this range is shown in Fig. 6b.
Fig. 6 Position of the system for: a) i = i and b) i <i < i
Fig. 7 Position of the system for: a) i <i < i +, and b) i +<i < 2 i
Angle i is changing linearly during the cable winding process, i.e. angular speed of
the winch rotation is constant, consti
. The defined smvar range represents the period
when cable winding/unwinding radius Ri changes its value. Upon entering this range,
during the cable winding, this radius starts to grow from value Ri = Ri0 + d/2 to value Ri =
Ri0 + 3(d/2) which is reached at the end of the smvar range. For an easier description of
the change of radius Ri, two sub-ranges of the smvar range will be considered:
1) The first sub-range is defined by the following change of angle i: i <i < i
+. This period of winding is shown in Fig. 7a and in this sub-range of the smvar
range, radius Ri is calculated by Ri = RT + d/2 . Radius RT becomes a changing variable in
the smvar range, where at the beginning of the range it has value RT = Ri0. During the first
sub-range, the change of this variable is described by the following Eq.:
2 2
T i0 i iR (R d / 2) (d / 2 sin( )) d / 2 cos( ) (10)
376 M. FILIPOVIĆ, LJ. KEVAC
2) The second sub-range is defined by the following change of angle i: i +<i <
2 i. This period is shown in Fig. 7b and in this sub-range of the smvar range, radius Ri
is calculated by Ri = RT + d/2, where radius RT is:
2 2
T i0 i iR (R d / 2) (d / 2 sin( )) d / 2 cos( ) (11)
Fig. 8 a) Radius Ri and b) the first derivative of radius Ri over the smvar range
Fig. 9 a) Length lwi and b) the first derivative of length lwi over the smvar range
Change of the winding/unwinding radius achieved in this fashion is smooth, as can be
seen from Fig. 8a, where variation of radius Ri over the smvar region is presented. Figure 8b
shows the first derivative of this radius, i.e. variable iR
, where one can see a smooth change
of the winding/unwinding radius. It can be seen that during the cable winding process the
radius is slowly growing towards the already defined value of Ri = Ri0 + 3(d/2).
Upon entering the smvar range, points T and A are slowly changing their positions.
Because of that distance lwi gradually decreases in its value during this period of winding.
This phenomenon can be seen in Fig. 9a, where variation of distance lwi over the smvar
range is presented. This change has a similar dynamics like radius R, only it is decreasing
during the cable winding process. Figure 9b shows the change of the first derivative of this
variable, iwl .
The Basic Theoretical Principles of the Kinematics of Smooth Cable Winding/Unwinding on a Winch 377
Fig. 10 a) Angle and b) the first derivative of angle over the smvar range
Fig. 11 a) Position of the system for i = and b) angle i: 0 < i < 17
Because of the change of positions of points T and A, angle I is decreasing in the smvar
range. The change of this angle over the smvar range is shown in Fig. 10a, while Fig. 10b
shows the first derivative of this variable, i .
At the moment when angle i reaches the following value:
ii 2 (12)
the system goes out of the smvar range and enters a new con range. At this moment,
winding/unwinding radius Ri has the following value:
2/d3RR 0ii (13)
From this moment on, the system for smooth cable winding/unwinding on the winch
enters the period when angle i has values defined by:
iii 32 (14)
Winding/unwinding radius Ri, length lwi, and angle i have constant values over the new con
range and they keep the values achieved when angle i had value of 2 i, see Eq. (12).
Figure 11a shows one example of the system during the new con range defined by Eq. (14):
position of the system for i=3.
378 M. FILIPOVIĆ, LJ. KEVAC
Based on the process defined in this Section, it can be concluded that the smooth cable
winding/unwinding process on the winch is accomplished by a cyclical alternation of the con
and smvar ranges.
3. THE PROGRAM PACKAGE SMOWIND – OW
Based on mathematical Eqs. (1–14), a program package SMOWIND – OW (SMOoth
Winding for One Winch) has been synthesized in MATLAB. This program package
includes definition of the motion dynamics of only one two-cylinder winch for the cable
smooth winding/unwinding process. A smooth trajectory of the winch is defined for the
overall range of angle i: 0 < i < 17rad. It is presumed that angular speed of this winch
is constant. The program is generated so that the motion takes place only in the direction
of the cable winding on the winch. It is assumed that the cable unwinding takes place in
the same way but in the opposite direction. This program package gives an ability to the
user to track the change of dynamics of all the relevant variables, e.g. winding/unwinding
radius, length between the winch and hanging point, etc. The program package presumes
application of a two-cylinder winch (Fig. 2a), but with small modifications this program
package can be used for generation of the same results for the spiral winch (Fig. 2b), if
required. By using this program package, the user can track changes of the first
derivatives of all the relevant variables during any part of the winding process within the
defined overall range of angle i. The cyclical character of the winding process is shown
in detail in the next Section where the simulation experiments performed by the program
package SMOWIND – OW are presented.
4. CYCLICALITY OF THE PROCESS
In Section 2, the basic principles of kinematics of the smooth cable winding on one
two-cylinder winch, shown in Fig. 2a, are presented. The cable winding process has been
shown for the values of angle i given by following inequality: 0 < i < i, see Fig. 11a.
Based on this analysis, it is concluded that a smooth cable winding process involves
cyclical alterations of the con and smvar ranges. With a constant growth of angle i, i.e. with
a continuous cable winding, the previously defined principles of winding should be applied
to achieve a smooth growth of radius Ri and a smooth decrease of angle i and length lwi. By
using the program package SMOWIND – OW, which was outlined in Section 3, the
simulation experiments for a linear full scale increase of angle i, 0 < i < 17, have been
generated. The change of angle i is shown in Fig. 11b. From this figure it can be seen that
this angle has a linear change, i.e. its first derivative is constant consti
(the angular
speed of the winch is constant). Figure 12a shows the change of radius Ri for this period of
winding. During the winding period, a growth of radius Ri has a cyclical character. It can be
noticed that radius Ri has a constant and gradual growth in smvar ranges, while it has a
constant value during con ranges. Figure 12b shows the first derivative of variable Ri. From
this figure it can be seen that the first derivative of radius Ri has a smooth and cyclical
change with maximal value of s/m0025.0R maxi
.
The Basic Theoretical Principles of the Kinematics of Smooth Cable Winding/Unwinding on a Winch 379
Fig. 12 a) Radius Ri, and b) the first derivative of radius Ri
Fig. 13 a) Angle i and b) the first derivative of angle i
Angle i is decreasing during the cable winding process on the winch. The change of this
variable is similar to the change of the winding/unwinding radius, as can be seen in Fig. 13a.
Also, Fig. 13b shows the first derivative of this variable. It can be seen that its maximum
absolute value is s/rad0047.0maxi .
Length lwi is also decreasing during the cable winding process and the character of its
change is almost the same as the character of the change of angle i, as can be seen in Fig.
14a. Figure 14b shows the change of its first derivative and it can be seen that its maximum
absolute value is s/m104.1wl
4
maxi
.
The change of the cable movement velocity is much smaller than that achieved with the
standard winch form, see Kevac et al. [13]. This presents only one advantage of the novel
winch in comparison with the standard one. What is essentially important about this new
constructive solution of the winch is that abrupt changes of the cable length velocity are
avoided.
It can be seen that first derivatives of all important variables iR
, iwl , i have small
smooth changes and thus their effect on the whole system’s dynamics is much better in terms
of the systems’ dynamic response.
The figures shown in this Section (Figs. 11b – 14) correspond to the idealized case of the
cable winding process on a two-cylinder winch. Also, in these figures only winding of one
cable on one winch under ideal conditions, when the angular speed of the winch is constant,
consti
, is analyzed.
380 M. FILIPOVIĆ, LJ. KEVAC
Fig. 14 a) Length lwi and b) the first derivative of length lwi
5. CONCLUSIONS
The concept of the nonlinear smooth cable winding/unwinding process on the winch has
been defined and analyzed. This presents a novelty in the literature published so far. It has
been developed due to our intention to define a new form of winches for a single-row radial
multi-layered smooth cable winding/unwinding process. Two novel mechanical
constructions of the winch have been defined: one named a two-cylinder winch and the other
named a spiral winch. The two-cylinder winch has been used for further kinematics
investigations. To explain the idea, the process of the smooth cable winding/unwinding on
one two-cylinder winch has been analyzed and modeled. A detailed synthesis and analysis
are performed of the winding process only since it is assumed that the process of unwinding
is identical except for its flowing in the reverse direction. Idealized conditions during the
winding process have been assumed, i.e. it is presumed that the winch is always rotating with
a constant angular speed. Under these conditions, it is discovered that the smooth cable
winding/unwinding process has two ranges: a range smvar when all the relevant variables
change their values: winding/unwinding radius Ri, angle i, and length lwi and a con range
when these variables have constant values. For the verification and validation of the defined
theoretical concept, a novel program package SMOWIND – OW has been developed using
MATLAB. By using this program package, the simulation experiments of smooth winding
of the cable on one winch have been made and the presented figures show the changes of:
radius Ri, angle i, length lwi and their first derivatives. From these figures it can be seen that
these variables have smooth changes during rotation of the winch.
Future research in this area would concern the inclusion of the proposed new
construction of the winch in a complex cable suspended system, which may consist of n
subsystems performing cable winding/unwinding process such in Aref et al. [14].
Acknowledgements: This research was supported by the Ministry of Education, Science and
Technological Development, Government of the Republic of Serbia through the following two projects:
Grant TR-35003, "Ambientally intelligent service robots of anthropomorphic characteristics", by
Mihajlo Pupin Institute, University of Belgrade, Serbia, and Grant OI-174001, "The dynamics of hybrid
systems of complex structure", by the SANU Institute Belgrade and Faculty of Mechanical Engineering
University of Nis, Serbia. We are grateful to Prof. Dr. Katica R. (Stevanovic) Hedrih from the
The Basic Theoretical Principles of the Kinematics of Smooth Cable Winding/Unwinding on a Winch 381
Mathematical Institute, Belgrade for the helpful consultations during this research and we are grateful to
our former colleague Zivko Stikic for his help during this research.
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