CHAPTER 2 BUILDING BLOCK APPROACH TO PARALLEL
2.5 Design Examples of 3-dof TOPM
2.5.4 Parallel manipulated cobra-head machine
The passive limb is selected to be PRP quad from Table 2. In case that the two prismatic joints are axially orthogonal to each other, the ambient space of the end-effector is the one axis of rotation with two axes of translations. The resulting parallel manipulator is the cobra-head machine as shown in Fig. 16. The direction of the translation may be determined by the axis of prismatic joint, so does the two axes of rotation determined by the axes of the revolute joints.
The end-effector will perform like the head of cobra that does forward, downward and pitch motion. The cobra-head machine may be used as the motion simulator.
2.6 Design Examples of 6-dof FSPM
A general Hexaslide-based machine tool comprises six distinct rails, as indicated in Fig. 17. The sliders move along their rails, while
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the legs of constant lengths are connected to the sliders through universal joints. The other end of each leg is linked to the tool or moving platform through spherical joints. The actuation of the sliders on their respective rail drives the moving platform in space. These designs are all based on scissor drives and are different only in rail arrangements. The up-to-date Hexaslide-based machines may include the Hexaglide as illustrated in Fig. 17(a), consisting of coplanar and parallel rails; the HexaM depicted in Fig. 17(b), consisting slanted rail, and the Linapod as shown in Fig. 17(c), comprising vertically-arranged rails. The Delta Hexaglide (or so called Hexglider) discussed in this study was developed by IMON Inc. The Delta Hexaglide consists of coplanar and triangular rails as illustrated in Fig.18. Figure 19 (a) displays the kinematic structure, and Fig. 19(b) demonstrates a photograph of the Delta Hexaglide platform mechanism.
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Chapter 3 Design of the Swinging-block and Turning- block Mechanism with special reference to the Mechanical Advantage
3.1 Reviews
The swinging-block and turning block mechanism are extensively applied in several mechanical fields. Examples of its use include the recent version of the freight truck loading mechanism, the camera variable zoom lens hood, and others [23]-[31]. Its primary advantage, the strong output torque, is generated by the conversion of a linear force into rotation, as often used in engine mechanisms, such as the oscillating-cylinder engine mechanism, depicted in Fig. 20 [32].
Furthermore, following the progress in motor technology in recent years, the high-torque and high-accuracy drive of the micro step-motor has been developed. The design that uses the swinging-block and turning-block mechanism with a confined output rotation angle, normally under π/ 2, depends on a high reduction ratio, such as 300:1 to support high-precision positioning. Nevertheless, a very small backlash is also required. The important limitation of mechanism is that the relationship between input and output angle is nonlinear. The transmission angle, which determines the mechanical advantage, may vary over a wide range so that the effective torque transmitted to the output link is variable. The mechanical advantage of a particular dimensional design must then be studied. The transmission angle
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optimizations for the drag link, the crank-and-rocker, and the four-bar linkage are derived in [33]-[38]. However, none of these studies are directly applicable to the swinging-block or turning-block mechanisms.
3.2 Swinging-Block and Turning-Block Mechanisms
Figure 21 presents kinematic inversions associated with various selections the of ground link of the RRRP kinematic chain [32]. Both the swinging block and the turning block are much less well-known than the slider-and-crank from the same RRRP family, since the output cylinder must swing, which raises manufacturing difficulties. However, current technological advances of the linear motor and the helical motor have greatly simplified the swinging cylinder, such as in the sensor pedestal design, shown in Fig.22.
The typical design of such a rotational control member may involve a gear head with the servomotor, which suffers from excessive weight and backlash problems. The alternative design adopts a direct-drive motor, which however, requires a higher electric power than specified. There the design of the turning block mechanism is well conceived since it exhibits a low weight-to-power ratio.
Figure 23 illustrates the kinematic structures of the swinging-block and the turning-block mechanisms. L represents the length of the ground-link. R represents the length of the output-link.
The slider-link, depending on the distance traveled by the motor, has a variable length S. With a single D.O.F., either the swinging block or the turning block mechanism is driven by the input variable S.
The simple trigonometric relation determines the input variable S 22
as a function of the internal angles θ and φ as follows.
φ θ sin
⋅sin
= L
S (3.1)
S⋅cosφ +L⋅cosθ = R (3.2) The cosine law yields,
S2 =R2 +L2 −2RL⋅cosθ (3.3) The internal angle φ is known as the transmission angle of the swinging block or the turning block mechanism. In Fig.23, Fi represents the input force, exerted from the linear actuator. TK represents the output torque transmitted to the output link, and is a function of the transmission angle, as follows.
TK = Fo ⋅R
= Fi ⋅sinφ⋅R (3.4)
The mechanical advantage is maximum only when φ = 90± o, discouraging the use of swinging block or turning block mechanism to beyond its positions of singularity, φ = 180o.
3.3 Maximum Average Mechanical Advantage
In practice, the swing angle of the output link is specified in the design of the swinging block or turning block mechanism; that is, on the range of θ is specified. A set of dimensions of the swinging block or the turning block mechanism must be determined to optimize the mechanical advantage over the specified range ± ε, about the middle-angle θο of the swing angle θ, as shown in Fig. 24. Its application must be limited to ε < 90o to avoid the singularity. For example, the turning block mechanism may be required to function
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over a range of swing angle of ε = 25o, a typical value for radar applications. Nevertheless, the workspace of the swinging block mechanism must also be considered.
According to Eqs. (3.1) and (3.2), the transmission angle φ relates to the swing angle θ as follows.
The average mechanical-advantage E could be expressed as the integral form of the torque with respect to the swing angle θ, over a specified range ε with respect to the designing parameter, the middle angle θ
Substituting Eq. (3.5) into the above equation yields,
θ θθ εε The maximum average mechanical-advantage with respect to the design parameter θo is obtained by finding the stationary value of the average output torque E, as follows.
sin( ) sin( ) 0
and maximum length extended by the linear actuator, respectively.
In general cases, over a finite swing range ε, the input force Fi, the ground link length L, and the output link length R, must all be non-zero, (8), yielding,
The optimal solution for θo is obtained, yielding the maximum average mechanical-advantage as,
cosθ cosε
The second derivative of Eq. (3.7), which equals the first derivative of Eq. (3.10) multiplied by a constant k, may be written as,
o
The middle-angle θo is selected to be positive, as shown in Fig.
24; such that sinθo > 0. Hence the sign of Eq. (3.12) depends on the sign of H(θo). For a design free of any singularity, ε < 90o, that is cos
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ε > 0, is required. Substituting Eq. (3.11a) into Eq. (3.13), yields,
However, substituting Eq. (3.11b) into Eq. (3.13), yields, 4 1 ( )2⎟⋅cosε
The maximum value is obtained from either Eq. (3.11a) or Eq.
(3.11b) by setting H < 0, which parameter depends on the R/L ratio of the design. That is, the result of Eq. (3.11a) for L > R and that of Eq.
(3.11b) for R > L are used to obtain the maximum value.
3.4 Optimal Design
Assuming no energy loss due to friction in the joints or any other viscous damping, the energy output to the output link equals the energy input from the linear actuator, since the total energy is conserved. That is,
∫
=∫
θθo−+εε θ (3.15) respectively. Given a constant input Fi, Eq. (3.15) may be reformulated as follows.F D
E i
ε
= 2 (3.16)
where D denotes the required travel span of the linear actuator, D =Smax − Smin
E is the average mechanical advantage, which was previously defined in Eq. (3.6). Equation (3.16) shows that the average mechanical advantage E is proportional to the distance traveled by the
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linear actuator D. Therefore, a linear actuator that can be extended farther is always preferred for its greater mechanical advantage.
According to Eq. (3.1), the transmission angles φmin and φmax are maximum average mechanical advantage. According to Eqs. (3.8), (3.17a) and (3.17b),
sinφmin =sinφmax (3.18)
Thus, the travel span of the linear actuator D can be related to the link length L, as follows.
{
sin(θ ε) sin(θ ε)η ⋅ + − −
= L o o
D
}
(3.19)where η represents the minimum mechanical advantage and,
The design problem concerns five design parameters, D, L, R, η and ε. These five design parameters uniquely determine the four turning block mechanism link lengths and one the middle swing-angle.
Of the five design parameters, the swing angle span ε is provided as a design specification. This set of design parameters can again by normalizing the link length. Consequently, only three normalized design parameters are to be determined; they are η, D/R and L/R.
Optimal design problems may be separated into two categories.
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The first is for L R. Equation (3.11a) is applied to find the optimal solution. Manipulating and simplifying Eqs. (3.17a), (3.11a) and (3.9a) yield,
≥
η =cosε (3.20)
For L R, the design parameters η and ε are not independent.
In design procedure, η can not be freely specified for a given swing span ε. Substituting Eq. (3.11a) into Eq. (3.19) and combining with equation (3.20) yields,
≥
=2⋅sinε R
D (3.21)
The second category of problem has L < R. Equation (11b) is applied to find the optimal solution. Manipulating and simplifying Eqs.
(3.17b), (3.11b) and (3.9b) yields,
for R⋅sinθ0 > L⋅sinε : η = ⋅cosε R
L (3.22a)
for R⋅sinθ0 < L⋅sinε : η =− ⋅cosε R
L (3.22b)
Since Eq. (3.22a) (3.22b) contradicts the condition that L < R, no optimal solution exists. The second category is discarded because of the need to obtain a good mechanical advantage.
3.5 Design Procedure:
The design procedure is summarized as follows.
Step 1: Specify ε.
Step 2: Set the L/R ratio to no less than 1.
Step 3: Obtain η and the D/R ratio from Eqs. (3.20) and 28
(3.21), respectively.
For the configuration illustrated in Fig. 25, R = 1, L = 2 and ε = 30o are set. The optimal value of the design parameter θο is obtained from Eq. (3.11a), yielding θο = 64.34o and D/R = 1. Figure 26 presents more general cases subjected to different ε versus D/R and ε versus η. Figure 27 plots the curved surface of ε and R/L versus θο.
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Chapter 4 Robotic Safeguard System and Workspace Analysis
4.1 Reviews
The conventional robotic safeguard systems have been developed from the mechanical hardware safeguard systems to the systems involving electrical hardware devices (such as emergency stop switch, dead-man switch, limit switch, etc.), and the safeguard systems inside and outside the robot working areas. The existing sensor warning systems for the robotic safeguard can be divided into the follows [39]:
warning sign system, safety barrier device, pressure pad, inferred, capacitor, microwave, ultrasound, magnetic field, video image, etc.
Sensors as defined in this context as the devices that detect if there anyone exists, based on the physical features. These methods have been used for a long time, and work well, however the robot application becomes wider, the conventional sensors warning method show its insufficiency of flexibility and impotence. The robot static positioning problem can be solved via the forward and backward kinematics [40], therefore the robotic movement can be displayed as the animation, and the collision detection can be performed by the computers.
Three levels [41, 42] of the robotic safety envelopes are defined.
Level 1 is the maximum envelope, Level 2 is the restricted envelope, and Level 3 is the operating envelope. The robot’s virtual boundary is defined as the Level 3 area, which is dynamically varied with the
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operating conditions of the manipulator. The active robotic safeguard system involves not only the static protection areas (Level 1 and Level 2), but also the dynamic area (Level 3). The robot language is implemented for the robot movements, which involve the three levels of the robotic safety commands.
The International Standards Organization (ISO) introduced the Open Systems Interconnection (OSI) Reference Mode [43], the layered network architecture, with the goal of international standardizing protocols governing the networking communication.
However Transmission Control Protocol/Internet Protocol (TCP/IP) [44, 45, and 46] doesn’t directly follow the OSI model. Although each network model has the goal of facilitating communication among different types and models of computers, and operating systems, the implementations of each network model present a variety of aspects.
Whereas the OSI model was driven by a large standards organization, it took a long time to formulate a draft and adopt it as a standard. In a different situation, TCP/IP was driven by the immediate need of the United States government. The development of TCP/IP isn’t burdened with the same stringent requirements as OSI. Local Area Network (LAN) [47] is a data communication network, typically a packet communication network, limited in geographic scope. A local-area network generally provides high-bandwidth communication over inexpensive transmission media. A local-area network is composed of hardware elements and software elements. Hardware elements belong to three basic categories: a transmission medium, a mechanism for control of transmission over the medium, and an interface between the network and devices that are connected to the network. The software
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elements are the sets of protocols, implemented in the devices connected to the network, that control the transmission of information from one device to another via the hardware elements of the network.
These protocols function at various levels from data-link layer protocols to application layer protocols. Also, LANs are characterized by a large and often variable number of devices requiring interconnection. LANs have a high bandwidth channel with short propagation delays, however shared by many independent users. A Web server [48] does a great deal of work in making Web pages and sites available to browsers. They are the linking mechanism between you and the Web, between people and pages. Web servers consist of special hardware and software that make it possible to carry out browser request. In this thesis, the client-server architecture is defined as the basis for communication between two robotic programs called the client and the server. A server is any application that provides a service to a network user. A client is any program that makes a request to a server. In general, a client and a server run on different computers.
Client-server architecture contrasts with the classical centralized architecture popularized by typical mainframe installations. In a centralized environment, the “clients” are little more than dumb terminals that act as simple data entry / display devices. There’s a minimum of work done at the terminal. The user typically fills in the fields of a form before sending the field data to the central computer.
All processing and screen formatting are done on the central computer, and dumb terminal simply displays the preformatted data. In a client-server environment, the client has much greater ability and more freedom with the final visual presentation of the data to the user.
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Instead of the data being preformatted to match the way it will be viewed, they are transferred in its “raw” format to the application running on the client computer, which “decides” itself how to display that data. Thus, the “front end” that the user sees can be customized while the “back end” remains unchanged. The Centralized Monitoring and Control Computer is the “client” and the individual robot is the
“server”. Any program can be opened to handle several connections simultaneously, to play both client and server at the same time.
4.2 The Active Multi-Robotic Safeguard System Architecture
The traditional safeguard system is integrated with sensors, and then installed into the hazard areas statically. However, with the application of the robot increases, the traditional safeguard system shows its insufficiency of flexibility and efficiency. The intelligent safeguard system is generated, with some kinds of the high accuracy and performance devices integrated, and the software can be controlled for setting up the hazard areas dynamically, with the different operation types and locations of the robot. The omni-direction magnetic position trackers are integrated with the robots and the operator, with the client-server based networking system, software and hardware integrated, the complete real time data of the multi-robot kinematics and operator movement can be obtained, as shown in Figure 28.
The 3D space objects can be represented in the coordinate relative to the absolute coordinate system, and their position and orientation is in terms of the 4 by 4 homogeneous transformation
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matrix which combines both rotation and translation process in a single matrix. During the time t, the point Loc in object A relative to the absolute coordinate can be represented as
)
For calculating the collision detection between object A and object B, the point Loc on object A relative to the local coordinate of the local coordinate can be represented as
)
Substitute equation (4.1) into (4.2), then
[
A 0]
1 B A (0)) B
( (t) T (t) T (t)Loc
Loc = → − → (4.3)
Assume the end point Loc is inside the range of object B, then the object A and object B are in the collision condition.
As the depicted previously, the hazard areas determination for the intelligent safeguard system may vary from the robot operational conditions. In order to fortify the safeguard, the hazard areas may be enlarged. Figure 29 shows the coordinate system for the robotic collision detection. Object A refers to the operator, other people, or the robot’s manipulator “wearing” the positioning sensor, and object B represents the main robotic system with positioning sensor also.
Referring to this figure, the robot movement will be in slower speed when any objects are falling inside the safety envelope Level 2 (hazard zone), and the robot will be fully stopped when any objects are inside the safety envelope Level 3. The safety envelope Level 3 is defined as the robot’s virtual boundary in this thesis.
With the 3D monitoring display implemented, the robot false movement can be detected, then the three-level robotic safeguard system is functional, and the robot speed is slowed down, or the brake
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system works with the control system, to attain the emergency stop function. The real time robotic collision avoidance function can be used as the safeguard system eventually.
4.3 The Robot System Installation and the Kinematics Analysis
The robot systems have been installed with various safety-sensing devices for the complete safeguard system test. There are two kinds of robot systems used in this research. First, the U-type robot is a non-Cartesian coordinate kinematics mechanism, as shown in Figure 30. This type of the robot is widely used for the industrial field. The U-type robot mechanism entity has a three- D.O.F.
manipulator with a two- D.O.F. robot wrist. This open-chain robot system is easy to be assembled, and is convenient for performing its manipulator control in the laboratory. The other type of the robot system, as shown in Figure 31, is the parallel-linked robotic system designed for the laboratory used, in order to verify the system theory.
The kind of robot platform belongs to the six- D.O.F. Cartesian coordinate kinematics mechanism system, with feedback, high compliance and stability.
For obtaining the robot motion in the space, the kinematics is a very common problem to discuss the relation between robot joint space and Cartesian space. The kinematics analysis for the robot system is significant in this thesis, to integrate the robot virtual reality real time display with the real robot mechanism precisely. For instance, if we choose the U-type robot system as case of the motion mechanism for the robotic safeguard, its forward kinematics can be
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described as follows:
described as follows: