3Enr
4.1 Design of Parallel Kinematic Machines
4.1.3 Design Considerations
A general approach to the design of PKMs should cover the following issues [38]:
• Determination of the reachable workspace,
• Kinematics stiffness described by several local and global manipulability measures,
• Relation of driving and actuator forces,
• Overall elastic stiffness of the structure,
• Static stability analysis.
Kinematically, an n-DOF non redundant PKM also implies that each leg should also be an n- DOF serial kinematics chain, regardless of the number of legs. To simplify design and development efforts, there are a few additional considerations [39]:
• Symmetric Design - Each leg is identical to the others. Hence, each leg should have the same number of active joints. As the total number of (1-DOF) active joints in a 6-DOF non redundant PKM is six, the number of legs for a symmetric design can be six (1-DOF actuated joint per leg), three (two 1-DOF actuated joints per leg), or two (three 1-DOF actuated joints per leg).
• Types of joints - Four types of commonly used joints are considered, i.e., 1-DOF revolute (R), 1-DOF prismatic (P), 2-DOF universal (U), and 3-DOF spherical (S) joints. Among
them, the spherical and universal joints are meant as passive joints, the prismatic joints are meant as active joints (they are ineffective as passive joints), and revolute joints can be used as either passive or active joints.
• Active joints are placed close to the based so as to reduce the moment of inertia and increase the loading capacity and motion acceleration.
• Passive 3-DOF spherical joints are used to reduce the number of passive joints and make the design compact.
• At most one (active) prismatic joint can be employed in each of the legs due to its heavy and bulky mechanical structure.
• Designing for Decoupled Motion Axes (DMA). This gives the robot simple kinematics for easy analysis, design, trajectory planning, and motion control. [39]
Figure 14 illustrates a graphical summary of the steps used in the parallel mechanism design process.
Mechanical Design
Structural Synthesis
—»{ Machine Topology
Stiffness Actuators - No.& type
HZ
SpeedWorkspace
1—»| Actuator Positioning Stiffness
HI
WorkspaceDimensional Synthesis
Dimensioning
Workspace Singularities
—H System Modelling
Kinematics Modelling Dynamics Modelling
Control System
Figure 14 Design criteria used in constructing PKMs
4.2 Structural Design of the Modified Delta Robot
The mechanical structure is based on that of a Flex-Picker pick and place parallel kinematics industrial robot, and is a scaled adaptation.
The design consists of 4 articulated legs; 4 servo motors (as used in model helicopters); a plate end effector with attached lasers; ball-cup joints and a mounting frame. The entire mechanical structure is 600 mm in length, 400 mm wide and 500 mm high. Figures 15 and 16 illustrate the parts and some assemblies. Figures 17 and 18 illustrate the complete assembly with detector boards in various views.
Figure 15 Significant Mechanical Parts a. Ball from ball in socket bearing
b. Socket/Ball cup c. Laser d. Upper leg
e. Servo motor with upper leg attached and mounting bracket f. Lower leg component
g. Servo motor
h. Servo motor with mounting bracket
Figure 16 End effector a. Vertical laser mounting arm
b. Multiple laser guide c. Multiple laser mounting
d. Laser mounting with guide attached
e. Laser mountings and guides attached to end effector
Figure 17 Mounting of servo motors and assembly of arms a. Servo motors and upper arms mounted on inertial frame
b. Lower arms and end effector attached to upper arms c. Knee joint
d. Ankle joint
Figure 18 Complete assembly
b.
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u
<1
8 .4a. Total view b. Side view
d.
c. Front view
d. Bottom view of end effector and horizontal detector screen (hidden base)
e. Back view of end effector and vertical f. Left side view
It must be noted that the lower leg components are held together via 2 springs (not shown), one just below the 'knee' and the other just above the 'ankle' for each leg (see Figure 19 for these joint labels). The ball cup joints give a large degree of freedom. These were made from ball in socket bearings. The upper legs swing from side to side whereas the lower legs can move up, down, left and right and can rotate about the 'knee' by sequencing sets of its basic motion (induced by rotating pairs of servos each to particular angles). The laser can move about a volume of space, which is roughly a hemisphere below the sensitivity area, the square cut-out on the servo mounting frame in Figure 17 a.
The frame work was made from angled aluminium (long bar of L shape aluminium). The lower legs and laser mounting were made from a stiff hard plastic. The lower legs were made from stainless steel rods used to construct model helicopters and aeroplanes. The ball and socket joints were made of steel. These materials gave the Flex-Picker model sufficient stiffness for all movement during testing.
Machine Topology
As this PKM is symmetric it may be described as 3-DOF 4 RSS (3 degrees of freedom, all translational with 4 branches containing a rotational actuator and 2 spherical joints).
Actuator Positioning
The actuators are located on the same plane and are arranged to form a cross. They are positioned such that the plane of rotation of each servo lies coincident with that of the servo directly opposite it, and the adjacent rotation planes are at 90° to each other.
4.3 Dimensional Synthesis