Design Considerations *
Walking Robot *
Power Transmission *
The purpose of this project was to design and construct a robotic mechanism and perform a kinematics analysis of the mechanism.
Robotics has always been a personal interest, and recently I made it a hobby. After switching project topics a couple of times during the course of the semester, I decided to do a robotics project that used kinematics.
Time was a major constraint in this project. I did not want to spend time fabricating components, as this could be extremely time consuming. With this being the case, I decided to search for a company that sold robotics products. This proved to be a very good decision, as I had more time to experiment with a variety of kinematics topics.
Robots are beginning to become a mainstay in our society. They have had a tremendous impact on manufacturing. They have also proved their value in performing jobs that would place a human at risk. Robots have even found themselves acting in Hollywood! Short Circuit’s Johnny 5 was my first glimpse at robotics. Then I saw The Making of Jurassic Park and I was hooked. The amount of engineering, design constraints, and kinematics analysis that went into the 9,000 pound, 40 foot tall Tyrannosaurus Rex was quite extensive. The animatronics characters at Walt Disney World require a similar amount of analysis. I eventually would like to design and build an animatronics figure. This is what eventually lead me to this topic.
The walking robot is a kinematics study in itself. It needs a gear train to gear down the motor so that enough torque is generated to move the legs. Secondly, some type of component is needed to create the walking motion of the legs. Finally, the legs must be connected, reducing the degrees of freedom in the system. (Adding another degree of freedom would require another control device.)
The power transmission system of the walking robot is shown in Figure 1.
The 3 VDC motor turns at 6,000 rpm with a torque rating of 6 g-cm. The gear train serves to reduce this speed, thus increasing torque. (Note: torque and speed are inversely proportional.) Performing an analysis of the gear train (based on the number of teeth) reveals that speed is reduced by a factor of 113. This means that torque is increased 113 times. Thus, the speed and torque at the output shaft are found to be
The module of the gears is 0.5. The module, m, is defined as
where d is the pitch diameter and N is the number of teeth (or cogs). The module is the reciprocal of another critical gear parameter known as the diametral pitch, pd. The diametral pitch is a fundamental gear definition that quantifies the number of teeth per millimeter. Gears with the same diametral pitch mesh properly. The gears used in this gear train have a diametral pitch of two (simply, there are two teeth per millimeter of gear.)
Click here to view the Mathcad analysis of the gear train.
In order to simulate the motion of the legs, two offset cranks are used. These cranks, one located on each side of the robot, are offset 180 degrees so that as one leg is driven forward, the other leg is driven backward. Timing links located between the front and rear legs ensure that front and rear legs are coordinated. This is important due to the natural instability (large tipping moments can be generated) of the motion. Slots in the legs allow for rotation and translation of the legs as the robot walks.
For the mechanism design portion of this project, I decided to construct a pneumatic arm that is located on a lifter plank. The arm was my first attempt at designing my own robotic mechanism. There are no design criteria or constraints other than being able to converse about the kinematics issues encountered during the project.
I found a kit that would enable me to design, build, and prototype a gripper quickly and inexpensively. German engineers originally developed the kit for prototyping and concept generation purposes. The kit shipped with six pneumatic cylinders, a miniature air compressor, and 530 components. The components fit together via sliding connections, press fits, and compression fits, so multiple scenarios are possible.
I assembled the pneumatic gripper by trial and error to see what would work and then attempted analyses to prove why the mechanism worked. The gripper is constructed from:
4 15-cm rods
4 75-cm rods
4 press-fit fasteners
3 various assembly blocks
4 spring-loaded compression fasteners
1 pneumatic cylinder
2 cover plates
1 pillow block type component
2 125-cm rods
3 pneumatic valves
Various length pneumatic hoses
The basic operating principle of the gripper is that as the pneumatic cylinder is actuated, the connection block slides. Four couplers, two attached to each finger, rotate the fingers in. The action reverses as the cylinder returns to its unextended position. Changing coupler lengths produces various mechanical advantages. The pivot point also affects the range of motion and the mechanical advantage.
The mechanical advantage is important because this determines the limitations of the gripper. The range of motion is equally important as it determines the size of the object that it can hold. It is important to realize that as the gripper moves throughout its range of motion, the mechanical advantage changes. The transmission angle, the angle between the coupler and the output member (also known as the follower), determines the mechanical advantage. As this angle approaches ± 90° , the mechanical advantage increases.
Click here to view the Working Model analysis of the gripper mechanism.
Therefore, gripper designs have the couplers approach ± 90° in order to gain mechanical advantage. With this in mind, I built the gripper mechanism (Figure 3.)
Two air cylinders lift the platform. The cylinders are pinned about half way up the platform and rotate the platform about 20-degrees. Due to the lack of force supplied by the cylinders, the weight of the gripper and the platform must be used to aid the system to returning to its unextended state. The platform is attached to the base plates via pin joint. A large spur gear is attached to the underside of the lifter platform for future use with a worm gear. This would allow the entire system to rotate 360-degrees.
Compressed air powers this system. Due to the nature of the air compressor, movements tend to be jerky. A compressor that outputs a higher volume will produce smoother motions over the range of motion. (The mechanical dinosaurs of Jurassic Park were powered with hydraulics due to its characteristic of producing smooth movements.)
The miniature air compressor used in this project is also a lesson in kinematics. The motor is coupled to the compressor via pulley. As the motor rotates, the pulley turns the compressor wheel. An offset crank compresses the air in the pneumatic cylinder, which consists of two springs, a diaphragm, and a piston. The crank causes the piston to move up and down, compressing air, which pushes on the diaphragm. As the crank rotates and pulls the piston up, the lower spring helps return the diaphragm to its original configuration. This process repeats, and the compressed air is transferred throughout the system through hoses, valves, and nozzles. I found it advantageous to minimize the hose length because as the length of the hose increases jerky movements are produced.
(NOTE: I discovered the kinematics issues of the air compressor as an afterthought.)
The final topic I explored was a selectable gearbox. The gearbox contains a 3 VDC motor, a pinion, and six gears (module = 0.5). A "switch" which slides the length of the gearbox allows for various gear ratios and shaft outputs. At the lowest setting, a gear ratio of 18:1 is observed. This means that the motor is geared down 18 times. The gearbox is very noisy at this setting due to gear chatter. A gear ratio of 120:1 is achieved in the second position. Less noise and speed, and higher torque is observed at this setting. Finally, in the last setting, a gear ratio of 800:1 can be had in the final setting.
This is a very versatile gearbox as it can be used for high speed applications or high torque requirements. It can be seen that as the gear ratio increases, it takes more force to stall the motor. This particular gearbox would be an ideal tool for anyone who is starting to learn about gears and power tranmissions.
This project allowed me to explore topics covered in class. Power transmission is a key issue in robotics. Positions, velocities, accelerations, and jerks are also a major issue, depending on application. I have seen robotic mechanisms that use several mechanical components to produce desired motions: gears, pulleys, cylinders, cams, etc. The components, of course, all have advantages and these advantages can really help the mechanism if used correctly. For example, cams are good for generating large amounts of force. Gears can be used to control fine movements, increase/decrease speed and velocity, or change directions of motion. It all depends on the application. Now that this class has concluded, I feel that I have only begun to learn about the various mechanisms in use. My ultimate goal as a robot enthusiast, is to design and construct an autonomous robot. This project has definitely pointed me in the right direction.