Presentation

Introduction and Background

The focus of my final project was to design the 5-bar slider slot mechanism. This mechanism turns the rotational input into vertical motion at the slider. It has a point of high acceleration, the direction depending on the input rotation. Applications of this technology are in automating simple manufacturing processes, like hammering items on a conveyor belt. When the rotation is counterclockwise, the power stroke will be downward. The dimensions of the links and the location of the pin can all be changed to make it a Grashoff mechanism, which can be run using a simple motor. The frequency of this process can also be tuned by changing the dimensions of the mechanism.

Design Process

I started by identifying what I would use to build specific parts of the mechanism. Conducting the project from home, I decided to use Lego bricks, since they were sturdy and easy to build with. I experimented with different types of bricks, to see what works, and develop a sense of the friction between components. I realized using Lego Technic bricks and axels gave an extremely low friction pin joint.

Figure 1. Pin Joint

For the slider mechanism, I started with square bricks in rectangular slots, but there was too much friction for smooth translation. Then I used a cylindrical brick in the slot, and it gave much smoother translation, probably due to much less contact with the edges of the slot.

The pin was identified by using smooth cylindrical pieces. I could extend it by connecting multiple of the cylindrical pieces by pin connecters. This would then be stabilized by connecting the final cylinder piece to a brick with a hole in the center. This allows me to build a stable platform using other bricks and building the pin at any position in the mechanism. The slotted link was designed by using the Technic bricks and placing one short brick between two long bricks, which provided a slot that was able to slide easily over the pin.

Figure 2. Slot and Pin Joint

Kinematic Analysis and Synthesis

The analysis of the kinematics was done in three parts. First, I took advantage of the pin providing a point on link three to calculate the angle of the third link with the input angle as the only input variable. Then I took the derivatives of this function with respect to time and found the function for the angular velocity of the third link using the input angle and the input angular velocity. Another time derivative gave the angular acceleration of the third link using the input angle, input angular velocity, and input angular acceleration.

These functions will reduce the unknowns in the vector loop equations.

The second part of the kinematic analysis was conducted using a vector loop equation for position analysis, and then takings its derivatives for velocity and acceleration analysis. For position analysis, I solved the equation:

The function for angle 3 reduced the number of unknowns from three to two, which could be solved by splitting the vector loop equation into real and imaginary parts, which gives two equations. Angle 4 can be solved for using the real parts, which can then be used to solve for the height in the imaginary parts. This equation is also used to solve for the mobility of the mechanism. The real part only has one variable, the fourth angle, and since everything else is constant or dependent on the input angle, the input angle will have to satisfy the real part of the equation.  

Velocity analysis is conducted by taking the derivative of eq(4). This gives the equation:

Using the analytical function for angular velocity of the third link reduces the unknowns again, and the only two variables left are the angular velocity of the fourth link and the velocity of the slider. This can be solved using linear algebra, seen below:

This is very useful, as it will translate very nicely into the MATLAB program that iterates through input angles.

An equation for the acceleration analysis is developed by taking the derivative of eq(5):

The angular acceleration of the third link can be solved for using eq(3), again reducing the number of unknowns to 2 and allowing the system of equations to be solved. I used a matrix, similar to the velocity analysis, seen below:

This again solves for the acceleration terms. There seem to be no Coriolis acceleration terms in the final acceleration equation. This is because the slider is restricted to vertical position only and prevents any part to slide and rotate at the same time.

Manufacturing and Assembly

The first iteration of the mechanism was built using the trial pieces mentioned in the design process. A major issue in that design is that it had a lot of play. It would rock front to back and had to be held down by hand to remain stable. One of the major solutions was to change the pin base from thin long pieces to a platform built from thicker bricks. This added more stability to the pin and slotted link joint, which was the central part of the design.

Another major upgrade was in the slotted link. The first iteration of the slotted link was created using a combination of T-shape, L-shape, and linear Lego Technic bricks. It was overly complicated but functional. The second iteration of the slotted link used the linear Technic bricks but joined them using capped axles through a piece with two vertical axel holes and a horizontal pin hole. One type had a horizontal pin hole in the middle, and the other had it on the end. This design was much more stable than the previous one.

Figure 3. Exploded Assembly of Slotted Link

The preliminary design was created to be hand cranked, but to make the final design run on a motor, I had to find a link that could attach at one end to the motor shaft or make one that could. Luckily, the cross-holes were able to wedge the flat part of the motor shaft, from which I built a link to connect to the slotted link.

The final feature in the assembly of the mechanism was creating a motor gridle. While running, the motor would wobble left to right, essentially changing the origin of the mechanism while rotating. I created a base and a fork at the top to hold the motor in place. This worked very well and essentially eliminated the wobbling. This also worked to hold the mechanism in place in the third dimension. Earlier, it would wobble front and back, but the girdle held it all in place.

Figure 4. Motor Girdle

Electronics and Software

I used a DC motor and a DC power source to power the mechanism. The motor has a 48:1 gear ratio and is powered using 4.5V DC power supply. Since my final prototype was a Grashoff mechanism, I did not need to control the specific degrees of movement and simply hooked the motor up to an H-bridge to control the direction of movement using MOSFETs and a switch.

Figure 5. H-Bridge Circuit  and Circuit Diagram

Final Prototype

Figure 6. Final Prototype

My final prototype is a Grashoff 5-bar slotted slider with input from a DC motor and vertical translational output. Depending on the rotation, the power stroke of the slider is either on its way down or up. Compared to previous iterations, the design is much more stable. It has dimensions seen in the table below.

Table 1. Dimensions of Final Prototype

An animation of the mechanism can be seen below. The yellow link is the input link, the purple link is the slotted link, the green link is the coupler, and the red line is the line of motion of the slider. The blue dot is the pin location, and the arrow is describing the acceleration of the slider.

Figure 7. Animated Kinematic Assembly

The position, velocity, and slider of the mechanism can all be calculated as a function of the input angle, and those plots can be seen below.

Figure 8. Plots of Slider Position, Velocity, and Acceleration

Figure 9. Final Assembly Video

Conclusions and Future Work

The 5-bar slotted slider mechanism, when given rotational input, produces vertical motion. This can be applied for many different types of processes like manufacturing on an assembly line. The output can be controlled by restricting the rotation between a range of angles and controlling the angular velocity and acceleration. Future work on this project would be to control the output of the slider to remain in its most optimal region, using the input angle and angular velocity to make sure it is always in the power stroke.

Appendix

Bill of Materials