Stress Analysis Project (24-262) – Spring
Brian Tang, Christy St. John, and Laura Posner
Given connecting pieces (screws, nuts, and washers), a small plastic sheet, aluminum sheets, a servo motor and a microcontroller, build a structure that lifts a 1 lb. weight 2 inches. The structure must weigh less than 20 oz. and cannot touch the wooden obstacle except for where it is clamped at the base.
Development of Our Structure
Our first structure consisted of a cubic 6” base and extending triangular brace that supported two horizontal I-beam-like members side-by-side, angled to the center of the obstacle’s large window. These I-beams formed a truss support for the 16” arm of the structure, composed of two vertical I-beam-like structures connected at each end to form a more unified arm. The servo motor was attached to hang below the far end of the arm, and we attached a simple L-shaped aluminum moment arm to the motor with a notch in it to accommodate the screw extruding from the weight. The torque of the motor caused the motor arm to rotate under the weight. Since the force of the 1 lb. weight was offset from the main axis of the long supporting arm, the weight exerted a moment on the arm during lift. Our first try was unsuccessful at lifting the weight due to excessive twisting of the long arm.
Luckily for the second design review, we were able to keep the cubic base and extending triangular brace since neither deformed much during lifts. We built a rectangular prism structure on top of the original I-beam-like truss in an attempt to maximize the amount of material far from the central axis.
Cubic Base and Truss
Our motor arm, however, was scrapped due to weakness in bending at the notch. We created a notched plastic rectangular motor arm stronger in resisting bending.
We then created a simplified version of our structure in SolidWorks and used it to calculate the deflection of our structure if a 2 lb. (to be conservative) weight were attached at the end. From these results, we saw that the truss structure was twisting. To curb this deformation, we attached a bar to twist the truss support in the opposite direction of the applied torque of the weight when lifted. At our second design review, we lifted the weight 1.5 inches but were unable to lift more due to bending and twisting deformation of the truss support and long arm as well as slipping of the weight on our motor arm. What differed from our SolidWorks assembly is that the force of the weight was not applied directly at the long supporting arm’s center, so the long arm twisted. For our final design review, we attached a small aluminum link to the motor arm. The link had a hole in it to fit around the weight screw and rotate continuously through lifting motion without slipping. We hoped that slipping was the main cause of our failure to reach 2 inches of lift.
Motor Arm Close-Up
Although the motor arm was more securely attached to the weight for our final design review, we were only able to lift the weight 1.75 inches.
Lessons from Stress Analysis Relationships
First Design Review: Using the torque-twist relationship [ΔΦ= TL / (GIp)], we can see that the relative rotation between the base and unsupported end of our arm was directly related to the arm’s length and indirectly related to its polar moment of inertia. Given that our arm length (16 inches) was large in comparison to the polar moment of inertia (on the order of the small average distance of the material from the arm center), the arm was unable to resist rotation well. We attempted to curb twisting by moving material further away from the central axis, thus increasing Ip and decreasing twist.
Second Design Review: Our first moment arm began bending after
repeated use. For our moment arm with
essentially a rectangular cross-section at the end, the distance in the
direction of bending (h, the thickness of the piece of aluminum) was the most
important contribution to bending deflection (1/12 * bh3),
so our thin piece of aluminum was weak in bending.
Final Design Review: From the torque-twist relationship, we can see that the force of the weight should have been as aligned as possible with the central axis of the long arm to reduce torque and therefore twisting. We could have accomplished this by moving the motor arm to the center of our long arm.
Theoretical Motor Calculations
Below are the calculations we used in order to ensure that our motor could lift the weight the required distance (ignoring structure deformation). The motor torque and angle of rotation required must not exceed the maximum values for the motor:
Minimum vertical lift required: 2.0 inches
Minimum distance between motor center and weight contact point: 3.0 inches (ignores rotating link)
Maximum servo motor torque: 72 oz-in.
Weight of object to lift: 1 lb (or 16 oz)
Torque required for lift: 3.0 inches * 16 oz = 48 oz; or (48/72) = 67% of maximum motor torque
Angle of rotation required: tan-1(2 in. / 3 in.) = 34° (ignores deflection of the structure)
Height lifted at full rotation: ~3 in., however the motor arm cannot fully rotate due to the horizontal distance between motor and weight
The most innovative part of our structure is the small piece of aluminum attached to our motor arm. The aluminum piece fits around the screw extruding from the weight and is able to rotate about its attachment to the motor arm in order to prevent slipping of the weight through the full rotation of the motor arm. Without this attachment, we may not have advanced beyond our initial 1.5 inch lift in the time frame between reviews. Our effective range of motion was limited by the slipping of the weight on the motor arm, and we would not have been able to alter that without majorly redesigning our long structure arm or the placement of the motor.