Every linear motion design starts with the same choice: How do you convert rotary motor motion into linear travel? The two most common answers are the Lead Screw (simple, cheap, friction-based) and the Ball Screw (complex, expensive, rolling-based). Making the wrong choice here is costly. Use a lead screw where you need precision, and you get backlash. Use a ball screw in a vertical lift without a brake, and your load crashes to the floor. In this guide, we compare them side-by-side. Table of Contents 1. The Physics: Sliding vs. Rolling 2. Efficiency & The "Back-Driving" Danger 3. Accuracy and Backlash 4. Selection Table Advertisement 1. The Physics: Sliding vs. Rolling The fundamental difference is friction. Lead Screws rely on Sliding Friction . The nut (often bronze or plastic) slides directly against the steel screw threads. This generates heat and wear. Ball Screws re...
Figure 1: Mathematical coefficients determine the physical shape. Poor math leads to physical defects like the "dip" shown on the right.
In [Polynomial Cam Function (Derivation of Fifth-degree function) - Part 2], we derived the equations for the Fifth-Degree (3-4-5) Polynomial.
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Now, we apply this math to the real world of Mechanical Cam Design. The shape of the physical cam is determined by plotting these functions. Unlike a standard Cycloid curve, the polynomial allows us to manipulate the Start Velocity (v0) and End Velocity (v1) of the follower.
However, this flexibility requires careful design. If the coefficients are not balanced, the physical cam profile can develop "dips" or negative slopes, causing the mechanical linkage to behave unpredictably.
Case 1: Standard Dwell-to-Dwell (Zero Velocity)
Figure 2: The standard profile (v0=0, v1=0). Safe, smooth, and identical to a cycloid curve.
Here, we set v0 = 0 and v1 = 0.
Visually, this looks identical to a Cycloid curve. It is the safest profile for standard cam applications where the follower starts from a dwell (rest) and ends at a dwell.
Case 2: The "Dip" Danger (Negative Displacement)
Figure 3: WARNING: High start/end velocities cause a "Dip" (Negative Displacement), leading to vibration and crash.
This is a critical design trap.
Here, we set both velocities greater than zero (v0 = 1, v1 = 3). Even though the final lift (hm) is positive, the path takes a detour!
Notice how the curve dips below zero at the start?
In a physical cam, this means the profile would be cut inwards. The follower would actually move backward first to gain momentum. If your mechanism isn't designed for this (e.g., a one-way clutch or limited clearance), this will cause a mechanical crash or severe vibration.
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Case 3: Smooth Forward Motion (Optimized)
Figure 4: Optimized coefficients (v1 reduced) eliminate the dip, creating smooth forward motion for flying transfers.
Here, we adjust the parameters (v0 = 1, v1 = 0.5).
By lowering the target end velocity, we eliminate the "dip." The cam follower now moves continuously forward. This is ideal for machines where the cam must synchronize with a linear conveyor belt for a "flying transfer" operation.
Case 4: Intentional Reciprocating Motion
Figure 5: Reciprocating motion. The follower overshoots and returns, useful for specific oscillating mechanisms.
Sometimes, you want the mechanism to oscillate.
Here, we set (v0 = 1, v1 = -1). The follower pushes forward past the target height, stops, and returns. Because this is defined by a 5th-degree polynomial, the acceleration remains finite throughout the reversal, meaning no infinite jerk and less wear on the cam surface.
More advanced applications of the Fifth-Degree Polynomial will be discussed in the next post.
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