Reverse Engineering a Screwdriver
The purpose of this project was to reverse engineer a Black & Decker Li2000 Screwdriver and analyze its mechanism using the skills learned in the course, such as gear analysis and CAD assembly. The screwdriver was first dissembled into its individual components and parts, and the dimensions of the gears inside the gear box were measured by using a caliper. All technical drawings were created by using PTC Creo Parametric, and were drawn as functional models without teeth rather than true-to-from models.
1. Gearbox Analysis
1.1. Number of Teeth
The gearbox contains two sets of epicyclic gear train, each of which consists of a ring gear (R), a sun gear (S), planetary pinions (P), and a planetary carrier (PC). The number of teeth (N) for each gear was found by directly counting them.
NR = 48 teeth
NS = 6 teeth
NP = 19 teeth
However, since a planetary carrier does not have real “teeth,” the following formula was used instead:
NPC = NS + NR = 6 + 48 = 54 teeth
1.2. Gear Ratio
The general gear ratio (GR) for a given gear train can be written as:
GR = Noutput/Ninput = ωinput/ωoutput = τoutput/τinput
where N = the number of teeth, ω = the angular velocity, and τ = the torque of the gear.
For each epicyclic gear train, the sun is the input gear and the planetary carrier is the output gear, and so, the gear ratio is:
GR = NPC/NS =54/6 = 9:1
However, since there are two gear trains, the overall GR for the multi-stage gear train is:
GRoverall = GR*GR = 9*9 = 81:1
In terms of its motor torque (τmotor) and RPM (ωmotor), the output torque and output RPM are:
GR = ωmotor/ωoutput = τoutput/τmotor = 81/1
τoutput = 81*τmotor
ωoutput = ωmotor/81
As the above gear ratio shows, an epicyclic gear train can produce a large torque from a small torque input (the output torque is 81 times the torque of the motor), which is needed for tightening or loosening screws. However, the screwdriver must remain light-weight since all users should be able to hold it in their hands without strain. An epicyclic gear train is an appropriate one to use for a compact gear train that can still produce considerable amount of torque.
1.3. Pitch Diameter
The pitch surface of a gear is the surface of an imaginary cylinder that can functionally replace the toothed gear, and the pitch diameter (PD) is the diameter of that pitch surface. To calculate the PD, the center distance (C), the distance between the centers of two meshing gears, was first measured using a caliper.
Center distance between planet and planet (CPP) = 0.500 in
Center distance between planet and sun gear (CPS) = 0.391 in
The center distance is defined as the midpoint of the pitch diameters of the two meshing gears:
C = (PD1 + PD2)/2
To find the PD of the planets:
CPP = (PDP + PDP)/2 = PDP = 0.500 in
To find the PD of the sun gear:
CPS = (PDP + PDS)/2
PDS = 2*CPS - PDP
= 2*(0.391 in) - (0.500 in) = 0.282 in
According to the sketch of the assembled epicyclic gear below, the PD of the ring gear is:
PDR = PDS + 2*PDP
= (0.282 in) + 2*(0.500 in) = 1.282 in
2. Product Structure
3. Mechanical Drawings
4. DMFA: Mistake-Proofing
Design for Manufacturing and Assembly (DFMA) mistake-proofing is a method employed to a product so that it is impossible for an error to occur. This principle is important in improving the quality and reliability of the product. There are several instances found where the screwdriver uses DFMA mistake-proofing. The image on the left shows the disassembled screwdriver.
4.1. Asymmetric Grooves
The asymmetric grooves of the motor housing and the motor are an example of DFMA mistake-proofing. The two components will fit only if the grooves are aligned: one side of the circle has a wider groove to ensure proper orientation. This allows the motor circuit to be oriented in way that corresponds to the forward/reverse switch.
4.2. Curved Hole for the Motor Node
The hole where the motor node goes through is follows the curvature of the shape of the motor circuit (Image 1). The hole prevents the motor end from moving in a way that does not go along the curvature. Therefore, the motor node will successfully be in contact with the metal strips to properly power the screwdriver.
4.3. U-Pin
U-pin ensures that the gearbox and the motor are secure in place. It eliminates the possibility of the two components being misaligned due to the small vibrations that can occur when the screwdriver is operating. If the gearbox and the motor are not secure, then the screwdriver will not function properly.
5. Special Mechanisms
5.1. Forward/Reverse Switch
The forward and reverse switch works through a simple electric circuit. The battery is connected to the motor by a metal circular strip which is in contact with the motor node at varying positions. For a forward switch (image 1), the top motor node moves to the right end and bottom motor node, to the left end. For a reverse switch (image 2), the top motor node moves to the left end and the bottom node, to the right end. Since the motor nodes are in contact with the metal strip in opposite combination to that of the forward switch, the electric current flows in the reverse direction, thus reversing the rotation of the hex spindle. The hex spindle is locked when the switch is in the middle position (image 3), since both of the motor nodes are not in contact with the metal strips and so, there is no current flowing through the circuit.
5.2. Tool Handle Pivot Lock
The handle pivot assembly mechanism consists of asymmetric grooved sockets, a spring, two caps that have asymmetric teeth, and a small nail (image 1). The spring is placed between the two caps and through the handle, and the nail secures them together. There is a gap between the cap and the teeth of the pivot bar. When the teeth of the socket and the pivot caps are in contact, the handle cannot rotate since the gears are rigid (image 2). However, because of the spring between the two caps, one cap can be pushed farther out of the socket, so that the teeth are no longer directly in contact with each other. Thus, the handle can rotate to whichever position the user desires. The widest U-shaped tooth locks the position in place by ensuring that the teeth of the socket and caps are in contact (image 3).
5.3. Power/Manual Option
By turning the hex spindle, the user can choose between an automatic or manual option for using the screwdriver. When the hex spindle is set to automatic spinning, the plastic ring gear (image 1) is away from the secondary epicyclic gear train, allowing the motor to drive the secondary epicyclic gear train and thus the hex spindle. However, for a manual option, the plastic ring gear is pushed towards the secondary epicyclic gear train and locks it (image 2). Since the hex spindle is locked, the hexagonal bits attached will not rotate under the manual option.
