In general, for a motor with integrated gearbox, specifications in the data sheet are "at the shaft" which is the shaft that comes out of the gearbox.
In the case of hobby RC servos, like the one you're linking to, it is always the case that the torque takes into account the gear reduction (because it's a bigger number, thus better marketing.)
When you say "lift 4-5 lbs" you do not specify the distance of the lever arm. For a winch that winds a cable, that arm is the distance from center-of-horn to outermost-layer-of-cable. If you attach an arm, it's distance from center of servo horn to center of weight, projected to the ground plane.
You also don't specify how far you need to lift the load.
And you should know that most motors (and certainly all cheaper, hobby-style servos) are specified in maximum "stall" torque, which is not a level of performance they can provide on a continuous cycle. If you stall the motor for more than a few seconds, you are likely to burn it out. The "holding torque" or "continuous torque" is typically 0.3 to 0.15 times the stall torque, depending on motor construction, cooling, etc. This important data isn't even generally available for hobby servos, but is often specified for industrial automation components.
Also note that that servo likely has, at most, a 180 degree rotation angle.
A better Stack Exchange to ask this question on might be the Robotics Stack Exchange. I don't know how to go about moving questions/answers, though.
The parameters you want to look for are moment of inertia and torque. Looking at the datasheet at the link you provide, page 5, you can find a table: what you are looking for is the second and the third column. The equation of your interest is \$\tau=I\alpha\$, that is the "rotational equivalent" of \$F=ma\$. Solving for \$\alpha\text{: }\alpha=\frac{\tau}{I}\$. Calculating alpha you can have a rough estimate of the time your servo needs to speed up to full rpm. Keep in mind two things:
- You will need to add upp the moment of inertia of your sistem
- You can probably set up the speed up time in the controller so it might be slower than expected for this reason
For example, looking at the first row:
$$\tau=0.32\ Nm\text{, }I=0.037\ kgcm^2= 3.7\cdot10^{-6}kgm^2\text{, so }\alpha=8.65\cdot10^3\frac{rad}{s^2}$$
If you want to speed up to the rated speed, that is \$\omega=3000\text{rpm}=3000\cdot \frac{2\pi}{60}\frac{rad}{s}=314.2\frac{rad}{s}\$, you can easily compute \$t=\frac\omega\alpha=\frac{314.2\frac{rad}{s}}{8.65\cdot10^3\frac{rad}{s^2}}=36.3ms\$
That's not that much isn't it? Again, I am assuming that the acceleration is costant with speed, which may or may not be true.
I suggest you to calculate the moment of inertia of the system you want to drive and then contact the manufacturer and ask them which servo will allow you to respect the speed up constraint that you have.
Best Answer
A servo motor can be any type of motor that has a control and feedback system that provides precise precise control of angular or linear position, velocity and acceleration of a driven load. For a valid comparison of speed and torque operation range vs. motor mass and volume, it is necessary to consider specific types of servo motors. Feedback devices and their requirements must also be considered.
There are also more than one type of stepper motors. Specific types need to be considered for a valid comparison.
Motor power is torque multiplied by speed. Motor torque is proportional to motor volume. Motor speed is less closely related to motor volume. To some extent, a motor of a given mass and volume can be designed for a specific torque and a wide range of speeds. In this case, the power is determined by the selected speed.
The continuous torque capability is related to the method of removing heat due to losses in the motor. Most motors have a means for the motion of the rotor to move air through the interior and/or over the outer surface of the motor. The physical and design of the motor influence the heat removal capability and thus the continuous torque capability. Higher rotor speed generally means more effective heat removal and higher continuous torque capability.
Not every servo motor is designed to provide continuous, or long term holding torque. Providing continuous torque with no rotor motion may require special cooling provisions or a physically larger motor.