Servo Torque for Arm
Calculate the static torque a servomotor needs to hold a horizontal arm, T = m·g·L, from the tip mass m, gravity g (9.81 m/s²) and the arm length L. The result, in N·m, is the minimum torque the servo must provide to keep the arm horizontal against the load weight — the most unfavorable position. It is essential in designing robotic arms, grippers and servo-driven mechanisms, sizing the motor with a safety margin over this value. For arms with their own mass, the center of mass is used. Enter the mass and the arm length.
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Servo torque for an arm
When designing a robotic arm, a gripper or any servo-driven mechanism, the first question is whether the servo has enough torque to lift and hold the load. The worst case is the arm horizontal and fully extended, because that is where the weight of the load produces the maximum moment about the servo axis. The required torque is T = m·g·L, the product of the mass at the tip, gravity (9.81 m/s²) and the arm length (the lever arm). The relationship exposes the real cost of reach: doubling the arm length doubles the required torque for the same load — long arms demand powerful servos or light payloads, which is why collaborative robots carry modest payloads relative to their reach. In practice, three refinements sit on top of this basic figure. First, the arm has its own mass, whose weight acts at the center of mass (at mid-length for a uniform arm) and adds its own torque. Second, a generous safety margin is needed (typically 2× to 3× the static torque), because the servo must also accelerate the load (dynamic torque = I·α), overcome friction and still hold accuracy under load. Third, servos are rated in kg·cm or N·m at a given supply voltage — converting and comparing is essential. An undersized servo yields arms that sag, chatter, overheat or simply refuse to lift the load. This calculation is the starting point for sizing any actuated robot joint. Enter the tip mass and the arm length.
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Forward Kinematics (2 DOF)
Compute the (x, y) position of the end of a planar 2-degree-of-freedom robotic arm from the joint angles: x = L1·cos(θ1) + L2·cos(θ1+θ2) and y = L1·sin(θ1) + L2·sin(θ1+θ2). This is forward kinematics — given the joint angles, find where the tool is. Fundamental in manipulator control and robot simulation. Enter the link lengths (L1, L2) and the joint angles (θ1, θ2) in degrees.
Robot Arm Reach
Calculate the maximum reach of a planar two-link robotic arm, R = L₁ + L₂, by adding the lengths of the two links (arm and forearm). The result, in the length unit, is the radius of the work envelope — the farthest distance the tip (end-effector) can reach when the arm is fully extended. It defines the robot's workspace and is the first sizing parameter of manipulators. The minimum reach (dead zone at the center) is |L₁ − L₂|, and the useful area is the annulus between the two radii. Enter the two link lengths.
Motor Torque from Current
Calculate the torque produced by a DC motor, T = K_t·I, from the torque constant K_t (N·m/A) and the armature current I. The result, in N·m, shows a DC motor's torque is directly proportional to current — which is why measuring current is the simplest way to estimate (and limit) torque and detect overloads. The torque constant K_t is a motor characteristic (numerically equal to the back-EMF constant K_e in SI units). It is the basis of torque control in servomotors and robotics. Enter the torque constant and the current.
DC Motor No-Load Speed
Calculate the no-load speed of a DC motor, ω = V ÷ K_e, from the applied voltage V and the back-EMF constant K_e (V·s/rad). The result, in rad/s, is the speed the motor reaches with no load, when the generated back-EMF nearly equals the applied voltage and the current drops to a minimum. It is the upper speed limit of the motor for a given voltage, the basis of the torque-speed curve (running from stall torque at zero speed to no-load speed at zero torque). It lets you estimate the operating range of servos and DC motors. Enter the voltage and the constant K_e.
Motor Power (Torque × RPM)
Compute a motor's mechanical power from torque and rotation, P = τ·ω = τ·2π·n/60, where τ is the torque (N·m), n the rotation (rpm) and P the power (W). It is the fundamental relation linking the three quantities of a rotating motor: the same motor delivers high torque at low speed or high speed at low torque, but the power is the product of the two. The basis of drive sizing. Enter the torque and the rotation.
Servo Angle from PWM
Convert a servo motor's PWM pulse width into the corresponding angle, angle = (pulse − 1000)/1000 · 180°, in the hobby standard where 1000 µs ≈ 0°, 1500 µs ≈ 90° (center) and 2000 µs ≈ 180°. Hobby and robotics servos are commanded by this pulse width, typically at 50 Hz. Knowing the relation helps to calibrate and program movements. Enter the pulse width in microseconds.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.