<< Click to Display Table of Contents >> Navigation: MechDesigner Reference & User Interface > DialogBoxes > Dialog: Servo and Gearbox Sizing 
Note: The options for a Linear Motor with a SlideJoint will become available in a later release.
Use the Kinetostatic Torque and Speed dialog to:
•Select a Planetary Gearbox from the major gearbox manufacturers
•Select a Servomotor from the major servo manufactures
•Plot the Load TorqueSpeed curve in four quadrants
•Plot the Servomotor Torque and Speed curve; find the Maximum and RMS Torque values
•Find the Servomotor Duty Cycle as a percentage of the machinecycle
How to open the KinetostaticTorque and Speed dialogbox 
STEP 1: Enable these: •Force toolbar > Calculate Forces •Force toolbar > Show Force Vectors You must see the MotorSymbol at a joint  see image below. This Motor Symbol is at the PinJoint that is the Power Source. STEP 2: If required, move the Power Source to a different joint, use: 
STEP 3: When the Motor Symbol is at the correct joint: 1.Click the MotorSymbol in the graphicarea The PinJoint shows in the SelectionWindow 2.RightClick the PinJoint 3.Click Edit element in the contextualmenu  or  The Kinematic Torque and Speed dialogbox opens. 
FOUR QUADRANT: TORQUE(LOAD) vs SPEED 
When you open the Kinetostatic TorqueSpeed dialog, you will see a plot of the Application (or Load) Torque vs Speed acting at the axis of the PinJoint, in all FourQuadrants. FourQuadrant  Why 4 Quadrants Many mechanism applications, when inertia is a significant or dominant load, require the servomotor to apply: •Positive Torque  when accelerating in the positive direction and also decelerating in the reversedirection •Negative Torque  when decelerating in the positive direction and also accelerating in the reversedirection. •Positive angular velocity  when advancing the axis and load •Negative angular velocity  when returning the axis and load 
AutoFilter checkboxThe AutoFilter checkbox is at the top and right of the dialog. ❑ AutoFilter OFF When AutoFilter is off, you can select from 1000s of Gearboxes. ☑AutoFilter ON We recommend that you enable the AutoFilter. When AutoFiler is enabled, the Gearboxes presented are limited to those that have a: •LowerTorque Capacity that is greater than the Torque required to move the Application Load. •UpperTorque Capacity that is determined by the RangeFactor. 
The RangeFactor is at the top of the dialog. 
Thus, the capacity of the Gearboxes that are listed for you are summarized by: ApplicationLoad ≤ Gearbox Capacity ≤ ApplicationLoad × RangeFactor Example: AutoFilter ON, RangeFactor: 1.3 Lower Gearbox Torque Capacity = Equivalent Application (Load) Torque (21.495 N.m.) Upper Gearbox Torque Capacity = Range Factor × Equivalent Application (Load) Torque (1.3 × 21.495 = 27.944 N.m.) 
Select a Gearbox ManufacturerThere are four Gearbox manufacturers from which you can choose: APEX, Neugart, Vogel, and Wittenstein 
Note: If you need us to list a different Gearbox Manufacturer, then please email us. 
Select a Gearbox ModelWhen you select a Gearbox Manufacturer, and AutoFilter is ON, and you have entered a RangeFactor, the list of Gearboxes is limited to those whose capacity can satisfy these inequalities: 



T2max ≤ T2MAX ≤ RF × T2max Maximum Application (Load) Torque ≤ Maximum Output Torque of the Gearbox ≤ RangeFactor × Maximum Application (Load) Torque T2m ≤ T2N ≤ RF × T2m Equivalent Application (Load) Torque ≤ Rated Output Torque Capacity of the Gearbox ≤ RangeFactor × Equivalent Application (Load) Torque n2max× i ≤ n1MAX Maximum Application (Load) Speed × Gearbox Ratio (i) ≤ Maximum Input Speed of the Gearbox n2n × i ≤ n1N Average Application (Load) Speed (or Equivalent, Mean) × Gearbox Ratio (i) ≤ Rated Input Speed of the Gearbox 
After you select a Gearbox model, its Gearbox Parameters Summary Sheet will show. This form is read only. On the left of the sheet, there should be four(4) × to indicate that the Gearbox has the capacity to drive the Application Load and satisfies the 4 requirements. Peak Torque ≥ Maximum Application Torque Rated Torque ≥ Equivalent Application Torque (Max Output Speed) ≥ Maximum Application (Load) Speed (Rated Output Speed) ≥ Equivalent Application (Load) Speed Notes: Parameters speed parameters in brackets ( ) are referred to the outputshaft. They are calculated from the GearRatio of the Gearbox. Other Parameters include: •Backlash •Stiffness •Efficiency •Shaft Diameter  the input shaft diameter, which is not in the list until you select a Servomotor. •Inertia  referred to the input, which is not in the list until you select a Servomotor. 
When you select a Gearbox, the Torque (N.m.) vs Speed (RPM) plot changes to indicate whether the Gearbox has the Capacity to drive the Application Load or not. The color code is : •Green : Torque AND Speed of the Load ≤ Rated Gearbox Capacity •Amber : Torque OR Speed of the Load ≥ Rated Gearbox Capacity ≤ Maximum Gearbox Capacity •Red : Torque OR Speed of the Load ≥ Maximum Gearbox Capacity 
Gearbox Torque and Speed Limits. The Show Gearbox Limits checklist box is above the Gearbox selection box. ❑ Show Gearbox Limits enabled The axes are autoscaled to the Maximum Torque and Speed, at the output of the Gearbox. ☑Show Gearbox Limits disabled The axes are autoscaled to the Maximum Torque and Speed Capacity, referred to the output of the Gearbox. This helps you compare the Torque and Speed Capacity of the Gearbox with the Application Load. The Limits of Torque and Speed are shown as boxes. Before you select a servomotor, the limit boxes and their color codes indicate the: •Dark Blue : Maximum Torque and Speed capacity of the Gearbox •LightBlue : Rated (or Nominal) Torque and Speed capacity of the Gearbox •LightBrown : Equivalent Torque and Speed of the Application Load 
Select a Servomotor ManufacturerThere are many Servomotor manufacturers from which you can choose one. When you select a Servomotor Manufacturer, MechDesigner finds those Servomotors that have the Torque and Speed Capacity required by the Application Load. 
Note: If you need us to list a different Servomotor Manufacturer, then please email us. 
Select a Servomotor ModelWhen you select a Servomotor Manufacturer, and AutoFilter is ON, and you have entered a RangeFactor, the list of Servomotor is limited to those whose capacity can satisfy these inequalities: 



d1max≤ D ≤ d1min The Servomotor Shaft Diameter, D, must fit directly into the Gearbox, d1. Note: Precision Planetary Gearboxes can accept a range of shaft diameters at their input. The Gearbox inertia, which is referred to its input, is different for each shaft diameter. Tmax ≤ Tmot max ≤ RF × Tmax Maximum Application Load Torque referred to the Gearbox inputshaft ≤ Maximum Servomotor Torque Capacity ≤ RangeFactor × Maximum Application Load Torque referred to the Gearbox input shaft Tm≤ TN ≤ RF × Tm Equivalent Application (Load) Torque referred to the Gearbox inputshaft ≤ Rated Servomotor Torque Capacity ≤ RangeFactor × Equivalent Application (Load) Torque referred to the Gearbox input shaft n1max ≤ Nmax Maximum Application Speed referred to the Gearbox inputshaft ≤ Maximum Servomotor Speed n1N ≤ N1N Average Application Speed (or Equivalent, Mean) ≤ Rated Servomotor Speed Pn ≤ Pr Application Power < Servomotor Power Capacity 
When you select a Servomotor model, its Servomotor Parameters Summary Sheet will show. This form is read only. To the left of the sheet, there should be five(5) × to indicate that the Servomotor has the capacity to drive the Application Load and also satisfies those 5 × requirements. Peak Servomotor Torque ≥ Maximum Application (Load) ÷ i Rated Servomotor Torque ≥ Equivalent Application (Load) Torque ÷ i Max Servomotor Speed ≥ Maximum Application (Load) Speed × i Continuous Servomotor Speed ≥ Equivalent Application (Load) Speed × i Rated Power > Nominal Load Power. Other Parameters include: •Vdc  Bus Voltage for Drive •Jm  Servomotor Inertia •D  Servomotor shaft diameters. 
When you select a Servomotor, colors of the dots for the Torque (N.m.) vs Speed (RPM) plot changes to indicate whether the Servomotor has the Capacity to drive the Application Load or not. The color code is : •Green : Torque AND Speed of the Load ≤ Rated Servomotor Capacity •Amber : Torque OR Speed of the Load ≥ Rated Servomotor Capacity ≤ Maximum Servomotor Capacity •Red : Torque OR Speed of the Load ≥ Maximum Servomotor Capacity 
Motor Torque and Speed Limits. The Show Motor Limits checklist box is above the Motor selection box. ❑ Show Motor Limits Enabled The axes are autoscaled to the Maximum Torque and Speed, at the Servomotor Drive Shaft. ☑Show Motor Limits Disabled The axes are autoscaled to the Maximum Torque and Speed Capacity of the Selected Servomotor This helps you compare the Torque and Speed Capacity of the Servomotor with the Application Load referred to its inputshaft. The Limits of Torque and Speed are shown as boxes. • Purple : Maximum Torque and Speed capacity of the Servomotor • Pink : Rated (or Nominal) Torque and Speed capacity of the Servomotor •LightBrown : Equivalent Torque and Speed of the Application Load 
The Torque we show in the graphicarea when we Display Force Vectors is the torque to move the mechanism only. It does not include the Torque to move the motor and gearbox. It is necessary to add the Torque to accelerate the motor and the gearbox to Torque in the graphicarea. Clearly, the Torque to move motor depends on the ....inertia of the motor and gearbox as well as the gearbox ratio. The higher the gear ratio, the less Torque the motor 'sees'. But the motor must run faster and accelerate more. This influences the overall power, as well as system efficiency. 
The performance characteristics of a brushless servo motor (motor/drive combination) are described by a torque/speed operating envelope. As shown below, the colored areas of the curve identify the Exceeded Duty, Continuous Duty, and Intermittent Duty working areas of the system. Exceeded Duty To maximum speed and/or the maximum torque, of the gearbox and/or servomotor must be exceeded. Usually, to make sure this cannot happen, there is a Current (amps) Limit on the Power Drive. Continuous Duty Zone (S1) The continuous duty zone is bounded by the maximum continuous stall torque up to the intersection with the intermittent duty line. The continuous torque line is set by either the motor’s maximum rated temperature, or the drive's rated continuous current output, whichever is less. The system maximum continuous or 'voltage line' is set by the voltage rating of the drives, the line voltage supplied, and the motor winding. The system can operate on a continuous basis anywhere within this area, assuming the ambient temperature is 40°C or less. Intermittent Duty Zone (S5) The intermittent duty zone is bordered by the peakstall torque and the system voltage line. The peak torque line is set by either the drives’ peak current rating, which the drive can give for a limited time, or the maximum rated peak current for the motor, whichever is less. Higher torque levels may be achievable at higher power levels. 
Typical Torque / Speed Duty Capability of a Brushless Servomotor. 
Peak Torque: (ԎPS ) The Peak Torque the Motor and Gearbox at Stall Speed Continuous Stall Torque: (ԎCS ). The Continuous Torque the Motor and Gearbox can give Continuously at Stall Speed. Maximum Speed: (ωMAX ) Maximum possible speed of the Motor and Gearbox. Not attainable when the voltage is limited by the drive. Knee Speed: (ωK ) The Speed at 'knee' in peak envelope that is the intersection of the Peak Torque with the Voltage Torque/Speed Limit Line. Continuous Rated Torque:(ԎCR ). The Continuous Torque at the Speed of the Rated Power. Rated Speed: (ωR ) The Rated Speed or Speed at Rated Power. The motor can operate at this speed with the supply voltage. 
The Reflected Inertia at the Motor shaft usually continuously changes in a machinecycle. With Constant Inertia Mechanical Systems it is easy to calculate Inertia Torque. With mechanisms, the Torque is dependent on reflected inertia that is a function of Acceleration, Velocity, and Position. PSMotion has developed algorithms to calculate these, which give a true indication of the reflected inertia at a motor shaft for even the most complex mechanisms. The equations below, are calculated at every instant in a machinecycle. Usually, you aim to make the Reflected Load Inertia = (Motor + Gearbox) Inertia. However, when the Load Inertia is not constant, it is more difficult to select the Motor and Gearbox. 

Speed: ωm = N × ωL αm = N . αL Torque Tm =  αm (JG + JM) + sign(TVD) TL = (TMD ∕ N ) ∕ η TT = Tm + TL 
N = Gear Ratio ωm = Motor Angular Velocity ωL = Load Angular Velocity TT = Total Torque Tm = Motor Torque TL = Load referred to Motor Shaft TVD = Viscous 'Drag' Torque. It is always opposite to the direction of motion TMD = Torque derived by MechDesigner at Motor Shaft ( f{PL , ωL, αL } ) JG = Inertia of Gearbox JM = Inertia of Motor αm = Motor Acceleration αL = Load Acceleration η = Gearbox Efficiency 