# Equations for Joint Motion in SC-Motion 2012

SC-Motion, a motion and dynamic simulation addin inside SpaceClaim has abilities to perform motion (kinematic) and dynamic simulation on SpaceClaim assemblies. The motion at the joint can be a rotation or a translation. These can be supplied as Equations as well, which is covered in the tutorial below (The embedded tutorial file can downloaded here )

A video with example motion equations is below. (The video can be downloaded here )

All the SpaceClaim assemblies and the corresponding motion equations can be downloaded here. The zip file further contains six zip files. Each of these contain SpaceClaim file and a .txt file with equation (for reference).

# Trace of a point using SC-Motion in SpaceClaim

SC-Motion is capable of a lot of things (kinematics and dynamics) and we have been adding new features every now and then. Our latest update is to trace a point on a link as it moves in a simulation. One can also use a custom point to plot kinematic data (position, velocity and acceleration).

In this tutorial, we are going to see how to trace an ellipse (and circle) in an Elliptical Trammel assembly.  Please follow the steps below:

1. Open Elliptical Trammel assembly (.scdoc )
2. Insert “Origin” (User Coordinate System or a Marker) on handle. By default, the origin is listed at assembly level. Rename it as “UCS1” and  move it to “handle” by dragging and dropping it.
3. Start “SC-Motion”. UCS1 is listed as a marker under Components>Handle.
4. Right click on UCS1 and “Enable Trace”. Optionally trace color can be set.
5. Simulate (with defined joint rotation) and see the trace drawn during the animation (It actually draws an ellipse, hence the name)
6. To add more tracepoints, go back to SpaceClaim and insert another “Origin”. Rename it as UCS2 and move it under Handle component.
7. Come back to SC-Motion, UCS2 is automatically added under Components>Handle. Right click and enable trace.
8. Simulate and animate and now you can see an ellipse and circle drawn together !!!
9. More tracepoints (in the form of markers) can be added.
10. Plot of these custom markers’ origin can be seen in the form of their position, velocity and acceleration.

# Bevel Gears Assembly and Simulation in SpaceClaim

This tutorial shows how to assemble Bevel Gears (that are imported) in SpaceClaim. These are typically used to transmit motion (and power) in intersecting shafts. They are also used in differential of vehicles, for transmission of power to the wheels.

When bevel gears are imported inside SpaceClaim, we need to define Gear Condition/Constraint between them, which is done by selecting two conical surfaces. The main task is to find out these mating cones. The following diagram shows the equations of determining the apex angle (actually half the apex angle) of cones, given the ratio R1/R2 = N1/N2 (ratio of number of teeth). Once the angles are found, conical surfaces are drawn and gear condition is defined between them.

In the video tutorial below:

1. We have imported a Bevel Gear Assembly from GrabCAD.
2. The revolute joints (consisting of a Align condition + Tangent condition) are defined so that gears have a freedom to rotation (degree-of-freedom) about their axes.
3. The pitch cones are determined in the form of surfaces (which do not add up to the mass of the components)
4. Gear condition is defined between them.
5. One of the bevel gears is rotated and the other rotates due to meshing.
6. Go to SC-Motion. Gear conditions are made use of in the solver and simulation is done.

The SpaceClaim assembly file (with Gear condition defined) can be downloaded here.

We have similar tutorials for External Gears, Internal Gears, Rack and Pinion, and Worm Gears.

# Worm Gear Assembly and Simulation in SpaceClaim

This tutorial shows how to assemble Worm Gears (that are imported) in SpaceClaim. These are typically used for very high reduction of speed in shafts (hence very high gain in torque) when the space is limited. The axes of shafts are skew and the angle between them is usually 90 degrees.

Update (July 20, 2012): Considered number of starts/threads in the worm in the equations.

When a worm gear assembly is imported inside SpaceClaim, we need to define Gear Condition/Constraint between them, which is done by selecting two cylindrical surfaces. The main task is to find out the radii of these mating cylinders (also known as Pitch Radius). The following diagram shows the equations of determining the radii Rg (Radius of gear) and Rw (Radius of worm) of the two cylinders, given the number of teeth in the gear(Ng), number of threads/starts in the worm (Nw) and the distance between the axes of the gears. We have two equations with Rg and Rw and solving for Rg and Rw is simple.

In the video tutorial below:

1. We have imported a Worm Gear Assembly from GrabCAD.
2. The revolute joints (consisting of a Align condition + Tangent condition) are defined so that worm and gear have a freedom to rotate (degree-of-freedom) about their axes.
3. The pitch cylinders are determined in the form of surfaces (which do not add up to the mass of the components)
4. Gear condition is defined between them.
5. Worm is rotated and the gear rotates due to meshing.
6. Go to SC-Motion. Gear conditions are made use of in the solver and simulation is done.

The SpaceClaim assembly file (with Gear condition defined) can be downloaded here.

We have similar tutorials for External Gears, Internal Gears, Rack and Pinion and Bevel Gears.

# Rack and Pinion Assembly and Simulation in SpaceClaim

This tutorial shows how to assemble Rack and Pinion (that are imported) in SpaceClaim. These are typically used to convert the rotary motion applied to the pinion into translatory motion of the rack.

When the rack and pinion assembly is imported in SpaceClaim, we need to identify the pitch circle (or cylinder) of the pinion and the pitch line (or plane) of the rack.  We then need to define “Gear Condition” between the cylinder and plane.  The following diagram shows the equations for determining the pitch circle diameter of the pinion. Once it is found, a line tangent to this circle and parallel to the rack surface is the pitch line. The circle and line are then pulled to make surfaces, between which Gear Condition is defined.

In the video tutorial below:

1. We have imported a Rack and Pinion Assembly from GrabCAD.
2. Define revolute joint (consisting of Align condition + Tangent condition) between pinion and the base part.
3. Define prismatic/translatory joint (consisting of Align condition + Angle condition) between rack and the base part.
4. Determine the pitch circle of the pinion. Draw a line tangent to this circle and parallel to the rack surface.
5. Make the circle and line as “Construction lines”, so that we can get surfaces when these are pulled. (which are without mass).
6. Gear condition is defined between cylindrical and planar surfaces.
7. Pinion is rotated about its axis and the rack translates due to proper meshing.
8. Go to SC-Motion. Define joint rotation for pinion and its rotation results in the translation of the rack.

The SpaceClaim assembly file (with Gear condition defined) can be downloaded here.

We have similar tutorials for External Gears, Internal Gears,  Worm Gears and Bevel Gears.

# Internal Gears Assembly and Simulation in SpaceClaim

This tutorial shows how to assemble gears (that are imported) in SpaceClaim. The type of gears considered is “Internal Gears”. These are typically used in planetary gears. This is in continuation of our earlier tutorial on assembling external gears in SpaceClaim. Please go through it to catch up in this tutorial.

Here, we have to find the pitch radii of the internal gear (larger number of teeth) and the external gear (lesser number of teeth). Then, Gear Condition needs to be defined between these pitch cylinders for perfect mating of the gears at hand. The following diagram shows the equations of determining the radii R1 and R2 of the two cylinders, given the number of teeth in the gears and the distance between the centers of the gears. We have two equations with R1 and R2 and solving for R1 and R2 is straight forward.

In the video tutorial below:

1. We have imported a Gear Assembly from GrabCAD.
2. Make the internal gear as fixed component and define Tangent condition between the mating planes of the gears.
3. The pitch cylinders are determined in the form of surfaces (which do not add up to the mass of the components).
4. Gear condition is defined between them.
5. Edit the property of Gear condition “Reverse Rotation Direction” so that the sense of rotation for external gears and internal gears are same (as opposed to that between two external gears, where the sense of rotation is reversed).
6. Try to move the external gear. It does not move as required. This is because, the gear condition only makes sure that the relative rotation of the gears are as per the ratio of number of teeth [This is as of SpaceClaim 2012 version].
7. Define a Tangent condition between the same set of pitch cylinders. Move the external gear and it follows the desired path. This needs to be defined so that external gear and internal gear mesh perfectly.
8. Go to SC-Motion. Since we do not have a revolute joint to define rotation, we have defined Gravity for the assembly and let the external gear move due to the action of gravity (Dynamic Simulation)

The SpaceClaim assembly file (with Gear condition defined) can be downloaded here.

We have similar tutorials for External Gears, Rack and Pinion, Worm Gears and Bevel Gears.

# External Gears Assembly and Simulation in SpaceClaim

This tutorial shows how to assemble gears (that are imported) in SpaceClaim. The type of gears considered is “External Gears”. These are typically used to increase or decrease the speed of shafts. Usually, one of the gears has lesser number of teeth (higher RPM/Speed) and the other has larger number of teeth (lower RPM).

When gears are imported inside SpaceClaim, we need to define Gear Condition/Constraint between them, which is done by selecting two cylindrical surfaces. The main task boils down to finding out the radii of these mating cylinders (also known as Pitch Radius). The following diagram shows the equations of determining the radii R1 and R2 of the two cylinders, given the number of teeth in the gears and the distance between the centers of the gears. We have two equations with R1 and R2 and solving for R1 and R2 is straight forward.

In the video tutorial below:

1. We have imported a Gear Assembly from GrabCAD.
2. The revolute joints (consisting of a Align condition + Tangent condition) are defined so that gears have a freedom to rotation (degree-of-freedom) about their axes.
3. The pitch cylinders are determined in the form of surfaces (which do not add up to the mass of the components)
4. Gear condition is defined between them.
5. One of the gears is rotated and the other rotates due to meshing.
6. Go to SC-Motion. Gear conditions are made use of in the solver and simulation is done.

The SpaceClaim assembly file (with Gear condition defined) can be downloaded here.

We have similar tutorials for Internal Gears, Rack and Pinion, Worm Gears and Bevel Gears.

# AR-CAD Listed as a SpaceClaim Solution Partner

Today, folks at SpaceClaim (Rich Moore, VP, Business Development and Bernard Beulow, VP, Corporate Marketing) informed us that AR-CAD has been listed as a solution partner of SpaceClaim. Solution partners are the companies whose software as addin/plugin extend the basic functionality of SpaceClaim Engineer.

As per SpaceClaim website,

SpaceClaim has formed strategic solution partnerships with the following companies to enhance the company’s 3D Direct Modeling software. These solution partners have bundled SpaceClaim Engineer with their software in order to to offer a specific solution to the market.

Do try out SC-Motion, our motion and dynamic simulation addin for SpaceClaim. For a brief overview of SC-Motion, go through our earlier blog post.

# Import CAD Assemblies in SpaceClaim and Simulate using SC-Motion

GrabCAD is a very good resource to share CAD models and is a bliss for engineers like us. Most of the CAD files we deal at AR-CAD are the assembly files which have some motion in them. Of late, we have been using a lot of their models in our work. In this tutorial we do the following:

1. Import IC Engine (Slider Crank) CAD file (STEP format) inside SpaceClaim, which is a CAD neutral software.
2. Rearrange SpaceClaim assembly slightly to make it more logical assembly.
3. Define Assembly Conditions/Constraints between different Components (parts)
4. Rotate the crank in SpaceClaim using Move command and see the movement of the mechanism. The piston goes up and down.
5. Start SC-Motion and define rotation at the crank
6. Perform Motion Simulation and see the animation.

We are grateful to Hardi Meybaum and Indrek Narusk who co-founded GrabCAD as an awesome platform for CAD Engineers/Designers

# Dynamic Simulation of Backhoe in SpaceClaim using SC-Motion

SpaceClaim has a distinct advantage that it can import and export files of almost all CAD formats. This lets us import CAD assemblies already available at websites like GrabCAD and use it in SpaceClaim. In this tutorial, we have done the following:

1. Imported a Solidworks assembly of Backhoe mechanism in SpaceClaim, which we got from GrabCAD.com (By Babak)
2. Defined Assembly Conditions/Constraints between different parts
3. Start SC-Motion inside SpaceClaim, which is a completely integrated addin for motion and dynamic simulation.
4. Brief overview of SC-Motion user interface
5. Set Joint Translation (Simple Harmonic Motion) to three linear actuators
6. Set/View Mass and Inertia properties of parts (The tutorial was recorded for SpaceClaim2011, which did not expose mass and inertia properties through its API for us. The values were entered manually. Starting from SpaceClaim 2012 version, they have been exposed. So, in SC-Motion 2012 version, these values are populated automatically, which can be modified for a manual input.
7. Define Gravity for dynamic simulation
8. Perform Dynamic Simulation and see the animation.
9. View and analyse plots of the forces required at the actuators to achieve this motion (This is called inverse dynamics). By doing so, we can get an idea of the maximum force that is required at each actuator and accordingly suitable actuator from the market can be used in actual.

We hope the tutorial would be useful for people to get started with Dynamic Simulation inside SpaceClaim.